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The work done during each step to lift and to reaccelerate (in the forward direction) and center of mass has been measured during locomotion in bipeds (rhea and turkey), quadrupeds (dogs, stump-tailed macaques, and ram), and hoppers (kangaroo and springhare). Walking, in all animals (as in man), involves an alternate transfer between gravitational-potential energy and kinetic energy within each stride (as takes place in a pendulum). This transfer is greatest at intermediate walking speeds and can account for up to 70% of the total energy changes taking place within a stride, leaving only 30% to be supplied by muscles. No kinetic-gravitational energy transfer takes place during running, hopping, and trotting, but energy is conserved by another mechanism: an elastic "bounce" of the body. Galloping animals utilize a combination of these two energy-conserving mechanisms. During running, trotting, hopping, and galloping, 1) the power per unit weight required to maintain the forward speed of the center of mass is almost the same in all the species studied; 2) the power per unit weight required to lift the center of mass is almost independent of speed; and 3) the sum of these two powers is almost a linear function of speed.
Cavagna et al. (Tue,) studied this question.