Pace and motor control optimization for a runner

We present a model which encompasses pace optimization and motor control effort for a runner on a fixed distance. We see that for long races, the long term behaviour is well approximated by a turnpike problem, that allows to define an approximate optimal velocity. We provide numerical simulations quite consistent with this approximation which leads to a simplified problem. The advantage of this simplified formulation for the velocity is that if we have velocity data of a runner on a race, and have access to his [Formula: see text], then we can infer the values of all the physiological parameters. We are also able to estimate the effect of slopes and ramps.