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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 (V̇o2-walk = V̇o2-gross - V̇o2-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 (V̇o2-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. [ABSTRACT FROM AUTHOR]

Accurate prediction of the metabolic energy that walking requires can inform numerous health, bodily status, and fitness outcomes. We adopted a two-step approach to identifying a concise, generalized equation for predicting level human walking metabolism. Using literature-aggregated values we compared 1) the predictive accuracy of three literature equations: American College of Sports Medicine (ACSM), Pandolf et al., and Height-Weight-Speed (HWS); and 2) the goodness-of-fit possible from one- vs. two-component descriptions of walking metabolism. Literature metabolic rate values (n = 127; speed range = 0.4 to 1.9 m/s) were aggregated from 25 subject populations (n = 5-42) whose means spanned a 1.8-fold range of heights and a 4.2-fold range of weights. Population-specific resting metabolic rates (...O2rest) were determined using standardized equations. Our first finding was that the ACSM and Pandolf et al. equations underpredicted nearly all 127 literature-aggregated values. Consequently, their standard errors of estimate (SEE) were nearly four times greater than those of the HWS equation (4.51 and 4.39 vs. 1.13 ml O2⋅kg-1⋅min-1, respectively). For our second comparison, empirical best-fit relationships for walking metabolism were derived from the data set in one- and two-component forms for three ...O2-speed model types: linear (∞...1.0), exponential (∞...2.0), and exponential/height (⋅...2.0/Ht). We found that the proportion of variance (R²) accounted for, when averaged across the three model types, was substantially lower for one- vs. two-component versions (0.63 ± 0.1 vs. 0.90 ± 0.03) and the predictive errors were nearly twice as great (SEE = 2.22 vs. 1.21 ml O2-kg-1⋅min-1). Our final analysis identified the following concise, generalized equation for predicting level human walking metabolism:...O2total = ...O2rest + 3.85 + 5.97⋅...²/Ht (where V is measured in m/s, Ht in meters, and ...O2 in ml O2⋅kg-1⋅min-1). [ABSTRACT FROM AUTHOR]

We formulated a "one-size-fits-all" model that predicts the energy requirements of level human walking from height, weight, and walking speed. Our three-component model theorizes that the energy expended per kilogram per stride is independent of stature at mechanically equivalent walking speeds. We measured steady-state rates of oxygen uptake of 78 subjects who spanned a nearly twofold range of statures (1.07-2.11 m) and sevenfold range of body masses (16-112 kg) at treadmill speeds from 0.4 to 1.9 m/s. We tested the size independence of the model by deriving best-fit equations in the form of the model on four stature groups (n ≥ 15): short, moderately short, moderately tall, and tall. The mean walking metabolic rates predicted by these four independently derived equations for the same set of reference subjects (n = 16; stature range: 1.30-1.90 m) agreed with one another to within an average of 5.2 ± 3.7% at the four intermediate speeds in our protocol. We next evaluated the model's gross predictive accuracy by dividing our 78 subjects into 39 stature-matched pairs of experimental and validation group subjects. The model best-fit equation derived on the experimental group subjects predicted the walking metabolic rates of the validation group subjects to within an average of 8.1 ± 6.7% (R² = 0.90; standard error of estimate = 1.34 ml O2·kg-1·min-1). The predictive error of the American College of Sports Medicine equation (18.0 ± 13.1%), which does not include stature as a predictor, was more than twice as large for the same subject group. We conclude that the energy cost of level human walking can be accurately predicted from height, weight, and walking speed. [ABSTRACT FROM AUTHOR]