Jenny David F, Jenny Patrick
Department of Mechanical and Process Engineering, Swiss Federal Institute of Technology, Switzerland.
Department of Mechanical and Process Engineering, Swiss Federal Institute of Technology, Switzerland.
J Biomech. 2020 Sep 18;110:109948. doi: 10.1016/j.jbiomech.2020.109948. Epub 2020 Jul 19.
In this paper the dynamics of human running on flat terrain and the required mechanical power output with its dependency on various parameters is investigated. Knowing the required mechanical power output is of relevance due to its relationship with the metabolic power. For example, a better understanding of the dependencies of required mechanical power output on weight, running and wind speed, step frequency, ground contact time etc. is very valuable for the assessment, analysis and optimization of running performance. Therefore, a mathematical model based on very few assumptions is devised. The purpose of the proposed model is to relate running speed and required mechanical power output as an algebraic function of the runner's mass, height, step rate, ground contact time and wind speed. This is relevant in order to better understand the mechanical energy cost of locomotion, and how much it depends on which parameters. The first of the main energy dissipation mechanisms is due to vertical oscillation, i.e., during each step some of the potential energy difference gets transformed into heat. The second mechanism is due to the anterior ground reaction force during the first part of stance and the third is due to aerodynamic drag. With the approximations of constant running speed and a sinusoidal vertical ground reaction force profile one obtains closed algebraic expressions for the center of mass trajectory and the required mechanical power output. Comparisons of model predictions and reported performance data suggest that approximately a quarter of the ground impact energy is stored during the first part of ground contact and then released during the remaining stance phase. Further, one can conclude from the model that less mechanical power output is required when running with higher step rates and a higher center of mass. Non intuitive is the result that a shorter ground contact time is beneficial for fast runs, while the opposite holds for slow runs. An important advantage of the devised model compared to others is that it leads to closed algebraic expressions for the center of mass trajectory and mechanical power output, which are functions of measurable quantities, i.e., of step rate, ground contact time, running speed, runner's mass, center of mass height, aerodynamic drag at some given speed, wind speed and heart rate. Moreover, the model relies on very few assumptions, which have been verified, and the only tuning parameter is the ratio of recovered elastic energy.
本文研究了人类在平坦地形上跑步的动力学以及所需的机械功率输出及其对各种参数的依赖性。了解所需的机械功率输出具有相关性，因为它与代谢功率有关。例如，更好地理解所需机械功率输出对体重、跑步和风速、步频、地面接触时间等的依赖性，对于跑步性能的评估、分析和优化非常有价值。因此，设计了一个基于极少假设的数学模型。所提出模型的目的是将跑步速度和所需机械功率输出表示为跑步者质量、身高、步频、地面接触时间和风速的代数函数。这对于更好地理解运动的机械能成本以及它对哪些参数的依赖程度是相关的。主要的能量耗散机制之一是由于垂直振荡，即在每一步中，一些势能差会转化为热量。第二种机制是由于站立阶段第一部分的前向地面反作用力，第三种是由于空气阻力。通过假设恒定的跑步速度和正弦垂直地面反作用力分布，可得到质心轨迹和所需机械功率输出的封闭代数表达式。模型预测与报告的性能数据的比较表明，大约四分之一的地面冲击能量在地面接触的第一部分被储存，然后在剩余的站立阶段释放。此外，从模型中可以得出结论，以更高的步频和更高的质心跑步时所需的机械功率输出更低。一个非直观的结果是，较短的地面接触时间对快速跑步有益，而对于慢速跑步则相反。与其他模型相比，所设计模型的一个重要优点是它能得出质心轨迹和机械功率输出的封闭代数表达式，这些表达式是可测量量的函数，即可测量步频、地面接触时间、跑步速度、跑步者质量、质心高度、给定速度下的空气阻力、风速和心率。此外，该模型依赖极少已得到验证的假设，唯一的调整参数是恢复弹性能量的比率。
