Power variation strategies for cycling time trials: a differential equation model

Journal of Sports Sciences
Graeme P Boswell

Abstract

In cycling time trials, competitors aim to ride a course in the fastest possible time and the implementation of a pacing strategy is therefore essential. In this study, a differential equation model of a cyclist incorporating continuous changes in velocity is formulated and applied to a selection of theoretical courses and athletes. The model is augmented with a constraint corresponding to a mean work rate and various pacing strategies are considered. The inclusion of continuous accelerations experienced by the cyclist forms an essential component in a model for courses comprising many changes of gradient, and a steady-state approximation, which has previously been used to assess pacing strategies, is not suitable. In addition to formulating a result on the mathematically optimal solution of the model equations subject to the mean power constraint, it is also shown that substantial time savings can be realized by cyclists increasing their work rates on uphill sections and suitably reducing their work rates elsewhere. However, the amount of time saved is highly course- and athlete-dependent with the greatest gains arising on courses with the longest continuous ascents by cyclists of greatest mass.

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Citations

Jan 11, 2014·Journal of Science and Medicine in Sport·Evan C JohnsonLawrence E Armstrong
Jan 5, 2013·Journal of Strength and Conditioning Research·Willard W Peveler
Mar 8, 2016·European Journal of Sport Science·Marc S Wells, Simon Marwood
Jul 15, 2016·Medicine and Science in Sports and Exercise·Erik AnderssonGlenn Björklund
May 3, 2016·Journal of Strength and Conditioning Research·Vitor P CostaCarl D Paton
Feb 9, 2017·Applied Physiology, Nutrition, and Metabolism = Physiologie Appliquée, Nutrition Et Métabolisme·Vitor Pereira CostaCarl David Paton
Dec 18, 2018·European Journal of Sport Science·Samantha Louise MossJamie Highton

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