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

J. de Jong, Robbert Fokkink*, Geert Jan Olsder, Arend Schwab

*Corresponding author for this work

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

2 Citations (Scopus)
71 Downloads (Pure)


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.

Original languageEnglish
Title of host publicationProcedia Engineering
Subtitle of host publicationThe Engineering of Sport 11
EditorsF.C.T. van der Helm, A.J. Jansen
Publication statusPublished - 2016
EventISEA 2016 - The Engineering of Sport 11 - Delft, Netherlands
Duration: 11 Jul 201614 Jul 2016

Publication series

NameProcedia Engineering


ConferenceISEA 2016 - The Engineering of Sport 11
Internet address


  • bicycling
  • maximum principle
  • power equation


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