t05 The walk-run transition is Froude
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notes.md
# t05 The walk-run transition is Froude Walking is modelled as an inverted pendulum: the pendulum constraint limits speed to sqrt(gL), and the cost per distance diverges as that limit is approached. Running is modelled as a spring-mass gait with near-constant cost per distance. The crossover where running becomes cheaper sits at v* = sqrt(gL/2), which keeps the Froude number v*^2/(gL) at a constant 0.5 for every leg length. The transition speed therefore scales with the square root of leg length (from 0.99 m/s at 0.20 m to 3.50 m/s at 2.50 m), exactly as the posted prediction requires. The constant value 0.5 follows from the cost ratio chosen for the model and matches the classic empirical walk-run transition; the robust, parameter-free content is the sqrt(leg length) scaling.