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 \(\dot{V}O2_{\mathrm {max}}\), then we can infer the values of all the physiological parameters. We are also able to estimate the effect of slopes and ramps.

我们提出了一个模型，其中包含固定距离跑步者的配速优化和运动控制工作。我们看到，对于长时间的比赛，长期行为可以通过收费公路问题很好地近似，它允许定义近似的最佳速度。我们提供的数值模拟与这种近似一致，这导致了一个简化的问题。这种简化的速度公式的优点是，如果我们有比赛中跑步者的速度数据，并且可以访问他的\(\dot{V}O2_{\mathrm {max}}\)，那么我们可以推断所有生理参数的值。我们还能够估计斜坡和斜坡的影响。