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.


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.


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



World record track data from updated with results from 2008 Olympics.

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