Optimization of Pacing Strategies for Cycling Time Trials Using a Smooth 6-Parameter Endurance Model

Abstract

Computing the optimal pacing strategy for cycling time trials can be formulated as an optimal control problem, where a mechanical model and a physiological endurance model form the dynamical system and time to complete the track is to be minimized. We review approaches that use the 3-parameter critical power model to compute optimal pacing strategies and modify it to become a smooth 6-parameter endurance model. Due to its 3 additional parameters, it is more flexible to model the physiological dynamics appropriately. Besides, we demonstrate that this model has favourable numerical properties that allow to eliminate purely mathematical workarounds to compute an approximate optimal pacing for the original 3- parameter critical power model. An established simplification of the 3-parameter critical power model is considered for a comparison of numerically computed optimal pacing strategies on an artificial track with continuously varying slope subject to these variants of the 3-parameter critical power model. It is shown, that the optimal pedalling power subject to the original model exhibits unrealistically large variations, which are smoothed heavily by the simplified model. The 6-parameter endurance model turns out to be a flexible model, that exhibits intermediate variations in the optimal pedalling power, while being numerically well behaved. The methods used in this contribution are extensible and can be used for the computation of optimal pacing strategies in conjunction with more sophisticated physiological models.