Overview of Article

This article will go over the route modelling of the Circuit of the Americas race track as it stands on 6/29/2019, describing the the physics behind the system, inputs of the system, its projected outputs, and the work left TO DO.

Physics of System

The main problem is understanding how the turns in the track limit the speed at which the car can take those turns. The physics behind this are quite simple. We could look at the radial force exerted on the car using F = ma, find the maximum force that the car can withstand, measure or estimate the mass of the car, and use a = v²/r to find the speed to take each turn at. However, we could also set a limit on the acceleration we want to experience and that eliminates the need for finding F and m. In this case, previous calculations had shown that MSXII could handle 1 g accelerations without rolling so that was chosen as an initial upper acceleration limit (Which could later be reduced if 1 g was found to be too great). Rearranging for speed gives v = (ar)^1/2.

Inputs of System

The required inputs are the radii of each turn, which can be used along with the limiting acceleration to find the maximum speed for each turn. However, the distance of each turn from the starting point is also useful to help coordinate with other strategy models.

Currently these measurements have been made manually from a map and scaled appropriately because the COTA track is relatively small, but for future track models it would be nice to find a method that takes less time and effort.

Outputs of System

The output is a series of speed limitations imposed by turns in the environment.

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