Normalized and xPower to Generate Pacing Strategies in Road Cycling

摘要

Normalized power and xPower have become standard measures for metabolic demand with road cycling. In contrast to average power these quantities account for the additional exertion resulting from time-variations of the pedaling power. In this contribution, we develop a method to use a slightly modified xPower to generate pacing strategies for road cycling time trials, where determining the optimal variations of the pedaling power is the ultimate goal. We tackle severe numerical issues related to singular arcs in optimal control, derive the necessary condition and use the Chebfun software system with its essential and unique capability to compute with Frechet derivatives automatically.