The dynamic limits of hop height: Biological actuator capabilities and mechanical requirements of task produce incongruity between one- and two-legged performance

Abstract

The maximum hop height attainable for a given hop frequency falls well below the theoretical limit dictated by gravity, h =  g/8 f2. However, maximum hop height is proportional to 1/ f2, suggesting that ground reaction force and, hence, force production capabilities of the leg muscles limit human hopping performance. Curiously, during one-legged hopping, subjects were able to produce substantially more than 50% the ground reaction force produced during two-legged maximum height hopping—66% on average and as much as 90% the total force produced during two-legged hopping. This implies that two legs together should be able to produce an average of 1.32 times and as much as 1.8 times the force actually measured during two-legged maximum height hopping. Why were our subjects unable to access this extra force capacity when hopping on two legs? Here, we show that this apparent bilateral deficit and other features of maximum height hopping can be explained by the interaction of the mechanical requirements of hopping with the force–velocity and force–length relationships that dictate the force production capacity of the leg muscles. Identifying the factors that limit performance in hopping provides an opportunity to understand how functional limits are determined in more complex activities such as running and jumping.