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

Abstract 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 $$2\;\textrm{km}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mspace/> <mml:mtext>km</mml:mtext> </mml:mrow> </mml:math> simulating various gradients and wind conditions. A parameter-dependent simulation showed between $$0.45\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0.45</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> and $$2.84\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2.84</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> 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 $$1.2\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>1.2</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> faster over $$21.3\;\textrm{km}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>21.3</mml:mn> <mml:mspace/> <mml:mtext>km</mml:mtext> </mml:mrow> </mml:math> . 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.