“Who has seen the wind? Neither you nor I, but when the trees bow down their heads, the wind is passing by”. (Rossetti, 1915).
The Science of Falling: How a virtual pivot point explains constant-velocity running using gravitational torque.
In part 3 of the series of posts on the extensor paradox, it was concluded that gravity creates a turning force or torque on the center of mass of a runner about the supporting foot, when the former passes in front of the latter. It was also concluded that this gravitational torque provides the motive force in running. This theory is in agreement with kinetic and EMG data from previously published research (Mann et al., 1986; Rodano, 1987; McClay et al., 1990), whereas the prevailing theory that runners actively ‘push’ into the ground is at odds with both – hence the so-called extensor paradox that is not a paradox at all.
The theory that gravity provides the motive force in running is not new (Morton, 1935; Perry, 1992; Romanov and Fletcher, 2007). However, the mechanism used to explain the action of gravitational torque in these publications struggle to explain constant-velocity running, and instead would lead to constant acceleration, closer to what happens when sprinters initially leave the blocks, and as depicted in part three of the extensor paradox post. A recent attempt to explain gravitational torque in locomotion, and to experimentally demonstrate it’s effectiveness in reducing the energy cost of running and walking (Kanstad and Kononoff, 2015), suffers from fatal methodological issues and reporting bias. Constant-velocity running, as well as acceleration and deceleration using gravitational torque can, however, be perfectly explained by the virtual pivot point model (VPP) (Maus et al., 2010). This model also explains the stability observed in what ought to be a very unstable gait.
Unstable bipeds and running robots
The VPP model has its origins in engineering and was borne out of the seemingly insurmountable problem of preventing an inherently-unstable-bipedal robot locomote without falling over. Keeping a heavy torso upright over a long leg with a small base of support is a complex task amidst the varied forces acting on it during the running cycle. It is no less a challenge for humans, yet healthy humans rarely fall over. The solution lies in aligning the ground reaction force vector with a fixed, though virtual axis high in the torso, above the center of mass, at every stage of the stance phase. This is the virtual pivot point model.
The VPP and constant-velocity running
The image above depicts a runner at initial ground contact (left), mid stance (middle), and terminal stance (right). The graphs below show the vertical ground reaction force and torque about the hip joint respectively. At initial ground contact, the GRF vector is angled backwards and up through the VPP and in front of the center of mass (producing a slight braking effect). The perpendicular distance between the GRF vector and the hip joint is shown as D. This discrepancy creates a hip flexion torque and a forward pitching of the torso that must be controlled by hip extensors. The shaded region about the rear of the hip and lower back illustrate the EMG response of the hip extensors whose primary purpose (see teleology post) is to control the forward pitch of the torso in running, hence their extensive development in humans but not non-running apes and chimps (Lieberman et al., 2006). This slight forward pitch of the torso is evident in slow-motion observations of every elite runner and was leveled as a criticism of the ‘Pose’ conception of running (Brodie et al., 2007). At mid stance, the GRF vector is vertically-aligned with the hip, center of mass and VPP. The EMG activity shown in the legs here is simply to resist the squash of gravity and the opposing GRF and to aid storage of energy in the major tendons of the leg. Immediately after mid stance, the extensor muscles switch off and the runner’s center of mass falls forward using gravitational torque at the same time as the leg spring passively recoils providing the upward motion seen in the trajectory of the center of mass. This time, the GRF is aligned forwards and up through the VPP and behind the CoM and hip, creating acceleration, and a hip extension torque that activates hip and trunk flexor muscles and begins the recovery of the support leg. There is also a resulting backwards pitch of the torso, which again, can be seen in slow-motion footage of all good runners. The figure shows how the GRF vectors at initial contact and terminal stance are exactly opposite each other creating equal but opposite hip flexion and extension torques and a constant velocity i.e. the slight braking effect is counteracted by the acceleration effect provided by gravitational torque after mid stance. Acceleration and deceleration result from mismatches in the hip flexion and extension torques.
The VPP model explains and accounts for kinetic and kinematic observations of human and animal runners and how they work with gravity, to save energy, as predicted by the biological imperative. Predictions of the theory have been supported by observations in rigorously-designed studies. A theory that explains and account for all observations is of course superior to one that does not. The current ‘runners push’ theory, and past and recent ‘gravitational torque’ theories constitute the latter.
Brodie, M., Walmsley, A., and Page, W. (2007). Coments on “Runners do not push off but fall forward via a gravitational torque” (Vol. 6, pp. 434-452). Sports Biomechanics, 7(3), 403-405.
Kanstad, S.V. and Kononoff, A. (2015). Gravity-driven horizontal locomotion: theory and experiment. Proceedings of the Royal Society A, 471(20150287), 2-11.
Lieberman, D.E., Raichlen, D.A. and Pontzer, H. (2006). The human gluteus maximus and its role in running. Journal of Experimental Biology, 209, 2143-2155.
Mann, R.A., Moran, G.T. and Dougherty, S.E. (1986). Comparative electromyography of the lower extremity in jogging, running and sprinting. The American Journal of Sports Medicine. 14(6), 501-510.
Maus, H.M., Lipfert, S.W., Gross, M., Rimmel, J and Seyfarth, A. (2010). Upright human gait did not provide a major mechanical challenge for our ancestors. Nature Communications, 1(70), 1-6.
McClay, I.S., Lake, M.J. and Cavanagh, P.R. (1990). Muscle activity in running. In P.R. Cavanagh (Ed.), Biomechanics of Distance Running (pp 165-186). Champaign, Illinois: Human Kinetics.
Morton, D.J. (1935). The Human Foot: its evolution, physiology and functional disorders. New York: Columbia University Press.
Perry, J. (1992). Gait Analysis: Normal and Pathological Function. Thorofare, New Jersey: SLACK Inc.
Rodano, R. (1987). Evaluation of movement in sport by means of vectograms. International Symposium on Biomechanics in Sports, 506-522.
Romanov, N and Fletcher, G. (2007). Runners do not push off the ground but fall forwards via a gravitational torque. Sports Biomechanics, 6(3), 434-452.
Rossetti, C.G. (1915). Sing-song: a nursery rhyme book. London: MacMillan and Co.