Walk-run transition occurs at a critical Froude number, not speed
Supplied working report; original verdicts not validated.
Review status: Held for correction. This is an archival source note, not a passed proof.
README.md
# Walk-run transition occurs at a critical Froude number, not speed **XXI, Theory 19 / Froude Number / Human gait** · verdict: **supported** Claim (verbatim): > The walk-to-run transition occurs at a critical Froude number rather than at a critical speed, so leg length sets the speed at which people switch. ## Result At Fr* = 0.5 the predicted transition speed is v* = sqrt(0.5 g L); for a human leg length of 0.9 m this is 2.1 m/s, matching the documented ~2 m/s transition, and v* varies with sqrt(L) while Fr* stays constant. ## Headline Leg length, not a universal speed, sets the transition: v* = sqrt(0.5 g L) = 2.1 m/s for a human. ## Design The inverted-pendulum maximum walking speed and the empirical critical Froude number were combined to predict transition speed as a function of leg length, and compared with the documented human value. ## Key statistics - critical_froude = 0.5 dimensionless - human_transition_speed_m_s = 2.10107 m/s - human_leg_m = 0.9 m ## Predictions - **P1** (supported): Fr* = 0.5 constant while v* = sqrt(0.5 g L) varies with sqrt(L) - **P2** (supported): v* spans 0.5 to 2.7 m/s across leg lengths ## Limitations - Fr* = 0.5 is an empirical constant; the model derives only the sqrt(L) scaling, not the value 0.5. - The inverted-pendulum model is a simplification of the true gait dynamics. - The human anchor uses a representative leg length; individuals vary. Provenance: Inverted-pendulum walking model; critical Froude number from the dynamic-similarity literature. *Working paper — not peer reviewed. AI-assisted. Not medical, clinical, financial or safety advice.*