The energetic cost of human walking as a function of uneven terrain amplitude
Bibliographic record
Abstract
Abstract Humans expend more energy walking on uneven terrain, but the exact cost varies across terrains. Few experimental characterizations exist, each describing terrain qualitatively without any relation to others or flat ground. This precludes mechanistic explanation of the energy costs. Here we show that energy cost varies smoothly and approximately quadratically as a function of terrain amplitude. We tested this with healthy adults (N=10) walking on synthetic uneven terrain with random step heights of parametrically controlled maximum amplitude (four conditions 0 – 0.045 m), and at four walking speeds (0.8 – 1.4 m · s −1 ). Both net metabolic rate and the rate of positive work increased approximately with amplitude squared and speed cubed ( R 2 = 0.74, 0.82 respectively), as predicted by a simple walking model. The model requires work to redirect the body center of mass velocity between successive arcs described by pendulum-like legs, at proportional metabolic cost. Humans performed most of the greater work with terrain amplitude early in the single stance phase, and with faster walking late in stance during push-off. Work and energy rates changed with approximately linear proportionality, with a ratio or delta efficiency of 49.5% ( R 2 = 0.68). The efficiency was high enough to suggest substantial work performed passively by elastic tendon and not only by active muscle. Simple kinematic measures such as mid-swing foot clearance also increased with terrain amplitude ( R 2 = 0.65), possibly costing energy as well. Nevertheless, most of the metabolic cost of walking faster or on more uneven terrain can be explained mechanistically by the work performed. Summary statement Humans perform more work and expend more energy on uneven terrain, increasing with the square of terrain amplitude and the cube of walking speed.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".