Optimum gradient of mountain paths

By combining the experiment results of R. Margaria (Atti Accad. Naz. Lincei Memorie 7: 299-368, 1938), regarding the metabolic cost of gradient locomotion, together with recent insights on gait biomechanics, a prediction about the most economical gradient of mountain paths (approximately 25%) is obtained and interpreted. The pendulum-like mechanism of walking produces a waste of mechanical work against gravity within the gradient range of up to 15% (the overall efficiency is dominated by the low transmission efficiency), whereas for steeper values only the muscular efficiency is responsible for the (slight) metabolic change (per meter of vertical displacement) with respect to gradient. The speeds at the optimum gradient turned out to be approximately 0.65 m/s (+0.16 m/s vertical) and 1.50 m/s (-0.36 m/s vertical), for uphill and downhill walking, respectively, and the ascensional energy expenditure was 0.4 and 2.0 ml O2.kg body mass-1.vertical m-1 climbed or descended. When the metabolic power becomes a burden, as in high-altitude mountaineering, the optimum gradient should be reduced. A sample of real mountain path gradients, experimentally measured, mimics the obtained predictions