Abstract
Jump height, defined as vertical displacement in the airborne phase, depends on vertical takeoff velocity. For centuries, researchers have speculated on how jump height is affected by body size and many have adhered to what has come to be known as Borelli’s law, which states that jump height does not depend on body size per se. The underlying assumption is that the amount of work produced per kg body mass during the push-off is independent of size. However, if a big body is isometrically downscaled to a small body, the latter requires higher joint angular velocities to achieve a given takeoff velocity and work production will be more impaired by the force-velocity relationship of muscle. In the present study, the effects of pure isometric scaling on vertical jumping performance were investigated using a biologically realistic model of the human musculoskeletal system. The input of the model, muscle stimulation over time, was optimized using jump height as criterion. It was found that when the human model was miniaturized to the size of a mouse lemur, with a mass of about one-thousandth that of a human, jump height dropped from 40 cm to only 6 cm, mainly because of the force-velocity relationship. In reality, mouse lemurs achieve jump heights of about 33 cm. By implication, the unfavourable effects of the small body size of mouse lemurs on jumping performance must be counteracted by favourable effects of morphological and physiological adaptations. The same holds true for other small jumping animals. The simulations for the first time expose and explain the sheer magnitude of the isolated effects of isometric downscaling on jumping performance, to be counteracted by morphological and physiological adaptations.
Highlights
Jumping is important for survival of many animals because it helps them to catch preys or escape from predators [1]
Galago senegalensis seems to be hors categorie, because it outperforms other mammals in both absolute and relative terms, but how does Microcebus murinus perform compared to humans? For centuries, the consensus in the literature has been that comparisons should be made in terms of absolute jump height, so Microcebus is not a good jumper compared to humans
Forces of SEE and PEE quadratically increased with SEE elongation only, while force of contractile elements (CE) (FCE) depended on length of CE, velocity of CE and active state [20]
Summary
Jumping is important for survival of many animals because it helps them to catch preys or escape from predators [1]. Jump height (h), defined as vertical displacement of the centre of mass (CM) in the airborne phase, has been found to vary substantially among differently sized primate species. H is about 0.33 m in a 100 g grey mouse lemur (Microcebus murinus) [2], up to about 2 m in a 300 g bushbaby (Galago senegalensis) [3], up to 0.7 m in a 34 kg bonobo (Pan paniscus) [4] and typically about 0.4 m in a 75 kg human [5]. Galago senegalensis seems to be hors categorie, because it outperforms other mammals in both absolute and relative terms, but how does Microcebus murinus perform compared to humans? Is absolute jump height a fair measure to compare jumping performance of differently sized primate species?
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