A Variational Approach to Determine the Optimal Power Distribution for Cycling in a Time Trial. (2016)

• Record Type: Journal Article
• Authors: de Jong, Jenny; Fokkink, Robbert; Olsder, Geert Jan; Schwab, A.L.
• Is Part Of: Procedia engineering. Volume 147(2016)
• Page Start: 907
• Page End: 911
• Publication Date: 2016
• Subjects: bicycling -- power equation -- maximum principle; Engineering -- Congresses; Engineering -- Periodicals; Engineering; Conference proceedings; Periodicals; 620.005
• DOI: 10.1016/j.proeng.2016.06.280
• Languages: English
• ISSNs: 1877-7058

Abstract

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.