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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\;\textrm{km}$$\end{document} simulating various gradients and wind conditions. A parameter-dependent simulation showed between 0.45%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.45\%$$\end{document} and 2.84%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2.84\%$$\end{document} 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%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.2\%$$\end{document} faster over 21.3km\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$21.3\;\textrm{km}$$\end{document}. 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.