Before we can discuss how air resistance (often called a drag force) affects falling bodies, you
need to have a basic understanding of how air resistance works.
Whenever the surfaces of two objects rub together, a friction
force is generated that acts on both objects and opposes their
relative motion. This is true even if one (or both) of the objects is
a fluid (a gas or liquid, such as air or water). When the fluid in
question is air, the friction force generated is called air
resistance or wind resistance.
How does friction, and in particular, air resistance work? Well,
nobody really knows - it is an active and important area of research.
Friction forces in general, and air resistance forces in particular,
are very complex. We do know that it is impossible to make simple,
accurate, theoretical statements about air resistance. On the other
hand, if you are willing to not take them too literally and carry them
too far...blah blah blah (The rest of the disclaimer goes here.)...
The air (fluid) resistance force on an object depends primarily on:
- the relative velocity of the object and the
fluid. The word "relative" is important here - as far as the force
is concerned, it doesn't matter if the object is moving and the
air (or other fluid) is at rest, or if the air is moving and the
object is at rest, or whatever.
The relationship between air
resistance force and velocity is not simple, but certainly more
velocity means more force.
For very small objects - microscopic to dust mote size - air
resistance force is approximately proportional to velocity, v. (This is called Stokes' Law.) This means that twice the velocity produces twice the air resistance force, three times the velocity produces three times the force, etc. A complication in dealing with such small particles is that the buoyant (Archimedes' Principle) force on them due to the air is often nearly as large as either their weight or the air resistance force on them.
larger, human-scale objects, like baseballs, cars, and people, the
air resistance force is approximately proportional to the square of the velocity, v2. In other words, twice the velocity produces four
times the force. To make matters even more complicated, there is no theoretical reason that the exponent attached to the velocity to be an integer! The air resistance force on a particular object may be proportional to v3/2, v0.9, or v2.6, for example.
- the shape of the object. A larger object must
push more air (or other fluid) out of the way in order to move
through it, so a larger area means more air (fluid) resistance.
This is why fast cars and airplanes need to be streamlined. The
exact relationship between shape and air resistance force is
difficult to predict, however. A shape that one would think would
be very effective in reducing air resistance often proves, in
practice, to act just the opposite. Even today, a great deal of
wind-tunnel testing and redesigning is necessary to effectively
streamline an object.
- the density of the fluid. Two identical objects
moving at the same speed will encounter different resistance
forces in different fluids. Dropping a rock through air and
dropping the same rock through water certainly produce different
motions. Generally, the more dense the fluid, the more resistance
force on the object.
That's not all. The viscosity (stickiness) of the fluid can have an effect on the air resistance force, as well as the texture of the surface of the solid object
last update November 4, 2007 by JL