### 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.

Original language | English |
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Title of host publication | Procedia Engineering |

Subtitle of host publication | The Engineering of Sport 11 |

Editors | F.C.T. van der Helm, A.J. Jansen |

Publisher | Elsevier |

Pages | 907-911 |

Volume | 147 |

DOIs | |

Publication status | Published - 2016 |

Event | ISEA 2016 - The Engineering of Sport 11 - Delft, Netherlands Duration: 11 Jul 2016 → 14 Jul 2016 http://www.isea2016.com/ |

### Publication series

Name | Procedia Engineering |
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Volume | 147 |

### Conference

Conference | ISEA 2016 - The Engineering of Sport 11 |
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Country | Netherlands |

City | Delft |

Period | 11/07/16 → 14/07/16 |

Internet address |

### Keywords

- bicycling
- maximum principle
- power equation

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## Cite this

*Procedia Engineering: The Engineering of Sport 11*(Vol. 147, pp. 907-911). (Procedia Engineering; Vol. 147). Elsevier. https://doi.org/10.1016/j.proeng.2016.06.280