The individual time trial as an optimal control problem. (September 2017)

• Record Type: Journal Article
• Authors: de Jong, Jenny; Fokkink, Robbert; Olsder, Geert Jan; Schwab, AL
• Other Names: Goff John Eric guest-editor.
• Is Part Of: Proceedings of the Institution of Mechanical Engineers. Volume 231:Number 3(2017:Sep.)
• Page Start: 200
• Page End: 206
• Publication Date: 2017-09
• Subjects: Bicycling -- individual time trial -- maximum principle -- optimal control -- power equation; Sports sciences -- Periodicals; Sporting goods -- Design and construction -- Periodicals; Sports -- Technological innovations -- Periodicals; Biomechanics -- Periodicals; 613.71
• DOI: 10.1177/1754337117705057
• Languages: English
• ISSNs: 1754-3371

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.