Applications of Mathematical Models of Road Cycling
Applications of Mathematical Models of Road Cycling
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公路自行车数学模型的应用
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
D. Saupe
中科院分区：
文献类型：
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作者：
Thorsten Dahmen;Stefan Wolf;D. Saupe
摘要本文讨论了公路自行车数学模型的几个用例。踏板力的力学模型是在真实赛道上进行公路自行车运动的准确室内测力计模拟的基础。再加上一个简单的生理模型的运动员的行使作为他/她的累积功率输出的函数，最佳的骑在山上的时间试验的策略计算。这两个模型的组合导致一个数学优化问题，可以通过离散化数值求解。物理模型敏感地依赖于对路线上的道路坡度的准确估计。为此，我们还提出了一种新的方法，结合基于模型的斜率估计与噪声测量从多个不同质量的GPS信号。总之，我们提供了一种方法来模拟道路自行车在现实世界的轨道上，分析自行车运动员的性能，识别和量化潜在的性能改善，以及指导运动员到底在哪里以及如何改变他/她的起搏策略，以实现这些收益。
Abstract This contribution discusses several use cases of mathematical models for road cycling. A mechanical model for the pedaling forces is the basis for an accurate indoor ergometer simulation of road cycling on real-world tracks. Together with a simple physiological model for the exertion of the athlete as a function of his/her accumulated power output, an optimal riding strategy for time trials on mountain ascents is computed. A combination of the two models leads to a mathematical optimization problem that can be solved numerically by discretization. The physical model depends sensitively on an accurate estimation of the road slope on the course. For this purpose, we also present a new method that combines model-based slope estimations with noisy measurements from multiple GPS signals of differing quality. Altogether, we provide a means to simulate road cycling on real-world tracks, to analyze cyclist performance, to identify and quantify potential performance improvement, as well as to instruct the athlete exactly where and how to change his/her pacing strategy to achieve these gains.