Brachistochrone on a Velodrome

The Brachistochrone problem, which describes the curve that carries a particle under gravity in a vertical plane from one height to another in the shortest time, is one of the most famous studies in classical physics. There is a similar problem in track cycling, where a cyclist aims to find the traj...

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Bibliographic Details
Published inarXiv.org
Main Authors Benham, G P, Cohen, C, Brunet, E, Clanet, C
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 05.03.2020
Subjects
Bicycling
Cycles
Exact solutions
Physics - Fluid Dynamics
Trajectories
Velodromes
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Summary:The Brachistochrone problem, which describes the curve that carries a particle under gravity in a vertical plane from one height to another in the shortest time, is one of the most famous studies in classical physics. There is a similar problem in track cycling, where a cyclist aims to find the trajectory on the curved sloping surface of a velodrome that results in the minimum lap time. In this paper we extend the classical Brachistochrone problem to find the optimum cycling trajectory in a velodrome, treating the cyclist as an active particle. Starting with two canonical cases of cycling on a sloping plane and a cone, where analytical solutions are found, we then solve the problem numerically on the reconstructed surface of the velodrome in Montigny le Bretonneux, France. Finally, we discuss the parameters of the problem and the effects of fatigue.
ISSN:2331-8422
DOI:10.48550/arxiv.1908.02224