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- Title
How to Ride a Cycling Time Trial.
- Authors
Yubin Gao; Jiaqi Liao; Lingxin Wang
- Abstract
A proper mathematical model can help cyclists plan their races better and more efficiently. And that is exactly what we do in this paper. We begin with the analysis of the energy supply system of the cyclists. According to basic biological knowledge, we divide the contribution of overall output power into three different energy supply systems: the ATP-CP system, the glycolysis system, and the aerobic system. We base our model on ordinary differential equations to describe the change of content of various substances in the human body during cycling. Based on our energy supply model, we define the power profiles of time trial specialists and of sprinters, with different genders considered. The comparison between our theoretical power curves and real-world power curves confirms the reliability of the energy model that we developed. To evaluate the power needed to maintain a given speed, we analyze the motion of the bicycle-cyclist system. We include in our model different drag resistances, hilly terrain, and sharp turns. We obtain an equation of motion for the relation between the acceleration and the propulsive force. We discuss optimal strategies on various terrains. The optimal strategy in most cases is to maintain a fixed speed, a threshold speed, all through the race. The exception is on a hilly course or a sharply curved road: Slowing down is generally needed. Accordingly, we propose a combination of optimal strategies on each specific terrain. To test our model in real-world conditions, we reconstruct several championship courses from their official roadmaps. Then we simulate the actual performance of cyclists of four different types on three courses. The simulation shows that the optimal time on the 2021 UCI Championship in Belgium is 53.02 minutes, very close to the champion's 57.78 minutes. We evaluate the sensitivity of deviations from our strategy: A 30% deviation adds only 3% time. For sensitivity to weather, we focus on direction and strength of wind; we find that wind greatly affects the strategy and the expected performance. Finally, we modify our model to cover team time trials (TTT), where drafting reduces overall aerodynamic resistance. We propose that cyclists rotate, taking pulls before and in the sprint stage. Such a strategy can improve speed by 14% compared to an individual cycling alone.
- Subjects
BELGIUM; TIME trials; EQUATIONS of motion; ORDINARY differential equations; POWER resources; CYCLING competitions; CYCLING
- Publication
UMAP Journal, 2022, Vol 43, Issue 4, p367
- ISSN
0197-3622
- Publication type
Article