Pace and motor control optimization for a runner

We present a model which encompasses pace optimization and motor control effort for runner on fixed distance. see that long races, the term behaviour is well approximated by turnpike problem, allows to define an approximate optimal velocity. provide numerical simulations quite consistent with this approximation leads simplified problem. The advantage of formulation velocity if we have data race, access his $$\dot{V}O2_{\mathrm {max}}$$ , then can infer values all physiological parameters. are also able estimate effect slopes ramps.