# Air Resistance

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.
For 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 Stanbrough