基于数学建模的赛道位置和能量关系探究

A Study of Track Position in Relation to Power Based on Mathematical Modeling

应用能耗方程将能量曲线定义为PO-Time曲线,选出两名不同类型的自行车运动员Time Teial Specialist和Puncheur,并给出他们不同性别的能量曲线。将赛道划分为5个不同难度的类型并给出不同类型所需要功率输出PO的范围,用Shapiro-Wilk和逐步回归法对数据进行分析,得知PO和不同类型赛道存在相关性P<0.05。通过设计全长45.75公里的多弯道高难度爬坡赛道,将模型应用于2021年东京奥运会计时赛、2021UCI世界锦标赛计时赛和自设赛道中,得出不同性别运动员在比赛进行中不同位置上的能量特征。考虑到风向和风力强度对运动员输出PO的影响、各种天气因素的改变导致运动员可能受到的影响间接影响功率输出PO,故引入环境影响因子来分析运动员受天气和环境影响的敏感程度。

In this paper,a power consumption formula is used to define the power curve as PO-Time curve.Two different types of cyclists,Time Teial Specialist and Puncheur,are selected and their power curves of both genders are given.The course is divided into 5 types of levels of difficulty.The range of the power output(PO)required by different types is given in Table 4.The data are analyzed by using a Shapiro-Wilk test and stepwise regression method.The correlation between PO and different types of tracks is P<0.05.A 45.75km multi-turn uphill track with high difficulty is designed in this part.The model is applied to the time trial event at the Tokyo 2020 Olympic Games,the time trial event of 2021 UCI Track Cycling World Championships and the independently designed track,and the power characteristics of the athletes of different genders at different positions as the race proceeds are obtained.Taking into account the influence of wind directions and wind strengths on athletes'PO,and the potential influence of changes of various weather factors on athletes,the PO is indirectly affected and therefore,environmental influencing factors are introduced to study the degree of sensitivity of weather and environmental influence on athletes.