Units of twistiness
I want to compare race tracks by analysing how twisty they are.
This is interesting because some race bikes in the TTXGP races go fast in a straight line but have to go round corners quite slowly while others go slower in a straight line but corner better.
I am trying to think up a simple way to describe the twistiness of the track (in 2D is fine for the moment).
For example is there a standard way I can compare:
File:Road America.svg - Wikipedia, the free encyclopedia
File:Infineon (Sears Point) with emphasis on Long track.svg - Wikipedia, the free encyclopedia
File:Monte Carlo Formula 1 track map.svg - Wikipedia, the free encyclopedia
Would simply counting the number of bends tell you how twisty the course was?
Road America: 11
Indianapolis Speedrome: 4
1) What counts as a "bend" can be difficult to decide. For example "Beau Rivage" (#2 at Monaco) or corner #4 at Road America don't look like corners. They are just slight variations on a straight. The angle and the length of the corner should also count towards the twistiness index.
2) Monaco  looks much more than three-times more "twisty" than Indianapolis . A circle isn't really twisty at all.
3) Monaco seems more twisty than Infineon because while there are a similar number of corners Monaco is a shorter track (Monaco = 3.340Km, Infineon = 4.05km). Should we calculate a ratio of corners to track length?
File:Monte Carlo Formula 1 track map.svg
File:Indianapolis Motor Speedway - Speedway.svg - Wikipedia, the free encyclopedia
You might want to calculate the curvature at each point, and then calculate the average curvature with respect to arc length. You'd need to have a good understanding of calculus to do this!