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Approximation and visualization of Indy 500 racetrack curvature for mechanical design.

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Racetrack Curvature

Jason Klein. Oct. 29, 2024

Converts lat/long coordinates of the Indy 500 racetrack to the ENU local tangent plane reference frame, which has units of meters. Then numerically computes the curvature at each point and visualizes the result.

result

Why?

As part of speccing the steering system, Selena wanted to know the minimum radius of a turn on the competition track and asked me if I happened to know. I didn't, but I did remember that the 2023 driver dash I wrote had access to a file called Indy500.json that had latitude and longitude coordinates of the actual path traveled during competition.

Combined with an ECEF-g to ENU coordinate frame converter I wrote over the summer (currently in a private repo), I was able to convert the geodetic coordinates to a frame with units in meters. I also tried using pymap3d which has this sort of converter, but it didn't get the units right.

I then compute the curvature by creating an approximating spline, using that to get analytical first and second derivatives of x and y, and then plugging those into the curvature formula. Computing the maximum curvature and then taking its reciprocal yields the minimum instantaneous turning radius of 26.597254392113534 meters, which agrees with the value I got when zooming into the plot and manually tracing out the osculating circle for the regions I expected to have the most curvature.

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