Modeling, Simulation, and Optimization of Pacing Strategies for Road Cycling on Realistic Tracks

In this study, we develop methods to model and simulate road cycling on real-world courses, to analyze the performance of individual athletes and to identify and quantify potential performance improvement. The target is to instruct the athlete where and how to optimize his pacing strategy during a time trial. We review the state-of-the-art mechanical model for road cycling power that defines the relationship between pedaling power and cycling speed. It accounts for the power demand to overcome the resistance due to inertia, rolling friction, road gradient, friction in bearings and aerial drag. For several model parameters the measurement proves to be difficult. Thus, we estimate four compound parameters from a fit of the dynamic model to varying real-world power and speed measurements. The approach guarantees precise estimation even on courses with moderately varying slope as long as that slope is known with sufficient precision. An experimental evaluation shows that our calibration improves the model speed estimation significantly both on the calibration course and on other courses with the same type of road surface. A sensitivity analysis allows to compute the change in speed for small parameter perturbations proving in detail that the influences of the coefficients for aerial drag and rolling friction dominate. We designed a simulator based on a Cyclus2 ergometer. The simulation includes real height profiles, virtual gears, a video playback that was synchronized with the cyclist’s current virtual position on the course and online visualization of course and performance parameters. The ergometer brake is controlled so that it imitates the resistance predicted by the outdoor road cycling model. The software can partly compensate the physical limitations of the eddy current brake. The road cycling model and thus the simulator resistance depend sensitively on an accurate estimation of the slope of the road. Commercial gps enabled bicycle computers do not provide a sufficient precision since the differentiation of the height data in order to compute the slope amplifies high frequency noise. A differential gps device provides height data of sufficient quality but only in case the satellite signals are not hidden by obstacles such as houses, trees, or mountains, which is often a serious limiting factor. For this purpose, we also present a method that combines model-based slope estimations with noisy measurements from multiple GPS signals of different quality.