Angle of incidence
|This article needs additional citations for verification. (September 2009)|
Angle of incidence is a measure of deviation of something from "straight on", for example:
- in the approach of a ray to a surface, or
- the angle at which the wing or horizontal tail of an airplane is installed on the fuselage, measured relative to the axis of the fuselage.
In geometric optics, the angle of incidence is the angle between a ray incident on a surface and the line perpendicular to the surface at the point of incidence, called the normal. The ray can be formed by any wave: optical, acoustic, microwave, X-ray and so on. In the figure above, the red line representing a ray makes an angle θ with the normal (dotted line). The angle of incidence at which light is first totally internally reflected is known as the critical angle. The angle of reflection and angle of refraction are other angles related to beams.
Determining the angle of reflection with respect to a planar surface is trivial, but the computation for almost any other surface is significantly more difficult. The exact solution for a sphere (which has important applications in astronomy and computer graphics) was an open problem for nearly 50 years until a closed-form result was derived by mathematicians Allen R Miller and Emanuel Vegh in 1991.
When dealing with a beam that is nearly parallel to a surface, it is sometimes more useful to refer to the angle between the beam and the surface, rather than that between the beam and the surface normal, in other words 90° minus the angle of incidence. This small angle is called a glancing angle or grazing angle. Incidence at grazing angles is called "grazing incidence".
Grazing incidence diffraction is used in X-ray spectroscopy and atom optics, where significant reflection can be achieved only at small values of the grazing angle. Ridged mirrors are designed for reflection of atoms coming at small grazing angle. This angle is usually measured in milliradians. In optics, there is Lloyd's mirror.
Angle of incidence of fixed-wing aircraft
On fixed-wing aircraft, the angle of incidence (sometimes referred to as the mounting angle) is the angle between the chord line of the wing where the wing is mounted to the fuselage, and a reference axis along the fuselage (often the direction of minimum drag, or where applicable, the longitudinal axis). The angle of incidence is fixed in the design of the aircraft, and with rare exceptions, cannot be varied in flight.
The term can also be applied to horizontal surfaces in general (such as canards or horizontal stabilizers) for the angle they make relative the longitudinal axis of the fuselage.
The figure to the right shows a side view of an airplane. The extended chord line of the wing root (red line) makes an angle with the longitudinal axis (roll axis) of the aircraft (blue line). Wings are typically mounted at a small positive angle of incidence, to allow the fuselage to be have a low angle with the airflow in cruising flight. Angles of incidence of about 6° are common on most general aviation designs. Other terms for angle of incidence in this context are rigging angle and rigger's angle of incidence. It should not be confused with the angle of attack, which is the angle the wing chord presents to the airflow in flight. Note that some ambiguity in this terminology exists, as some engineering texts that focus solely on the study of airfoils and their medium may use either term when referring to angle of attack. The use of the term "angle of incidence" to refer to the angle of attack occurs chiefly in British usage.
- Allen R Miller and Emanuel Vegh (1993). "Exact Result for the Grazing Angle of Specular Reflection from a Sphere". SIAM Review 35: 472–480. doi:10.1137/1035091.
- Phillips, Warren F. (2010). Mechanics of Flight (2nd ed.). Wiley & Sons. ISBN 978-0-470-53975-0.
- Kermode, A.C. (1972), Mechanics of Flight, Chapter 3, 8th edition, Pitman Publishing, London. ISBN 0-273-31623-0