  In order to determine the optimal strategy to run a race on a curved track
according to the lane number, we introduce a model based on differential
equations for the velocity, the propulsive force and the anaerobic energy which
takes into account the centrifugal force. This allows us to analyze numerically
the different strategies according to the different types of track since the
straight line is not always of the same length. In particular, we find that the
tracks with shorter straight lines lead to better performances, while the
double bend track with the longest straight line leads to the worst
performances and the biggest difference between lanes. Then for a race with two
runners, we introduce a psychological attraction to follow someone just ahead
and the delay to benefit again from this interaction after being overtaken. We
provide numerical simulations in different cases. Results are overall
consistent with the IAAF rules for lanes drawing, indicating that middle lanes
are the best, followed by the exterior lanes, interior lanes being the worst.
