The maximum running speed of legged animals is one evident factor for evolutionary selection---for predators and prey. Therefore, it has been studied across the entire size range of animals, from the smallest mites to the largest elephants, and even beyond to extinct dinosaurs. A recent analysis of the relation between animal mass (size) and maximum running speed showed that there seems to be an optimal range of body masses in which the highest terrestrial running speeds occur. However, the conclusion drawn from that analysis---namely, that maximum speed is limited by the fatigue of white muscle fibres in the acceleration of the body mass to some theoretically possible maximum speed---was based on coarse reasoning on metabolic grounds, which neglected important biomechanical factors and basic muscle-metabolic parameters. Here, we propose a generic biomechanical model to investigate the allometry of the maximum speed of legged running. The model incorporates biomechanically important concepts: the ground reaction force being counteracted by air drag, the leg with its gearing of both a muscle into a leg length change and the muscle into the ground reaction force, as well as the maximum muscle contraction velocity, which includes muscle-tendon dynamics, and the muscle inertia---with all of them scaling with body mass. Put together, these concepts' characteristics and their interactions provide a mechanistic explanation for the allometry of maximum legged running speed. This accompanies the offering of an explanation for the empirically found, overall maximum in speed: In animals bigger than a cheetah or pronghorn, the time that any leg-extending muscle needs to settle, starting from being isometric at about midstance, at the concentric contraction speed required for running at highest speeds becomes too long to be attainable within the time period of a leg moving from midstance to lift-off. Based on our biomechanical model we, thus, suggest considering the overall speed maximum to indicate muscle inertia being functionally significant in animal locomotion. Furthermore, the model renders possible insights into biological design principles such as differences in the leg concept between cats and spiders, and the relevance of multi-leg (mammals: four, insects: six, spiders: eight) body designs and emerging gaits. Moreover, we expose a completely new consideration regarding the muscles' metabolic energy consumption, both during acceleration to maximum speed and in steady-state locomotion.

中文翻译：

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大自然的方程式跑步法则：后期姿势中的肌肉力学是解释最大跑步速度的关键

有腿动物的最高奔跑速度是进行进化选择的一个明显因素-捕食者和猎物。因此，已经对动物的整个大小范围进行了研究，从最小的螨虫到最大的大象，甚至到灭绝的恐龙。最近对动物体重（大小）与最大奔跑速度之间关系的分析表明，似乎存在着最佳的体重范围，其中出现了最高的陆地奔跑速度。但是，从该分析得出的结论-即最大速度受白色肌肉纤维在体重加速过程​​中的疲劳限制为理论上可能的最大速度-是基于新陈代谢的粗略推理，忽略了重要的生物力学因素和基本的肌肉代谢参数。这里，我们提出了一个通用的生物力学模型来研究有腿跑步最大速度的变幅。该模型包含了生物力学上重要的概念：空气阻力抵消了地面反作用力，腿部的肌肉与腿的长度变化以及肌肉与地面的反作用力的传动以及最大的肌肉收缩速度包括肌腱动态和肌惯性-所有这些都随体重而变化。综合起来，这些概念的特征及其相互作用为最大腿部跑步速度的异速运动提供了机械学解释。这为根据经验发现的整体最大速度提供了一个解释：在大于猎豹或叉角羚的动物中，任何伸展腿部的肌肉都需要沉降的时间，从大约等距的等距线开始，以最高速度行驶所需的同心收缩速度变得太长，以至于腿部从等距运动到抬起的时间段内都无法达到。因此，基于我们的生物力学模型，我们建议考虑整体最大速度，以表明肌肉惯性在动物运动中具有重要的功能。此外，该模型为生物设计原理提供了可能的见解，例如猫和蜘蛛在腿部概念上的差异，以及多腿（哺乳动物：四只，昆虫：六只，蜘蛛：八只）身体设计和新兴步态的相关性。此外，我们在加速到最大速度和稳态运动过程中都公开了关于肌肉代谢能量消耗的全新考虑。