A numerical design methodology for optimal pacing strategy in the individual time trial discipline of cycling

In this paper, we have developed a numerical design methodology for computing optimal pacing strategies for the individual time trial discipline in professional cycling. These strategies minimise the finishing time for a given cyclist racing on a given course by optimising how their power output is distributed along the course. The method is based on a finite element formulation and adjoint sensitivity analysis is used to minimise the finishing time subjected to a physiological constraint based on the principle of normalised power. We apply the method to four hypothetical courses of 2km simulating various gradients and wind conditions. A parameter-dependent simulation showed between 0.45% and 2.84% improvements in finishing times compared to benchmark pacing strategies. The method is also applied on a real-world course and the results are compared to the pacing strategy of professional cyclist and ITT specialist Martin Toft Madsen. The optimised strategy is 1.2% faster over 21.3km. We believe that the method presented here constitutes a promising framework for efficient computation of optimal pacing strategies and with further research and a more accurate physiological model; this could prove an important tool for strategising in professional cycling.