A new dimensionless number highlighted from mechanical energy exchange during running

Abstract

This study aimed to highlight a new dimensionless number from mechanical energy transfer occurring at the centre of gravity (Cg) during running. We built two different-sized spring–mass models (SMM #1 and SMM #2). SMM #1 was built from the previously published data, and SMM #2 was built to be dynamically similar to SMM #1. The potential gravitational energy ( E P), kinetic energy ( E K), and potential elastic energy ( E E) were taken into account to test our hypothesis. For both SMM #1 and SMM #2, N Mo–Dela=( E P+ E K)/ E E reached the same mean value and was constant (4.1±0.7) between 30% and 70% of contact time. Values of N Mo–Dela obtained out of this time interval were due to the absence of E E at initial and final times of the simulation. This phenomenon does not occur during in vivo running because a leg muscle's pre-activation enables potential elastic energy storage prior to ground contact. Our findings also revealed that two different-sized spring–mass models bouncing with equal N Mo–Dela values moved in a dynamically similar fashion. N Mo–Dela, which can be expressed by the combination of Strouhal and Froude numbers, could be of great interest in order to study animal and human locomotion under Earth's gravity or to induce dynamic similarity between different-sized individuals during bouncing gaits.