Applications of Mathematical Models of Road Cycling

This contribution discusses several use cases of mathematical models for road cycling. A mechanical model for the pedaling forces is the basis for an accurate indoor ergometer simulation of road cycling on real-world tracks. Together with a simple physiological model for the exertion of the athlete as a function of his/her accumulated power output, an optimal riding strategy for time trials on mountain ascents is computed. A combination of the two models leads to a mathematical optimization problem that can be solved numerically by discretization. The physical model depends sensitively on an accurate estimation of the road slope on the course. For this purpose, we also present a new method that combines model-based slope estimations with noisy measurements from multiple GPS signals of differing quality. Altogether, we provide a means to simulate road cycling on real-world tracks, to analyze cyclist performance, to identify and quantify potential performance improvement, as well as to instruct the athlete exactly where and how to change his/her pacing strategy to achieve these gains.