Optimal speed in Thoroughbred horse racing

TL;DR

This paper develops a mathematical model combining mechanics, energetics, and motor control to determine the optimal speed strategy for Thoroughbred horses during races, considering energy use and track topography.

Contribution

It introduces a coupled differential equations model for race pacing, incorporating energetic and mechanical factors, and applies it to real race data for parameter identification.

Findings

Provides optimal speed profiles for race strategies

Predicts oxygen uptake and energy expenditure during races

Adapts strategies based on track topography

Abstract

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.