Grand Prix Racing - The Science of Fast Pinewood Cars

# Complete Model of A Grand Prix Race

The models developed so far in this manual have not considered the effect of air resistance. As we shall see, the addition of air resistance to the model energy relations is not easy and the result leads to more complicated mathematics. Indeed, as air is pushed aside increasing molecular kinetic energy, a bit of potential energy literally dissapears into thin air!

## Dissappear into thin air

By breaking up the simplified Grand Prix track into two parts, we get a close look at the differences in accelerations, speeds and times and the differences in the math it took to get there. The equations are very similar with hyperbolic versions of the functions occuring on the ramp part and trigonometric ones on the flat part. Also, because of the initial velocity on the flat track, we get the coasting distance and time with no extra effort. Most of the expressions derived in the links below appear together in the summary of the race model.

The complete model of a Grand Prix race incorporates all of the significant energy sources and sinks of the physical race. Only one lane is modeled; only one car. Analysis is split between the starting ramp section and a flat coasting section. For the total race time and other finish line expressions, look at the summary of the race model.

If you don't think this simple two part model is a good representation of your Grand Prix race, you might have other options.

Is this track model realistic? Yes, it is actually quite good matching kinematic computer results and actual race times pretty closely. One factor that was not included was the body rotation of the car at the sudden bend in this model's track. A real car on a track built like this (and some actually are!) is jolted by such a sudden angular change and loses more than just rotational energy. Tracks without this sudden jolt tend to preserve your car's momentum better but increase friction through centrifugal force.

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