The energy cost of walking is sensitive to speed but not gravity; for running it's the other way around: model and experiment

We contrast walking and running by looking at the effects of speed and gravity on subject-preferred step length and consequent energy use. First, we reproduced some classic reduced-gravity experiments. At normal gravity and at an artificially reduced gravity, oxygen consumption and self-selected step length were measured at various speeds. Next, we used a minimal model that has a point-mass body, energy lost to ground collisions, and legs with inertia. A work-based metabolic cost is assumed. In the model, the proxy for self-selection of step length is the assumption that at each speed and gravity level, the step length minimizes energy use. Our experiments confirm previous experiments: for walking the specific energetic cost of transport is highly sensitive to speed but not much to the magnitude of artificially reduced gravity and, conversely, that for running the energetic cost is highly sensitive to gravity but not to speed. These converse trends are also predicted by the minimal model. For walking, the minimal-model-predicted costs of both the step-to-step transition at heel-strike and of leg swing increase with speed but are not influenced by gravity. For running, as gravity is reduced from earth-normal, the model-calculated energy-minimizing step frequency decreases so the predicted metabolic cost of leg swing is decreased. At any gravity level, as running speed increases at given step length, the model-predicted cost of each running collision decreases. So, energy minimizing step length uses longer stride lengths (and times) resulting in the famous near-constant specific cost of transport for running. The general agreement of the experiments and the simple model highlights the differences between the energy costs for walking and for running.