Path optimization for a race course

[aeb2335]

Ok, so here is my question

In grade school we all learned that the shortest distance between two points is a straight line. We also know from intuition that cars can't withstand infinite amounts of radial or tangential acceleration otherwise the car will skid i.e traction circle. Via this intuition experienced drivers in an auto racing situation in an effort to reduce the time it takes to go around a race circuit the driver will take a "racing line". Which most people simply "see" and do not calculate.

My end goal is to figure out what the racing line or path of a (or any) given race course is and corresponding velocities subject to the maximum allowed forces from the traction circle.

From what I have read I think the most general way to solve something like this without discreetly computing paths is to use variational analysis; but I really don't understand it. Is there a less technical resource on the subject? Or an alternative solution?

also is there be a way of doing this via viewing the course as a field of curvature and then finding the gradient of the curvature path?

 

[Navin A S]

The best way to approach this problem is to use a combination of variational analysis and optimization techniques. Variational analysis is a mathematical tool used to find the minimum energy path, or the most efficient path, between two points. This technique can be applied to race tracks as well, as it can help determine the optimal route for a driver to take in order to finish the track in the least amount of time.Optimization techniques can also be used in tandem with variational analysis in order to further refine the racing line. These techniques involve identifying parameters or variables that affect the course, such as corner radius, width of the track, etc. By changing these parameters, the optimal route for a driver can be determined.In terms of viewing the course as a field of curvature, this is possible but may not be necessary for the purpose of finding the optimal racing line. However, further research into this method may be beneficial as it could provide additional insights into the physics of driving around a race track.