Followinga few entries on sports here and there, I was wondering what kind of law follow the running records with respect to the distance. The data are available on Wikipedia, or here for a tidied version. It collects 18 distances, from 100 meters to 100 kilometers. A log-log scale is in order:
It is nice to find a clear power law: the relation between the logarithms of time T and of distance D is linear. Its slope (given by the lm function) defines the power in the following relation:
Another type of race consists in running backwards (or retrorunning). The linear link is similar
with a slightly larger power
So it gets harder to run longer distances backwards than forwards…
It would be interesting to compare the powers for other sports like swimming and cycling.