Numerical optimization of pacing strategy in cross-country skiing based on Gauss pseudo-spectral method

In cross-country skiing competitions, the choice of pacing strategy is of decisive significance to athletes' performance. A reasonable pacing strategy is essential for athletes to improve their performance. In this paper, the mathematical models of cross-country skiing simulation and pacing optimization are established, including motion model, athlete power output model, and optimization model. The actual competition data of a Chinese athlete in Guyangshu 1.5 km track was compared with the model simulation results. The whole process time error is less than 3%, which verifies the accuracy of the motion and power output model. Gauss pseudo-spectral method is applied to the optimization model. By changing the distribution of athletes' power output, the racing time is minimized under the condition that the total energy output remains unchanged. Compared with the pacing strategy before optimization, the optimized racing time was shortened by 12.6 s, which verifies the effectiveness of the optimization model. Optimized results show that in the first significant uphill section, a recommendation is to use a more conservative strategy, while in the latter half of uphill sections the power output should be increased.