Abstract
The fastest land animals are of intermediate size. Cheetah, antelope, greyhounds and racehorses have been measured running much faster than reported for elephants or elephant shrews. Can this be attributed to scaling of physical demands and explicit physiological constraints to supply? Here, we describe the scaling of mechanical work demand each stride, and the mechanical power demand each stance. Unlike muscle stress, strain and strain rate, these mechanical demands cannot be circumvented by changing the muscle gearing with minor adaptations in bone geometry or trivial adjustments to limb posture. Constraints to the capacity of muscle to supply work and power impose fundamental limitations to maximum speed. Given an upper limit to muscle work capacity each contraction, maximum speeds in big animals are constrained by the mechanical work demand each step. With an upper limit to instantaneous muscle power production, maximal speeds in small animals are limited by the high power demands during brief stance periods. The high maximum speed of the cheetah may therefore be attributed as much to its size as to its other anatomical and physiological adaptations.
Highlights
Greyhounds, racehorses and especially cheetahs are, in absolute terms, fast for terrestrial animals
Given the uncertainty surrounding many of the empirical speed measurements [30,31], and the sweeping nature of the assumptions to the work and power demand and supply models, it would be inappropriate at this stage to put too much emphasis on the detail of the model fit
Small animals would only achieve absolutely high running speeds with disproportionately low stance durations and are prevented from very high speeds owing to the power demands during stance
Summary
Greyhounds, racehorses and especially cheetahs are, in absolute terms, fast for terrestrial animals. We treat the internal workings of the limb as a suitably tuned black box and view the following properties to be ‘uncheatable’ with gearing, and mechanistically revealing: per muscle mass, we assume (a) a constrained maximum work per contraction, (b) a constrained power during the contraction, and consider the implications if there is (c) a limiting physiological capacity to power muscle activation These assumptions are clearly incorrect in detail: the muscles of small, fast animals may be relatively fast and powerful. If the mechanical demand can only be supplied when the leg is loaded, with the foot on the ground, the stance power demand Pstance,D depends on both the mechanical work demand ((3.1), the product of (2.2) and (2.4)) and the stance duration Tstance (4.1) In this case, assuming a constraining, constant maximal muscle power supply available, matching the mechanical power demand during stance to the muscle power supply provides a second constraint relationship for maximal running speed Vlim,P: Pstance,D
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