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The Froude number (sounds like “food” with an “r”) is a useful parameter to study how locomotion changes with body size. It is a dimensionless variable that relates a scalar dimension of the body (typically leg length) to the forward velocity of the body. Theoretically, animals of different sizes that rely on pendulum-like mechanics for gait will use the same form of locomotion at a given Froude number (e.g., a T-Rex and a chicken traveling at the same Froude number would look the same). The Froude number is defined as:

where  = the speed of movement (in m/s)

= the acceleration due to gravity (in m/s)

= the effective length of the limb (in m)

(a) Using the simple inverted pendulum model from the previous question, explain why the walk-run transition theoretically occurs at. (Note: the model is redrawn below with the linear speed and gravitational acceleration shown.)

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