Fig. 3. (A) Walking models predict that the rate of external mechanical work dissipated in collisions is proportional to the fourth power of step length l (keeping step frequency fixed; Kuo, 2002). The simplest two-dimensional (Fig. 1A) and anthropomorphic three-dimensional passive dynamic walking models (Fig. 1B) both give similar predictions. (B) The anthropomorphic model predicts that leg motion also contributes to external work rate, with a term proportional to the square of step length. Step length is expressed as a fraction of leg length, L. Mechanical work rate shown is made dimensionless by dividing by , where M is body mass and g is the gravitational acceleration. C,D, constants. See Materials and methods for details.