Optimizing running a race on a curved track

Amandine Aftalion 1 Pierre Martinon 2
2 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées
Abstract : In order to determine the optimal strategy to run a race on a curved track according to the lane number, we introduce a model based on differential equations for the velocity, the propulsive force and the anaerobic energy which takes into account the centrifugal force. This allows us to analyze numerically the different strategies according to the different types of track since the straight line is not always of the same length. In particular, we find that the tracks with shorter straight lines lead to better performances, while the double bend track with the longest straight line leads to the worst performances and the biggest difference between lanes. Then for a race with two runners, we introduce a psychological attraction to follow someone just ahead and the delay to benefit again from this interaction after being overtaken. We provide numerical simulations in different cases. Results are overall consistent with the IAAF rules for lanes drawing, indicating that middle lanes are the best, followed by the exterior lanes, interior lanes being the worst.
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Contributor : Pierre Martinon <>
Submitted on : Tuesday, November 27, 2018 - 6:22:06 PM
Last modification on : Friday, April 19, 2019 - 4:55:31 PM


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  • HAL Id : hal-01936993, version 1
  • ARXIV : 1811.12321


Amandine Aftalion, Pierre Martinon. Optimizing running a race on a curved track. 2018. ⟨hal-01936993⟩



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