Ecole des Hautes Etudes en Sciences Sociales, PSL Research University, Centre d'Analyse et de Mathématique Sociales, Paris, France.
Inria Paris and LJLL Sorbonne Université, Paris, France.
PLoS One. 2019 Sep 5;14(9):e0221572. doi: 10.1371/journal.pone.0221572. eCollection 2019.
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 types of track since different designs of tracks lead to straights of different lengths. In particular, we find that the tracks with shorter straights lead to better performances, while the double bend track with the longest straight leads to the worst performances and the biggest difference between lanes. Then for a race with two runners, we introduce a psychological interaction: there is an attraction to follow someone just ahead, but after being overtaken, there is a delay before any benefit from this interaction occurs. We provide numerical simulations in different cases. Overall, the results agree with the IAAF rules for lane draws in competition, where the highest ranked athletes get the center lanes, the next ones the outside lanes, while the lowest ranked athletes get the inside lanes.
为了根据跑道号码确定在曲道上比赛的最佳策略,我们引入了一个基于速度、推进力和考虑离心力的无氧能量的微分方程模型。这使我们能够根据赛道类型进行数值分析,因为不同的赛道设计导致直道长度不同。特别是,我们发现直道较短的赛道会有更好的表现,而直道最长的双弯道则会导致最差的表现和最大的跑道差异。然后,对于有两名选手的比赛,我们引入了一种心理互动:有人在前面领跑时会有跟随的吸引力,但被超越后,需要一定的时间才能从这种互动中获益。我们在不同情况下提供了数值模拟。总的来说,结果与国际田联在比赛中制定的跑道抽签规则一致,即排名最高的运动员获得中间跑道,其次是外道,而排名最低的运动员则获得内道。