Numerical optimization of pacing strategy in cross-country skiing

When studying events involving locomotive exercise, such as cross-country skiing, one generally assumes that pacing strategies (i.e. power distributions) have a significant impact on performance. In order to better understand the importance of pacing strategies, a program is developed for numerical simulation and optimization of the pacing strategy in cross-country ski racing. This program computes the optimal pacing strategy for an arbitrary athlete skiing on a delineated course. The locomotion of the skier is described by introducing the equations of motion for cross-country skiing. A transformation of the motion equations is carried out in order to improve the simulation. Furthermore, a nonlinear optimization routine is connected to the simulation program. Simulation and optimization are performed on a fictional male skier. Results show that it is possible to attain an optimal pacing strategy by simulating cross-country skiing while connecting nonlinear optimization routines to the simulation. It is also shown that an optimal pacing strategy is characterized by minor variations in speed. In our opinion, this kind of optimization could serve as essential preparations before important competitions.