A variational approach to determine the optimal power distribution for cycling in a time trial

de Jong, J.; Fokkink, R.J.; Olsder, G.J.; Schwab, A.L.

doi:10.1016/j.proeng.2016.06.280

A variational approach to determine the optimal power distribution for cycling in a time trial

Title

A variational approach to determine the optimal power distribution for cycling in a time trial

Author

de Jong, J. (Universiteit Utrecht)
Fokkink, R.J. (TU Delft Applied Probability)
Olsder, G.J. (TU Delft Discrete Mathematics and Optimization)
Schwab, A.L. (TU Delft Biomechatronics & Human-Machine Control)

Contributor

van der Helm, F.C.T. (editor)
Jansen, A.J. (editor)

Date

2016

Abstract

The optimal pacing strategy of a cyclist in an individual time-trial depends on terrain, weather conditions and the cyclists endurance capacity. Previous experimental and theoretical studies have shown that a suboptimal pacing strategy may have a substantial negative effect. In this paper we express the optimal pacing problem as a mathematical optimal control problem which we solve using Pontryagin's maximum principle. Our solution of the pacing problem is partly numerical and partly analytical. It applies to a straight course without bends. It turns out that the optimal pacing problem is a singular control problem. Intricate mathematical arguments are required to prove that the singular control times form a single interval: optimal pacing starts with maximum power and decays through a singular control, which may be degenerate, to minimum power.

Subject

bicycling
maximum principle
power equation

To reference this document use:

http://resolver.tudelft.nl/uuid:436f77ab-7d34-405d-b7a4-de44c6d16623

DOI

https://doi.org/10.1016/j.proeng.2016.06.280

Publisher

Elsevier

Source

Procedia Engineering: The Engineering of Sport 11, 147

Event

ISEA 2016 - The Engineering of Sport 11, 2016-07-11 → 2016-07-14, Delft, Netherlands