Energetically optimal running requires torques about the centre of mass

Bipedal animals experience ground reaction forces (GRFs) that pass close to the centre of mass (CoM) throughout stance, first decelerating the body, then re-accelerating it during the second half of stance. This results in fluctuations in kinetic energy, requiring mechanical work from the muscles. However, here we show analytically that, in extreme cases (with a very large body pitch moment of inertia), continuous alignment of the GRF through the CoM requires greater mechanical work than a maintained vertical force; we show numerically that GRFs passing between CoM and vertical throughout stance are energetically favourable under realistic conditions; and demonstrate that the magnitude, if not the precise form, of actual CoM-torque profiles in running is broadly consistent with simple mechanical work minimization for humans with appropriate pitch moment of inertia. While the potential energetic savings of CoM-torque support strategies are small (a few per cent) over the range of human running, their importance increases dramatically at high speeds and stance angles. Fast, compliant runners or hoppers would benefit considerably from GRFs more vertical than the zero-CoM-torque strategy, especially with bodies of high pitch moment of inertia--suggesting a novel advantage to kangaroos of their peculiar long-head/long-tail structure.