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.

在本文中，研究了人类在平坦地形上行驶的动力学以及所需的机械功率输出（取决于各种参数）。由于所需的机械功率输出与代谢功率之间的关系，因此知道其具有相关性。例如，更好地了解所需的机械功率输出对重量，行驶和风速，阶跃频率，地面接触时间等的依赖性对于评估，分析和优化行驶性能非常有价值。因此，设计了基于很少假设的数学模型。提出的模型的目的是将跑步速度和所需的机械功率输出与跑步者的体重，身高，步速，地面接触时间和风速的代数函数联系起来。为了更好地了解运动的机械能成本，以及它在多大程度上取决于哪些参数，这一点很重要。第一个主要的能量耗散机制是由于垂直振荡引起的，即，在每个步骤中，一些势能差都转化为热量。第二种机制是由于在姿态的第一部分中的前部地面反作用力，第三种是由于气动阻力。在恒定的行驶速度和正弦垂直地面反作用力曲线的近似值下，人们获得了质心轨迹中心和所需机械功率输出的封闭代数表达式。模型预测和报告的性能数据的比较表明，大约有四分之一的地面冲击能量在地面接触的第一部分存储，然后在剩余的姿态阶段释放。此外，可以从该模型得出结论，以较高的步速和较高的质心运行时，所需的机械动力输出较少。不直观的结果是较短的地面接触时间有利于快速运行，而相反的情况则适用于慢速运行。与其他模型相比，该设计模型的一个重要优点是，它导致了质量轨迹中心和机械功率输出的闭合代数表达式，这些表达式是可测量量的函数，即步速，地面接触时间，行驶速度，跑步者的质量，质心高度，在给定速度，风速和心率下的空气阻力。此外，该模型依赖于很少的假设，这些假设已经过验证，唯一的调整参数是恢复的弹性能的比率。