### Abstract

In a cycling time trial, the rider needs to distribute his power output optimally to minimize the time between start and finish. Mathematically, this is an optimal control problem. Even for a straight and flat course, its solution is non-trivial and

involves a singular control, which corresponds to a power that is slightly above the aerobic level. The rider must start at full anaerobic power to reach an optimal speed and maintain that speed for the rest of the course. If the course is flat but not straight, then the speed at which the rider can round the bends becomes crucial.

involves a singular control, which corresponds to a power that is slightly above the aerobic level. The rider must start at full anaerobic power to reach an optimal speed and maintain that speed for the rest of the course. If the course is flat but not straight, then the speed at which the rider can round the bends becomes crucial.

Original language | English |
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Pages (from-to) | 200-206 |

Number of pages | 7 |

Journal | Institution of Mechanical Engineers. Proceedings. Part P: Journal of Sports, Engineering and Technology |

Volume | 231 |

Issue number | 3 |

Publication status | Published - 4 May 2017 |

### Keywords

- Bicycling
- individual time trial
- maximum principle
- optimal control
- power equation