Meeting Abstract
Bipedal walking is a particularly economical gait for humans and it is conventionally modeled by the inverted-pendulum construct of a rigid leg tracing a circular arc. At slow to moderate walking speeds, this model predicts low mechanical cost of transport (CoT-mech), which is determined by the impulse needed to reverse the downward velocity at the end of each arc. At moderate to fast walking speeds, however, CoT-mech is predicted to increase precipitously. An analytical solution for CoT-mech of the inverted-pendulum model predicts CoT-mech to increase as a squared function of speed. However, our experimental data from ten human subjects across a full range of walking speeds contradict the predictions of the inverted-pendulum model and show that human walkers exhibit only a moderate increase in CoT-mech with increasing speed. We use multiple regression to determine a function relating CoT-mech to both speed and the square of speed — in normalized terms, the square root of Froude number and Froude number. CoT-mech of walking humans was found to increase as a quadratic function of speed, having a positive squared term and a negative linear term. Using values of step length and velocity from our human data set, the analytical solution for an inverted-pendulum model shows the same squared term but yields a positive linear term. Expressing the linear term as a fraction of the squared term, gives -0.73 for the experimental CoT-mech and 0.31 for the analytical solution. Hence, the linear term in the simple inverted-pendulum model adds to the squared increase, whereas in walking humans, the linear term subtracts from the squared increase. Overall, the change in CoT-mech across the human walking speed range shows only a 1.5-fold increase, compared to the 9-fold increase predicted by the conventional inverted-pendulum model.
