How Fast Can You Run?

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After Summer Olympic Games there is often increased interest in the physiology of distance running. Remarkably, a log-log plot of world-record times shows a very nearly linear function of distance, between 100 m and 100 km. This is shown by the blue and red curves for men and women, respectively. All are outdoor track records.

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How do you suppose your running times would compare to those of world-class athletes? Several physiologically significant measures of running speed and endurance, including myoglobin oxygen uptake and lactic acid accumulation in muscles appear to follow a sigmoid-type dependence. This can be approximated by an appropriately-scaled error function. The assumed parameters are largely guesswork, but the author has tried to match them to his own running ability during his younger years.

I define a "fitness parameter" , running from 0 to 10, with the following rough correspondences: , world-class runner; , well-conditioned athlete; , good physical condition; , somewhat out-of-shape; and , confirmed couch potato. By setting the sliders in this Demonstration you can estimate your running time for any distance between 100 m and 100 km, shown by a black curve. Based on your fitness, there is a maximum distance you are allowed to run. We don't want to risk any heart attacks for Mathematica users!

I would like to invite any authority on sports physiology who happens upon this Demonstration to improve on the naive fitness model given here.

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Contributed by: S. M. Blinder (March 2011)
Open content licensed under CC BY-NC-SA


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Details

World record track data from http://www.trackandfieldnews.com/records/ updated with results from 2008 Olympics.



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