Storage and utilization of elastic strain energy during jumping

Based upon the optimal control solutions to a maximum-height countermovement jump (CMJ) and a maximum-height squat jump (SJ), this paper provides a quantitative description of how tendons and the elastic elements of muscle store and deliver energy during vertical jumping. After confirming the ability of the model to replicate the major features of each jump (i.e. muscle activation patterns, body-segmental motions, ground reaction forces, jump height, and total ground contact time), the time histories of the forces and shortening velocities of all the musculotendon actuators in the model were used to calculate the work done on the skeleton by tendons as well as the series-elastic elements, the parallel-elastic elements, and the contractile elements of muscle. We found that all the elastic tissues delivered nearly the same amount of energy to the skeleton during a CMJ and an SJ. The reason is twofold: first, nearly as much elastic strain energy was stored during the SJ as the CMJ; second, more stored elastic strain energy was lost as heat during the CMJ. There was also a difference in the way energy was stored during each jump. During the CMJ, strain energy stored in the elastic tissues came primarily from the gravitational potential energy of the skeleton as the more proximal extensor muscles were stretched during the downward phase of the jump. During the SJ, on the other hand, energy stored in the elastic tissues came primarily from the contractile elements as they did work to stretch the tendons and the series-elastic elements of the muscles. Increasing tendon compliance in the model led to an increase in elastic energy storage and utilization, but it also decreased the amount of energy delivered by the contractile elements to the skeleton. Jump height therefore remained almost the same for both jumps. These results suggest that elastic energy storage and utilization enhance jumping efficiency much more than overall jumping performance.