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Math Help - Effect of change of Speed

  1. #1
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    Effect of change of Speed

    Hi there, I am wondering if someone could guide me through a problem.

    I have the following data (derived from a horse race):

    The distance is 1760 yards (1 mile). The standard (expected) time is 96.04s. Thus the avg speed to attain this is 18.32yps.
    The distance is broken down into two sections, s1 = 0y-1320y; s2 = 1320y-1760y. Effectively s1 is 75% of the race distance.
    We know that the optimal way of pacing the race is to run s2 at 105% of the total race speed.
    Therefore, we can estimate the time and avg speed for each section to run optimally: s1 = 73.18s (18.04yps); s2 = 22.86s (19.24yps)

    The race is run and the winners' data reads as follows: t = 97.44s (+1.40) (18.06yps); s1 = 74.60 (+1.42) (17.69yps); s2 = 22.84 (-0.02) (19.26yps)

    What I am trying to establish is a method of calculating the relationship between s1 and s2, so if the speed of s1 increase, to what end does the speed of s2 decrease? Thus I can make adjustments for 'time loss' due to inefficiency of pacing.

    Any help incredibly gratefully received!

    Gavin
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  2. #2
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    Re: Effect of change of Speed

    I don't have any idea what you are trying to do. If the speed of the horse running the s1 portion increases, that will increase the average speed of the entire race, so the horse must run even faster along s2 if it is to pace itself optimally (where it runs s2 at 105% of the total average race speed).
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  3. #3
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    Re: Effect of change of Speed

    ok sorry, I must explain. In s2 it always runs as fast as it possibly can. Thus, the speed of s2 has an inverse relationship with the speed of s1. So, if for example the horse runs +5s to optimal standard in s1, it is not physically possible to retrieve those 5s in s2 as this is outside what is physically possible. It will retrieve some of that time, so i am wondering if the a way of calculating a stable relationship?
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  4. #4
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    Re: Effect of change of Speed

    Quote Originally Posted by cloudwalking View Post
    ok sorry, I must explain. In s2 it always runs as fast as it possibly can. Thus, the speed of s2 has an inverse relationship with the speed of s1. So, if for example the horse runs +5s to optimal standard in s1, it is not physically possible to retrieve those 5s in s2 as this is outside what is physically possible. It will retrieve some of that time, so i am wondering if the a way of calculating a stable relationship?
    It depends on the horse. Some horses can push themselves more than others, just like humans. It seems unlikely that a "stable relationship" exists (to quote your pun).
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  5. #5
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    Re: Effect of change of Speed

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