跟上探索自行车比赛骑手的步伐

Keeping Up with the Exploration of Cycling Race Riders

摘要: 本文旨在为攀登者、短跑运动员、拳击运动员、轮滑运动员、计时赛专家这五类不同的自行车计时赛参赛对象设计最佳的比赛方案，使他们在比赛过程中的能量分配尽可能地合理，并且冲线的时间达到最短。为了实用起见，我们还要将得到的方案应用到三种不同的比赛实况中去，分别是2021年东京奥运会计时赛、UCI世界锦标赛计时赛以及一条我们自行设计的计时赛路线。此外，为了更加贴合实际，我们需要在模型中添加一些能够反映不同干扰因素的参数，以此优化我们的模型。而在本文中，我们利用逐步回归法、插值法，成功地帮助参赛骑手选择了比赛最佳策略。首先，我们对骑速、机能指标与能耗等指标进行了相关性分析，通过逐步回归来建立了能耗方程，结合能耗方程与相关资料，我们定义出了五种类型骑手的功率配置。其次，我们对题干中所提到的三种计时赛图进行了取点，选择构建了车手的骑行速度关于时间的函数。针对功率与位置关系的刻画，我们综合考虑了力、速度、功率、时间、位置的关系，建立了微分方程模型进行求解。我们发现随着车手的路程增加，其功率先呈现迅速增长的趋势，但增长速率越来越缓，再以保持不变的功率行驶。我们通过计时赛程在减速时能减到适合转弯的速度的确保以及第三阶段计算出来的的位移小于赛程图中的位移的验证，检验出模型是适合三种计时赛程的。接下来，考虑到实际问题中还有风力的干扰，且车队中处于前排的车手会受到阻力的影响，我们在问题二微分方程模型建立的基础上，增加风力和速度的比例系数，得到新的微分方程模型。总的来说，在车手们互相轮换的机制下，风力对车队速度没有造成显著性影响。然后，考虑到整条赛道转弯处的夹角是不同的，并且骑手们对分裂时机比赛策略的选择以及对突发情况的临时处理的策略都可能会导致动力目标的错过。综合考虑骑手p-t功率分布，我们的结论是：所求解出的骑手p-t功率分布与目标功率分布是存在一定差异的。最后，考虑到团体计时赛的实际比赛情况，第四名冲线骑手的速度、功率都是适中的。我们对上述已经得到的微分方程模型进行了扩展，确定出了能量与时间的关系。根据绘制的能量示意图，我们得出了结论为骑手在第二阶段匀速的时间最长，并且能量分配最合理。综合来看，该模型具有较强的灵活性和推广性。我们也可以通过提高拟合精度和添加新的影响因素来改进模型。

Abstract: We aim to design optimal race scenarios for five different categories of cycling time trial partici-pants: climbers, sprinters, boxers, rollerbladers and time trial specialists, giving them the best pos-sible energy distribution during the race and the shortest possible time to the line. For purposes of practice, we also apply the solutions to three different race scenarios: the Tokyo 2021 Olympic Games time trial, the UCI World Championship time trial and a time trial course of our own design. In addition, in order to better fit the reality, we need to add some parameters that reflect different disturbing factors in the model to make the model optimal. In this paper, we use stepwise regres-sion method and interpolation method to successfully help the riders to choose the best strategy for the race. Firstly, we analyzed the correlation between riding speed, functional index and energy consumption, established the energy consumption equation by stepwise regression, and combined the energy consumption equation with relevant information, defining the power configuration for five types of riders. Secondly, we made an interpolation of the three time trial graphs mentioned in the question and chose to construct the rider’s riding speed as a function of time. For the portrayal of the power-position relationship, we integrated the relationship between force, speed, power, time and position, building a differential equation model to solve it. We found that as the rider’s distance increases, its power first shows a rapid growth trend, but the growth rate becomes slower and slower, and then travels at constant power. We tested that the model was suitable for the three-time trials by ensuring that the time trial can be reduced to a speed suitable for turning when decelerating and by verifying that the displacement calculated in the third stage is smaller than the displacement in the race diagram. Next, considering that there is wind interference in the actual problem and the riders in the front row of the team will be affected by the drag, the new differential equation model is obtained by increasing the scale coefficients of wind and speed on the basis of the differential equation model of problem 2. In general, under the mechanism of riders rotating with each other, wind has no significant effect on team speed. Taking into account that the pinch angles at the turns are different throughout the course and that the riders’ choices of split timing race strategies and strategies for ad hoc handling of unexpected situations may lead to missed power targets. Considering the rider p-t power distribution together, we concluded that the solved rider p-t power distribution was somewhat different from the target power distribution. In conclusion, considering the actual race situation of the team time trial, the speed and power of the fourth rider crossing the line are moderate. We extended the differential equation model already obtained above to determine the relationship between energy and time. Based on the energy schematic, it was concluded that the rider had the longest time at constant speed in the second stage and the most reasonable energy distribution. Taken together, the model is highly flexible and generalizable. We can also improve the model by improving the fitting accuracy and adding new influencing fac-tors.