How do low horizontal forces produce disproportionately high torques in human locomotion?

Abstract

Although horizontal ground forces are only ∼15% of vertical forces, they account for 47% and 33% of the metabolic cost in walking and running. To explain these disproportionately high metabolic costs, we hypothesized that low horizontal ground forces generate relatively high torques on body segments during locomotion and this is mediated by long moment arms. We compared external force moment arms and discreet torques applied to the body segments by horizontal and vertical forces during walking and running. Sixteen subjects (21.9±1.9 years) walked at 1.5m/s and ten subjects (23.2±2.0 years) ran at 3.83m/s. Segmental torques in the sagittal plane were partitioned into components due to horizontal and vertical forces and quantified by their angular impulses. The mean (±S.E.) ratios of horizontal to vertical ground forces (GF ratio) and angular impulses (AI ratio) in walking were 0.131 (±0.003, 95% confidence interval (CI) 0.124–0.137) and 0.530 (±0.018, CI 0.497–0.569). Results were similar in running. In both gaits the AI ratios were significantly greater than the GF ratios because the respective CI's did not overlap. The horizontal forces produced 53% and 41% as much angular impulse on the body segments, as did the vertical forces in walking and running despite being only 13% as large. In the two movements the moment arms for the horizontal forces averaged across foot, leg, thigh, and trunk body segments were 3.8 fold larger than those for the vertical forces. The data supported the hypothesis and suggest that the relatively low horizontal vs. vertical forces accounted for a disproportionately higher percentage of the angular impulses placed on the body segments and this effect was due to relatively long moment arms for horizontal forces. These results partially explain the relatively large metabolic cost of generating relatively low horizontal forces.