Surface Area and Air Resistance
How does more surface area make something with air
resistance fall slower?
Air resistance determines the fastest that something will fall in
Earth's atmosphere. This is called terminal velocity.
Terminal velocity depends upon how much air resistance there is
versus weight. Air resistance is controlled by the surface area
over which the air acts (called a cross section) and speed. A
body's shape in the direction of fall is very important - so
important that it overcomes all other factors!
For example, the terminal velocity of a 220 lb. skydiver is around
220 miles an hour, give or take a bit. A streamlined 220 pound bomb
can approach far higher speeds when falling!
And do not forget: all falling bodies accelerate (speed up) by the
same amount until they hit terminal velocity. This acceleration
depends upon Earth's gravity and is known to its friends as g, or
"little g". Little g is about 32 feet per second every second or
9.80 meters per second each second.
R. W. "Bob" Avakian
B.S. Earth Sciences; M.S. Geophysics
Oklahoma State Univ. Inst. of Technology
Surface area does not determine how fast something falls. Air
resistance is not determined by how much surface area an object has. A
way to model air resistance is an object having to push the air
molecules out of the way. Shape is just as important, some times more
important, than size. Even how an object is rotating can affect air
resistance. Probably the two most important things are called
cross-sectional area and shape. A wider object has to push more air out
of the way for every meter it falls. An object provided with a pointed
bottom has to push less hard to do this than the same object with a flat
bottom. This is why the front end of a missile is pointed. Also, an
object falling faster has to push more air more quickly that the same
object falling slowly.
As for falling slower, this also depends on how the air resistance
compares to weight. When objects are hardly moving, such as when they
are first released, there is no air resistance. As objects speed up,
air resistance increases. High resistance objects will eventually reach
a speed where air resistance pushing up is just as big as gravity
pulling down: the object has reached its greatest speed. It keeps
falling without continuing to get faster. Low resistance objects may be
able to reach higher speeds, but not always. A big hollow ball that
weighs twice as much as a pencil will not fall faster than a pencil
because a pencil has to push so little air out of the way to make room
for itself. On the other hand, a steel pencil will fall faster than a
wood pencil because it takes a higher speed for the air resistance to
build up to the weight of the very heavy steel pencil.
Dr. Ken Mellendorf
Illinois Central College
Air resistance, or drag force, is a complicated phenomenon. The
surface area of an object is not a good predictor of drag on the
object. The shape of the object plays a strong role, but other factors
such as speed and size also play important roles.
Hope this helps,
Your's is a far more complicated question than I suspect you suspected.
Surface area is only one of a number factors that play a part in air
resistance (or any other fluid for that matter). For example: It is no
accident that golf balls are dimpled. The surface area increases a bit from
the indentations, but the range of a golf ball is significantly extended.
It is no accident that a tennis player (at least a competitive one where it
matters) likes to get the fresh set of tennis balls in a match. It is no
accident that a baseball pitcher "rubs up" a new ball thrown in by the plate
On the other hand as your question implies, 'Why wear a parachute?'
The area of physics you are dealing with is "hydrodynamics" and more
specifically "aerodynamics". Both are mathematically challenging,
complicated areas of engineering and physics.
What Galileo "discovered" or "predicted" was that in the absence of a
resisting fluid (e.g. air) that in such a vacuum the feather and the
elephant will fall the same distance in the same time interval. The damage
to the feather and to the elephant is a different issue because momentum,
too, is conserved.
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Update: June 2012