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Math Help - Units of twistiness

  1. #1
    OMX
    OMX is offline
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    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
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  2. #2
    OMX
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    Would simply counting the number of bends tell you how twisty the course was?
    Road America: 11
    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
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  3. #3
    MHF Contributor Bruno J.'s Avatar
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    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!
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