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A simple spring-mass model of running does not apply to elephants

All legged terrestrial locomotion measured to date involves two basic mechanisms: (1) a pendulum-like transfer between the kinetic and potential energy of the centre of mass (CoM) as seen, for example, in walking and to a lesser extent in slow galloping; and (2) a spring-like bouncing mechanism, as seen in running, hopping and high-speed galloping (Cavagna et al. 1977). This latter mechanism has been modelled as a simple spring-mass system oscillating at its natural frequency, and the model quantitatively matches the bouncing gait in a remarkable variety of vertebrates (Cavagna et al. 1988) and invertebrates (Blickhan and Full 1987). Recent measurements on high-speed locomotion in elephants (Genin et al. 2010), however, show that the CoM of elephants at 2.8–5 m s only goes up and down ,1 cm each step. This small vertical displacement is of great advantage to a massive elephant because it reduces the work that must be done against gravity each step, the work done to maintain the movements of the CoM (Wext), and furthermore it reduces the peak ground reaction forces that must be supported by the muscles and bones. However, this small vertical displacement of the CoM would normally result in little energy being stored and recovered from elastic energy. In this study, we determine if an elephant must lose the ability to use elastically stored energy in an effort to minimise muscle and bone stress, work done against gravity and Wext.