Optimal pacing strategy for a race of two competing cyclists
Optimal pacing strategy for a race of two competing cyclists
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两名自行车选手比赛的最佳配速策略
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
D. Saupeand
中科院分区：
文献类型：
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作者：
Thorsten Dahmen;D. Saupeand
背景资料：对于两个或多个竞争或合作的骑自行车者的情况下的最佳起搏策略，只有少数方法考虑滑流。然而，通过将滑流效应纳入两名运动员在平坦跑道上比赛的模型中，已经显示出，落后的运动员如何能够将自己定位在与另一名运动员的击球距离处，以及何时应该开始最后冲刺。（Pitcher，2009：中距离跑步的两个跑步者模型的最佳策略。SIAM Journal on Applied Mathematics，70（4），1032 - 1046）。目的：我们将这种方法转移到具有真实世界高度数据的固定长度轨道上的自行车。特别是在下降时，涉及高速，并增加了滑流策略的重要性。方法：我们采用标准的机械自行车模型，考虑踏板功率，重力，摩擦力，惯性和空气阻力。标称空气阻力乘以滑流系数，当骑自行车的人位于他的对手后面时，滑流系数最小（Pitcher，2009）。我们的生理模型定义了剩余的无氧能力，当脚踏功率超过/福尔斯低于临界功率时，剩余的无氧能力非线性地降低/增加（Gordon，2005：在自行车计时赛期间优化功率分布。Sports Engineering，8（2），81 - 90）.两个骑自行车的人的机械和物理参数可能不同。我们使用最先进的最优控制方法进行数值计算（Patterson等人，2013年：GPOPS-II：一个MATLAB软件，用于使用hp-自适应高斯正交配置法和稀疏非线性规划求解多相最优控制问题。ACM Transactions on Mathematical Software，39（3）.）。结果如下：图1显示了在法国圣吉尔达斯-德斯-布瓦至雷东（2013年环法自行车赛第3赛段）的比赛中，两名自行车选手的最佳起搏策略。讨论和结论：滑流对自行车运动中的起搏策略有显著影响。结合机械自行车模型，最优控制算法可用于计算最后冲刺的最优策略。未来的工作应该考虑到，骑自行车的人往往会合作，以保持领先的珀洛东之前，他们在最后冲刺阶段的竞争。
Background: For optimal pacing strategies in the case of two or more competing or cooperating cyclists only few approaches take slipstreaming into account. However, by incorporating the slipstream effect in the model of a race of two runners on a flat course, it has been shown, how the trailing runner can position himself at striking distance behind the other and when he should start the final sprint. (Pitcher, 2009: Optimal strategies for a two-runner model of middle-distance running. SIAM Journal on Applied Mathematics, 70(4), 1032–1046). Purpose: We transfer this approach to cycling on a track of fixed length with real-world height data. In particular on descents, high speed is involved and increases the significance of the slipstreaming strategy. Methods: We adopt the standard mechanical bicycling model that accounts for pedaling power, gravity, friction, inertia, and aerial drag. The nominal aerial drag force is multiplied by a slipstream factor that has its minimum when the cyclist is located closely behind his opponent (Pitcher, 2009). Our physiological model defines the remaining anaerobic capacity that de-/increases non-linearly when the pedaling power exceeds/falls below critical power (Gordon, 2005: Optimizing distribution of power during a cycling time trial. Sports Engineering, 8(2), 81–90). The mechanical and physical parameters may be different for the two cyclists. We use a state-of-the-art optimal control method for the numerical computations (Patterson et al., 2013: GPOPS-II: A MATLAB software for solving multiple-phase optimal control problems using hp-adaptive gaussian quadrature collocation methods and sparse nonlinear programming. ACM Transactions on Mathematical Software, 39(3).). Results: The optimal pacing strategy for two cyclists on a competition between Saint-Gildas-des-Bois to Redon (stage 3 of the Tour de France 2013), France, is shown in Figure 1. Discussion and Conclusion: Slipstreaming has a significant impact on pacing strategies in cycling. Incorporated into the mechanical bicycling model, optimal control algorithms can be used to compute the optimal tactic for the final sprint. Future work should take into account that the cyclists will often cooperate to stay ahead of the peloton before they compete in the final sprint phase.