Transitions

Understanding race dynamics in a rigorous way depends on the ability to get reulsts from the race model. But, there is a type of "uncertainty principle" that engineers must deal with. More often than not, modeling closely to reality results in models that cannot be solved directly or that can't even be solved reasonably using a computer. The closer you get, the harder it is to get meaningful results.

Modeling the transition between the ramp and flat parts of the typical Grand Prix track presents exactly this kind of problem. To overcome these difficulties, some constraints need to be discovered that will let us get at the behavior we want to study without making the model irrelevant. Where can such constraints be found?

In the simple closed race model, the problem was "solved" by assuming that the transition didn't contribute vastly different behavior to the race. The transition was minimized to zero length and some "sanity checks" were made to show that this was reasonable - at least for some tracks.

Considerations

Other typical tracks have long gradual transitions. It is this type that is explored here. To begin, let's preview some of the considerations that come into focus on a gentle transition.

1. Gravitation - Bending the track makes front axle and tread friction greater
2. Centrifugal force - Bending the track increases axle and tread friction
3. Body rotation - Your car body and wheels rotate from the ramp angle to horizontal
4. Energy loss - Some energy is lost in each of the above and maybe more
5. Transit time - Your car's trajectory is shortened (as it was in the "zero" case)

To address these issues and find limits on how they can affect the finish time in a race, a few models are presented:

• A model of the forces on each axle for arbitrary track surface angles
• A model of a circular arc track section
• A model of a catenary track section

It's too bad that neither of the more typical transitions result in closed dynamic expressions, but the limit results are quite useful in comparing with the "zero" transition case.

TBD