STATURESTATURE Mechanics
This page is intended for coaches, researchers, and technically minded lifters who want to understand exactly what the engine computes — and why. Every formula is derived from published, peer-reviewed biomechanics literature.
STATURE derives all limb-length estimates from three foundational references:
Biomechanics and Motor Control of Human Movement, 4th ed. John Wiley & Sons. The primary source for segment-length ratios as fractions of standing height. Winter’s Table 4.1 provides male and female norms derived from large-scale population studies. These ratios are used directly for STATURE’s default limb-length estimation.
Space requirements of the seated operator. WADC Technical Report 55-159. The primary source for segment mass as a fraction of total body weight. Dempster’s cadaver-dissection data established male segment mass ratios that remain the most widely cited values in biomechanics textbooks. Uncertainty is approximately ±10–15% for individual variation within sex.
“Adjustments to Zatsiorsky-Seluyanov’s segment inertia parameters.” Journal of Biomechanics, 29(9), 1223–1230. Used for female segment mass ratios. De Leva’s gamma-ray scanning measurements are more precise than Dempster’s cadaver dissection and provide sex-differentiated values that better reflect female fat distribution patterns.
These sources are widely used in sports science, physical therapy, and ergonomics research. They represent the best available peer-reviewed norms for population-average segment proportions.
Given a lifter’s standing height (h), STATURE computes each limb segment length by multiplying h by the population-average ratio from Winter (2009). For example, a 1.80 m male has an estimated femur length of 1.80 × 0.276 = 0.497 m.
| Segment | Male Ratio | Female Ratio | Male @ 1.80 m | Female @ 1.65 m |
|---|---|---|---|---|
| Head + Neck | 0.130 | 0.130 | 23.4 cm | 21.4 cm |
| Torso | 0.288 | 0.285 | 51.8 cm | 47.0 cm |
| Upper Arm | 0.186 | 0.183 | 33.5 cm | 30.2 cm |
| Forearm | 0.146 | 0.143 | 26.3 cm | 23.6 cm |
| Hand | 0.108 | 0.106 | 19.4 cm | 17.5 cm |
| Femur | 0.276 | 0.276 | 49.7 cm | 45.5 cm |
| Tibia | 0.215 | 0.215 | 38.7 cm | 35.5 cm |
| Foot Height | 0.039 | 0.039 | 7.0 cm | 6.4 cm |
| Foot Length | 0.152 | 0.152 | 27.4 cm | 25.1 cm |
Source: Winter, D.A. (2009). Biomechanics and Motor Control of Human Movement. Note: Ratios sum to 0.948 for the vertical chain (head + torso + femur + tibia + foot height), not 1.0. STATURE normalizes segments to standing height after applying ratios.
When a user specifies that their legs are “long” or “short”, STATURE applies a standard-deviation modifier. The modifier formula is:
A coefficient of 0.045 represents a 4.5% change in segment length per standard deviation, consistent with the coefficient of variation (CV) for long bone lengths in the human population (typical CV: 4–5%). Short/Long options use ±1.5 SD (±6.75%), and Very Short/Very Long use ±3.0 SD (±13.5%).
For each lift, STATURE runs a joint-angle solver to determine the bar path and the configuration of each limb segment at every phase of the movement.
The squat solver enforces the physical constraint that the barbell must remain over the foot’s mid-point throughout the descent. Given femur length, tibia length, torso length, and ankle dorsiflexion range, the solver iterates through trunk angles (20°–80°) and ankle angles (10° minimum dorsiflexion) to find the deepest position at which the bar-over-midfoot constraint is satisfied.
Vertical bar displacement equals the vertical distance the hip travels from standing position to the bottom of the squat. This displacement is the primary input to the work calculation.
The hip moment arm in the squat is approximated as the horizontal distance from the hip joint center to the barbell’s vertical projection. This arm is determined by the ankle angle, femur length, and the bar’s fore-aft position relative to the hip (set by squat variant: high bar, low bar, or front rack).
For the deadlift, the lumbar moment arm is the horizontal distance from the L4–L5 disc to the bar, computed from the forward lean angle required to bring the bar to the floor starting position while maintaining a neutral spine.
Mechanical work per repetition is computed as:
The demand factor is a normalized ratio of this lifter’s work per rep to the work per rep of an average-proportioned reference at the same height and weight:
The reference profile is created using Winter’s segment ratios at zero SD offset — population-average proportions at the same height and mass. Because both profiles share height and mass, the demand factor isolates the effect of proportions alone.
The BASE_DEMAND_FACTOR constants are engineering estimates calibrated to produce intuitive magnitudes across lift families. They affect the displayed demand factor value but do not affect comparison ratios or work calculations between lifters.
| Lift | Base Demand Factor | Rationale |
|---|---|---|
| Squat | 1.0 | Baseline reference |
| Deadlift | 1.1 | Greater posterior chain involvement |
| Bench Press | 0.9 | Smaller ROM, body fully supported |
| Pull-up | 1.2 | Full bodyweight is the load |
| Push-up | 0.8 | Bodyweight only, no external load |
| OHP | 1.0 | Comparable total-body demand to squat |
| Thruster | 1.5 | Squat + press compound |
STATURE’s demand factor outputs have been calibrated against publicly available strength data from StrengthLevel.com (153 million+ recorded lifts) and published powerlifting meet results. The calibration checks that:
Kinematic outputs (bar displacement, joint angles) have also been spot-checked against published squat kinematics studies (Schoenfeld, 2010; Wretenberg et al., 1996) for 165 cm and 185 cm male subjects at parallel depth.
STATURE’s model is intentionally transparent about what it does and does not capture:
Winter’s ratios are population averages. Individual segment lengths can deviate by ±1–3 SD from these means. STATURE provides SD modifier inputs for users who know their proportions; without them, estimates carry ±10–15% uncertainty.
The model assumes optimal technique for each variant — specifically, the bar-over-midfoot constraint in the squat and conventional hip-hinge mechanics in the deadlift. Poor technique can add or remove demand that the model does not capture.
The demand factor measures mechanical difficulty, not neural or metabolic demand. Lifters with different muscle fiber compositions or motor unit recruitment patterns may experience the same mechanical demand very differently. These factors are not modeled.
For heights substantially outside the standard population range (>2 m or <1.5 m), STATURE assumes geometric similarity (isometric scaling). No allometric data exists for extreme statures in this context.
Despite these limitations, demand factor comparisons between two similarly sized lifters with known proportions are reliable to approximately ±5–8% — sufficient to identify meaningful biomechanical advantages and disadvantages.