Walking economy is predictably determined by speed, grade, and gravitational load

The metabolic energy that human walking requires can vary by more than 10-fold, depending on the speed, surface gradient, and load carried. Although the mechanical factors determining economy are generally considered to be numerous and complex, we tested a minimum mechanics hypothesis that only three variables are needed for broad, accurate prediction: speed, surface grade, and total gravitational load. We first measured steady-state rates of oxygen uptake in 20 healthy adult subjects during unloaded treadmill trials from 0.4 to 1.6 m/s on six gradients: -6, -3, 0, 3, 6, and 9°. Next, we tested a second set of 20 subjects under three torso-loading conditions (no-load, +18, and +31% body weight) at speeds from 0.6 to 1.4 m/s on the same six gradients. Metabolic rates spanned a 14-fold range from supine rest to the greatest single-trial walking mean (3.1 ± 0.1 to 43.3 ± 0.5 ml O₂·kg_-body^-1·min^-1, respectively). As theorized, the walking portion (V̇o_2-walk =  V̇o_2-gross - V̇o_{2-supine-rest}) of the body's gross metabolic rate increased in direct proportion to load and largely in accordance with support force requirements across both speed and grade. Consequently, a single minimum-mechanics equation was derived from the data of 10 unloaded-condition subjects to predict the pooled mass-specific economy (V̇o_2-gross, ml O₂·kg_{-body + load}^-1·min^-1) of all the remaining loaded and unloaded trials combined (n = 1,412 trials from 90 speed/grade/load conditions). The accuracy of prediction achieved (r² = 0.99, SEE = 1.06 ml O₂·kg^-1·min^-1) leads us to conclude that human walking economy is predictably determined by the minimum mechanical requirements present across a broad range of conditions.NEW & NOTEWORTHY Introduced is a "minimum mechanics" model that predicts human walking economy across a broad range of conditions from only three variables: speed, surface grade, and body-plus-load mass. The derivation/validation data set includes steady-state loaded and unloaded walking trials (n = 3,414) that span a fourfold range of walking speeds on each of six different surface gradients (-6 to +9°). The accuracy of our minimum mechanics model (r² = 0.99; SEE = 1.06 ml O₂·kg^-1·min^-1) appreciably exceeds that of currently used standards.