Modelling of Racing

In order to determine the optimal strategy to run a race according to the distance to run, we introduce a model based on a system of differential equations for the velocity, the propulsive force and the anaerobic energy. The system does not rely on statistics but couples mechanics, energetics (both aerobic and anaerobic), neural drive to an economic decision theory of cost and benefit. For a fixed distance to run (from 100m to 10 000m), we find how effort is minimized to produce the best running strategy. This takes into account the effect of the bend, of the lane and the psychological interaction with a neighbour on the next lane. We even suggest how present tracks could be modified to improve record times and decrease discrepancy between lanes.