The optimal locomotion on gradients: walking, running or cycling?

Abstract

On level ground, cycling is more economical than running, which in turn is more economical than walking in the high speed range. This paper investigates whether this ranking still holds when moving on a gradient, where the three modes are expected to be mainly facing the same burden, i.e. to counter gravity. By using data from the literature we have built a theoretical framework to predict the optimal mode as a function of the gradient. Cycling was found to be the mode of choice only below 10-15% gradient, while above it walking was the least expensive locomotion type. Seven amateur bikers were then asked to walk, run and ride on a treadmill at different gradients. The speed was set so as to maintain almost constant the metabolic demand across the different gradients. The results indicate that the "critical slope", i.e. the one above which walking is less expensive than cycling (and running), is about 13-15%. One subject was loaded during bipedal gaits with a bicycle-equivalent mass, to simulate to cross-country cycling situation. The critical slope was close to 20%, due to the higher metabolic cost of loaded walking and running. Part of the findings can be explained by the mechanically different paradigms of the three locomotion types.

Effect of load and speed on the energetic cost of human walking

“…2) and about 1.0 m s À1 for C net (Fig. 4); these values are identical or close to values found during unloaded walking in other studies (Ardigo et al 2003;Bobbert 1960;Cotes and Meade 1960;DeJaeger et al 2001;di Prampero 1986;Zarrugh et al 1974). The difference between the two optimal speeds can be explained by looking at how they are calculated.…”

“…However, previous studies have shown that: (1) for a given unloaded walking speed, the metabolic rate increases exponentially with increasing positive gradient (Ardigo et al 2003;Bobbert 1960;Margaria 1938); and (2) the energy expenditure per unit of total mass is a constant for a given positive gradient and speed (Goldman and Iampetro 1962). Thus, in uphill walking, the optimal speed should be the same with or without a load, but should decrease with increasing positive gradient.…”

“…For example, using published data (Bobbert 1960;Margaria 1938), the optimal speed for gross cost minimization would be reduced to about 1.0 m s À1 for walking up a +10% gradient. The downhill energy cost is rather independent of speed and no precise optimal speed can be detected (Ardigo et al 2003;Margaria 1938). Note that the Pandolf equation (Pandolf et al 1977) leads to a fixed optimal speed whatever the positive gradient for any fixed load, suggesting that this predictive equation is limited in its use and interpretation vis-a-vis the effect of grade on the energy cost.…”

Muscle activities during walking and running at energetically optimal transition speed under normobaric hypoxia on gradient slopes

“…This could be related to relatively smaller percent differences of ventilation between normoxia and hypoxia during walking on the level slope at faster walking speeds (S1 Fig and S1 Table). An upward shift of the U-shaped CoT curve had been reported when walking on the uphill slope [7,13,33,42], pregnant or obese [32,43], or aged [44,45] only at normoxia. Horiuchi et al [14] recently reported that a significantly slower ES was observed when FiO 2 was 11%.…”

Body Segment Differences in Surface Area, Skin Temperature and 3D Displacement and the Estimation of Heat Balance during Locomotion in Hominins

“…The term a in Equation 1 is a constant pertaining to the production of heat by metabolism and work. Normally a is assumed to equal 2 for walking and 4 for running [11]. The term Ta in Equation 2 is ambient temperature in degrees centigrade.…”