Ostrich Running Lab: Spring-Leg Biomechanics (2D)

Leg & Tendon

Leg stiffness (k) 12000 N/m

Tendon energy-return efficiency 88%

Gait

Target speed 8.0 m/s

Body mass 90 kg

Live Readout

Actual speed

0.0 m/s

Gait

Walk

Stride length

0.0 m

Stride frequency

0.0 Hz

Peak GRF

0.0 ×BW

Measured energy return

—

Froude number

0.00

Walk→run threshold

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How it works

Ostriches are the fastest bipedal runners alive (up to ~70 km/h) because of a real spring-mass leg: the gastrocnemius–Achilles tendon complex stretches and recoils like a spring, storing and returning elastic strain energy each stride instead of paying for it all with muscle. This lab runs two mechanically distinct models of a single effective stance leg, switched automatically by the walk→run transition:

Walk (v < v_t): compass-gait inverted pendulum
  θ'' = (g/L)·sinθ           (rigid strut, continuous contact)
  ω+ = ω-·cos(2α)·η          (heel-strike collision loss)

Run (v ≥ v_t): damped spring-leg (SLIP)
  F_leg = k·(L0−ℓ) − c·ℓ'     (stance, ℓ = leg length)
  x'' = 0, y'' = −g           (flight, aerial phase)

v_t = √(Fr_c·g·L0),  Fr_c ≈ 0.5

Touchdown angle is set each step by a proportional speed controller (α adjusts toward the target speed slider — the same strategy hopping robots and running animals use to regulate stride without a fixed gait plan). The tendon-efficiency slider (η) scales the velocity that survives heel-strike in the walk and the internal damping coefficient (c) in the run; "measured energy return" compares actual mechanical energy just after push-off to just before touchdown, so it reflects what the dynamics really did, not just the slider value.

Ground reaction force — vertical stance force in multiples of body weight; running shows a single bell-shaped peak per step, walking a flatter double-hump.
Froude number — v²/(g·L), the dimensionless speed used across biomechanics to predict the walk-run transition independent of body size.

Stance leg / GRF Flight / swing leg Hip trajectory