The individual time trial as an optimal control problem

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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.
Original languageEnglish
Pages (from-to)200-206
Number of pages7
JournalInstitution of Mechanical Engineers. Proceedings. Part P: Journal of Sports, Engineering and Technology
Issue number3
Publication statusPublished - 4 May 2017


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

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