Optimal pacing in a cycling time-trial considering cyclist's fatigue dynamics

Optimal pacing of one's effort during a cycling time-trial or even during leisurely long bicycle rides can be a challenge not only for a novice rider but also for the experienced. The rider's level of fatigue, upcoming elevation changes, and varying wind speed all contribute to the problem complexity. This paper formulates the pacing strategy for a bicycle time-trial as an optimal control problem with the goal of finishing in minimum time while considering pedaling force constraints imposed by velocity and rider's fatigue. A phenomenological dynamic model for a rider's fatigue is constructed and the model parameters are estimated using experimental data from road tests. Assuming prior knowledge of the route elevation profile, the optimal control problem is solved using dynamic programming which generates a feedback strategy: Given measured bicycle velocity and the estimated rider's state of fatigue, the solution suggests a pacing strategy that if followed can reduce total travel time. Preliminary simulation results based on experimental data from a century (100 mile) ride show the potentials of the proposed approach.