Hopping is more than just a child's game for John Bertram. When Bertram sees a person bouncing around on one or two legs, he sees part of a running step. ‘Hopping and running are bouncing gaits where kinetic and potential energy are in sync and involve the same bending and straightening motion of the leg’, says Bertram. As hopping or bouncing on two feet offers a mechanical analogy for running, Bertram and his colleague Anne Gutmann decided to measure the metabolic cost of bouncing – as if rope skipping on two feet – and then compare the values with predictions from calculations simulating different aspects of how the leg functions during a bounce to learn more about the energetics of the movement.
In order to collect the colossal quantity of measurements – which added up to a total of 3–4 h of bouncing on a force plate while measuring the oxygen consumption for each individual – Gutmann recruited six fit young athletes who could bounce for extended periods without developing the burning muscle sensation associated with the switch to anaerobic respiration. ‘If they exceeded their aerobic threshold, the oxygen consumption would not be a valid measure of total energy use’, explains Bertram. In addition, Gutmann required the athletes to bounce in time with a metronome at different rates while adjusting the height of each two-legged hop in response to computer feedback, which Bertram admits was ‘a bit like training people to rub their belly and pat their head at the same time while doing a workout’. However, after months of dedicated exertion from the athletes, Gutmann eventually had over 250 force and oxygen consumption measurements from bounces ranging in height from 7 to 25 cm at speeds of 1.5 to 3.7 bounces s−1 from which to calculate metabolic costs per time over the entire range of bouncing performances.
Gutmann then built a series of mathematical simulations – taking into account the athletes’ muscle force, muscle force rate, muscle impulse (which is the total force generated over the duration of the bounce) and mechanical work done as the bent leg propelled the body upward – and then used each model to calculate the metabolic cost per bounce, metabolic cost per time and metabolic cost per height for each bounce combination. Comparing the results of the calculations with the genuine physical costs, the duo was impressed to find that the simulation that best mimicked the athlete's performance was based on the total force exerted over the course of the bounce – the impulse.
‘We were surprised that a work-based model did not do a better job of predicating metabolic cost per [two-footed] hop’, admits Bertram, who was also intrigued that the other muscle-based models performed poorly, even though they appear to accurately predict the metabolic costs of running. However, when Gutmann revisited the force rate model of running, she realised that it only predicted the metabolic cost of running accurately over the narrow set of stride frequencies that runners naturally select when running on a treadmill.
Considering the implications of this study for our understanding of human running, Gutmann says, ‘We need to base our metabolic cost models [for running] on data collected across a wide range of conditions to create more generally applicable models, which is what we have attempted to do in this study’. And the duo hopes that this investigation will inspire future studies to better understand the role of the mechanics of the musculoskeletal system and energy use in running.
