王照清,余雨蔓,代汶均,景鹏飞

• 1:北京师范大学物理学系

摘要(Abstract)：

近些年来，公路自行车赛引起众多关注，如何使运动员在比赛中获得更好的成绩成为众多研究的目标。为给出自行车运动员在比赛过程中功率分配方案，本文首先建立了公路自行车赛车手的功率曲线模型，然后分析对比了不同赛车选手的特点；再通过分析赛车手的在不同性质路段的动力学模型，获得运动员经过具体赛段的时间和速度随功率的变化。我们运用蒙特卡罗方法得到了不同赛车手在不同路段最佳的功率和速度分配曲线，并将模型应用于2021公路自行车UCI世锦赛，得到不同类型运动员具体功率和速度曲线在路程中的分布。通过这一模型我们可以得知，赛车手在赛程中尽力保持匀速状态并在擅长的路段进行一定的加速可以得到最佳的比赛结果。最后我们分析了该方法得到的结果的稳定性。

关键词(KeyWords)： 蒙特卡罗方法;自行车公路赛;自行车运动员功率模型

Abstract:

Keywords:

基金项目(Foundation): 北京科技大学2021年度本科教育教学改革面上项目(JG2021M54);北京科技大学2021年度本科教育教学改革重点项目(JG2021Z05)资助

作者(Author): 王照清,余雨蔓,代汶均,景鹏飞

参考文献(References)：

• [1] LOUCKS A B,KIENS B,WRIGHT H H.Energy availability in athletes[J].Journal of Sports Sciences,2011,29(sup1):S7-S15.
• [2] BARRETO G H,OLIVEIRA L,SAITO T,et al.The Road to the UCI:Profiling a professional Brazilian female road cycling team[J].2020.http://dx.doi.org/10.31236/osf.io/wnpjk
• [3] OLDS T.The optimal altitude for cycling performance:a mathematical model[J].Excel,1992(8):155-155.
• [4] POWERS SK,WILLIAMS J.Exercise-induced hypoxaemia in highly trained athletes[J].Sports Med.1987,4:46-53.
• [5] KOLBE T,DENNIS S C,SELLEY E,et al.The relationship between critical power and running performance[J].Journal of Sports Sciences,1995,13(3):265-269.
• [6] PERONNET F,THIBAULT G.Mathematical analysis of running performance and world running records[J].Journal of Applied Physiology,1989,67(1):453-465.
• [7] FOSTER D C,SCHRAGER M,SNYDER A C,et al.Pacing strategy and Athletic performance[J].Sports Medicine,1994,17(2):77.
• [8] van INGEN SCHENAU G J,De KONING J J,De GROOT G.The distribution of anaerobic energy in 1000 and 4000 metre cycling bouts[J].International Journal of Sports Medicine,1992,13(6):447-451.
• [9] MARINO F E.Anticipatory regulation and avoidance of catastrophe during exercise-induced hyperthermia[J].Comparative Biochemistry and Physiology Part B Biochemistry and Molecular Biology,2004,139(4):561-569.
• [10] FOSTER C,SNYDER A C,THOMPSON N N,et al.Effect of pacing strategy on cycle time trial performance[J].Medicine and Science in Sports and Exercise,1993,25(3):383-388.
• [11] OLDS T.Modelling Human locomotion applications to cycling[J].Sports Med.2001,31(7):497-509.
• [12] ZIGNOLI A.Influence of corners and road conditions on cycling individual time trial performance and ‘optimal’ pacing strategy:A simulation study[J].Proceedings of the Institution of Mechanical Engineers,Part P:Journal of Sports Engineering and Technology,2021,235(3):227-236.
• [13] MORTON R H.A three component model of human bioenergetics[J].Math Biology.1986,24(4):451-466.
• [14] LEO P,SPRAGG J,PODLOGAR T,et al.Power profiling and the power-duration relationship in cycling:a narrative review[J].European Journal of Applied Physiology,2022,122(2):301-316.
• [15] PETHICK J,WINTER S L,BURNLEY M.Physiological evidence that the critical torque is a phase transition,not a threshold[J].Medicine & Science in Sports & Exercise,2020,52.
• [16] VOGT S,SCHUMACHER Y,ROECKER K,et al.Power Output during the Tour de France[J].Sports Med.2007,28(9):756-761.
• [17] 蔡睿，陈亮，何申杰，等.公路自行车的动力学分析及仿真研究[J].中国体育科技，2014,50(1):4.CAI R,CHEN L,HE S J,et al.Analysis on the dynamics and simulation of road cycling[J].China Sport Science and Technology,2014,50(1):125-128.
• [18] KIM K U,SHIN B S.Modeling motion resistance of rigid wheels[J].Journal of Terramechanics,1985,22(4):225-236.
• [19] MUELLER A.Modern robotics:Mechanics,planning,and control[bookshelf][J].IEEE Control Systems Magazine,2019,39(6):100-102.
• [20] XU Y,DAI Y,ZHANG H.Strategy arrangement of road cycling individual time trial based on topology optimization algorithm[C]//Proceedings of the 6th International Conference on Medical and Health Informatics.2022:242-246.
• [21] HAAKONSSEN E C,BARRAS M,BURKE L M,et al.Body composition in female road and track endurance cyclists:Normative values and typical changes in female road and track endurance cyclists[J].European Journal of Sport Science,2015:1-9.
• [22] HOPKINS W G,ANDERSON M E,LEE H,et al.The Lmi:A new practical index of lean mass for monitoring athletes[J].Medicine & Science in Sports & Exercise,2002,34(5):S237.
• [23] ATKINSON G,PEACOCK O,PASSFIELD L.Variable versus constant power strategies during cycling time-trials:Prediction of time savings using an up-to-date mathematical model[J].Journal of Sports Sciences,2007,25(9):1001-1009.
• [24] James C.Martin,et al.Validation of a mathematical model for road cycling power[J].Journal of Applied Biomechanics,1998,14(3).