Hi Isaiah, I'm currently doing my Math Internal Assessment for IB diploma and am looking at using the euler spiral to find the optimal driving line for the 2018 Singapore grand prix and compare it to the driving line taken by Lewis Hamilton in his 1:36:15min lap around the circuit. I was wondering if you could share the readings you used to identify which segment of the euler spiral corresponded to the corner that you are looking at. It'll really be a massive help! Thank you so much!

Interesting stuff, but as a racer, I could offer you some thoughts on one thing for certain:

Your lines seem to suggest a single change of radius with respect to time, and that's not what happens in a real corner. The line begins with a curve (a spiral perhaps, but perhaps not) where the radius is decreasing as the car is slowing to some minimum, and then as the car accelerates, that radius starts to increase. Those two curves are not the same, because no racing car accelerates as quickly as it decelerates, but obviously at the moment of transition, they have the same radius.