1. ## 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
with
File:Infineon (Sears Point) with emphasis on Long track.svg - Wikipedia, the free encyclopedia
and
File:Monte Carlo Formula 1 track map.svg - Wikipedia, the free encyclopedia

Ideas, suggestions?

OMX

2. Would simply counting the number of bends tell you how twisty the course was?
Infineon: 14
Monaco: 13
Indianapolis Speedrome: 4

Problems:
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 [1] looks much more than three-times more "twisty" than Indianapolis [2]. 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?

[1]File:Monte Carlo Formula 1 track map.svg
[2]File:Indianapolis Motor Speedway - Speedway.svg - Wikipedia, the free encyclopedia

3. 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!