Optimal pacing in road cycling using a nonlinear power constraint

Abstract

In the individual road cycling discipline known as a time-trial, variable power pacing under variable grade conditions leads to improved performance. However, it is unclear whether these power variations result in an optimal finishing time. Typical pacing strategies use an average power constraint, which requires maintaining a constant speed regardless of grade fluctuations; however, this is physiologically infeasible for cyclists. We used an exponentially weighted average (EWA) power constraint in which a nonlinear relationship between the power output and physiological cost was assumed. We defined the optimal pacing (OP) strategy by minimizing the total cycling time subject to the EWA power constraint, and set the EWA of the power output of both the OP and constant power (CP) strategies to the same baseline value. The model showed that the OP strategy outperformed the CP strategy in terms of minimizing the finishing time under variable grade conditions, the power distribution of the OP strategy was identical to that of the CP strategy under constant grade conditions, and the average power output of the OP strategy was always lower than that of the CP strategy under variable grade conditions. Numerical simulations were performed on two hypothetical 40-km courses using both the CP and OP strategies. We found that under variable grade conditions, the time-saving rates of the OP strategy relative to the CP strategy were 2.7 and 2.8% for the two simulated courses.