论文标题
纯种赛马的最佳速度
Optimal speed in Thoroughbred horse racing
论文作者
论文摘要
这项工作的目的是提供数学分析，以了解纯种马在比赛过程中如何调节其速度以优化性能。因为纯种马无法以最高速度进行整个比赛，而是确定要设定的速度以及何时释放速度爆发是必不可少的。我们的模型依赖力学，能量（有氧和厌氧）和运动控制。它是一个在速度，推进力和厌氧能量上耦合的普通微分方程的系统，它导致我们解决的最佳控制问题。为了确定对纯种马匹有意义的参数，我们使用法国盖洛普（France Galop）提供的Chantilly（法国）种族的速度数据，法国盖洛普（France Galop）是法国法国赛马赛车的统治机构。然后，我们对性能优化的数值模拟，然后提供了沿种族，种族中的氧气进化以及能量或推进力的最佳速度。它还可以预测马匹如何根据赛道的地形（高度和弯曲）改变其努力和速度。
The objective of this work is to provide a mathematical analysis on how a Thoroughbred horse should regulate its speed over the course of a race to optimize performance. Because Thoroughbred horses are not capable of running the whole race at top speed, determining what pace to set and when to unleash the burst of speed is essential. Our model relies on mechanics, energetics (both aerobic and anaerobic) and motor control. It is a system of coupled ordinary differential equations on the velocity, the propulsive force and the anaerobic energy, that leads to an optimal control problem that we solve. In order to identify the parameters meaningful for Thoroughbred horses, we use velocity data on races in Chantilly (France) provided by France Galop, the French governing body of flat horse racing in France. Our numerical simulations of performance optimization then provide the optimal speed along the race, the oxygen uptake evolution in a race, as well as the energy or the propulsive force. It also predicts how the horse has to change its effort and velocity according to the topography (altitude and bending) of the track.
