2015/08/03 by Amandine Aftalion, Aftalion, Amandine, Camilla Fiorini +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Physics and Astronomy · #Adipose Tissue and Metabolism #Cardiovascular and exercise physiology #Sports Performance and Training #math.OC #physics.med-ph #q-bio.TO
paper · pdf · doi:10.48550/arxiv.1508.00523
As pointed out by the referee, the simulations are wrong, but no corrected version will be made
arxiv created 2016/03/10 · arxiv updated 2016/03/11
In order to describe the velocity and the anaerobic energy of two runners competing against each other for middle-distance races, we present a mathematical model relying on an optimal control problem for a system of ordinary differential equations. The model is based on energy conservation and on Newton's second law: resistive forces, propulsive forces and variations in the maximal oxygen uptake are taken into account. The interaction between the runners provides a minimum for staying one meter behind one's competitor. We perform numerical simulations and show how a runner can win a race against someone stronger by taking advantage of staying behind, or how he can improve his personal record by running behind someone else. Our simulations show when it is the best time to overtake, depending on the difference between the athletes. Finally, we compare our numerical results with real data from the men's 1500 -- m finals of different competitions.