Scaling and jumping: Gravity loses grip on small jumpers - Scholz, M. N.; Bobbert, M. F.; Knoek van Soest, A. J. (Journal of Theoretical Biology, 2006)
There are several ways to quantify jumping performance, a common definition being the height gained by the body's centre of mass (CM) in the airborne phase. Under this definition, jump height is determined by take-off velocity. According to the existing literature on jumping and scaling, take-off velocity, and hence jumping performance is independent of size because the energy that differently sized geometrically scaled jumpers can generate with their muscles is proportional to their mass. In this article it is shown, based on a simple energy balance, that it is incorrect to presume that jump height does not depend on size. Contrary to common belief, size as such has does have an effect on take-off velocity, putting small jumpers at a mechanical advantage, as is shown analytically. To quantify the effect of size on take-off velocity, a generic jumper model was scaled geometrically and evaluated numerically. While a 70-kg jumper took off at 2.65 m/s and raised its CM by 0.36 m after take-off, a perfectly geometrically similar jumper of 0.7 g reached a take-off velocity of 3.46 m/s and raised its CM by 0.61 m. The reason for the better performance of small jumpers is their higher efficacy in transforming the energy generated by the actuators into energy due to vertical velocity of the CM. Considering the ecological and evolutionary relevance of different definitions of jump height, size-dependent efficacy might explain why habitual jumping is especially prominent among small animals such as insects.