*by Ollie Brower*

An analysis of a rolling soap box wheel is complex because wheel is both spinning in the air and moving through it. Each part of the wheel has a different drag coefficient, and the velocities of all points on the wheel are constantly changing with respect to the ground, or the still air it is going through.

If a derby racer is traveling at 20 mph, then its wheels are rotating with constant angular velocity. But the only portions of each wheel that move at this steady 20 mph ground speed are the axles and wheel pins. All other parts of the wheel are continually moving either faster or slower, depending on their positions in the wheel and to the ground.

If we follow the path of a point on the tire of one wheel, we'll see that it follows the humped curve traced in figure 1. This path also graphs the relative velocity of this point as it rotates through one revolution. The point will actually be at rest the moment it contacts the asphalt of the track, but will quickly accelerate to 40 mph as it approaches a position at the top of the wheel.

The aerodynamic behavior of a derby wheel is important because four wheels rotating at high angular and linear velocities disturb a lot of air. The amount of energy required to move anything through air increases in value by the third power of the velocity of the object. (Not to be confused with the increase in drag - Drag increases with the square of the speed.)

Specifically:

Where:

- A is the functional cross sectional area of the racer.
- Cd is the coefficient of drag of the racer.
- p is the density of the air.
- V is the velocity of the racer with respect to the air.

The amount of energy lost by the racer to rotate four wheels through the air depends upon a complex determination of the instantaneous relative velocities and drag coefficients of all parts of the wheels. Further complicating the issue, the rear wheels partially draft from the front wheels. This means that the front wheels will have slightly more drag than the rear wheels.

Not much can be done to offset this large amount of energy loss, as all racers are limited by the current rules of wheel enclosures. Some of this energy loss can be reduced by designing and using your axle trees to create turbulence in front of or next to your wheels, or by reducing the drag between the wheel and the axle tree. (Hatfield and Fulton of Indiana have done an excellent job in this area)

TURBULENT CAUSING AXLE TREES

Another area of improvement is streamlining the ends of your axles with the wheel pins. Having the pins fit over the ends of the spindles and not under or over the spindle will reduce air drag. Creativeness in this field was shown by Mark Finsterwald the last few years.