Quentin Mercier's research while affiliated with French National Centre for Scientific Research and other places

The distribution of energetic resources in world-class distance running is a key aspect of performance, with athletes relying on aerobic and anaerobic metabolism to greater extents during different parts of the race. The purpose of this study is to model 10,000 m championship performances to enable a deeper understanding of the factors affecting running speed and, given that more than half the race is run on curves, to establish the effect of the bends on performance. Because a limitation of time split data is that they are typically averaged over 100-m or 1,000-m segments, we simulate two 10,000 m runners' performances and thus get access to their instantaneous speed, propulsive force and anaerobic energy. The numerical simulations provide information on the factors that affect performance, and we precisely see the effect of parameters that influence race strategy, fatigue, and the ability to speed up and deal with bends. In particular, a lower anaerobic capacity leads to an inability to accelerate at the end of the race, and which can accrue because of a reliance on anaerobic energy to maintain pace in an athlete of inferior running economy. We also see that a runner with a worse running economy is less able to speed up on the straights and that, in general, the bends are run slower than the straights, most likely because bend running at the same pace would increase energy expenditure. Notwithstanding a recommendation for adopting the accepted practices of improving aerobic and anaerobic metabolism through appropriate training methods, coaches are advised to note that athletes who avoid mid-race surges can improve their endspurt, which are the differentiating element in closely contested championship races.

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.

Thanks to velocity data on races in Chantilly (France), we set a mathematical model which provides the optimal pacing strategy for horses on a fixed distance. It relies on mechanics, energetics (both aerobic and anaerobic) and motor control. We identify the parameters useful for the model from the data. Then it allows to understand the velocity, the oxygen uptake evolution in a race, as well as the energy or the propulsive force and predict the changes in pacing according to the properties (altitude and bending) of the track.