How to Stay Ahead of the Pack: Optimal Road Cycling Strategies for two Cooperating Riders

Within road-cycling, the optimization of performance using mathematical models has primarily been performed in the individual time trial. Nevertheless, most races are 'mass-start' events in which many riders compete at the same time. In some special situations, e.g. breakaways from the peloton, the riders are forced to team up. To simulate those cooperative rides of two athletes, an extension of models and optimization approaches for individual time trials is presented. A slipstream model based on experimental data is provided to simulate the physical interaction between the two riders. In order to simulate real world behavior, a penalty for the difference in the exertion levels of the two riders is introduced. This means, that even though both riders aim to be as fast as possible as a group, neither of them should have an advantage over the other because of significantly different levels of fatigue during the ride. In our simulations, the advantage of cooperation of two equally trained athletes adds up to a time gain of about 10% compared to an individual ride.