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Fig. 3. Mechanics of leg swinging as a function of frequency f, in terms
of torque, work, and force/time, were modeled reasonably well by a forced
pendulum (Equations 9,
10,
11). (a.) Hip torque amplitude,
T0, increased approximately with f2
above natural frequency fn (R2=0.96).
(b.) Rate of mechanical work,
 (+), increased
approximately with f3 (R2=0.93). (c.)
Rate of force/time,   ,
increased approximately with f 4
(R2=0.95). Metabolic cost is hypothesized to increase with
both rate of work and force/time, for frequencies above the natural frequency
fn=0.64 Hz. Data fits were performed using dimensionless
variables (right-hand axis) with body mass, gravitational constant, and leg
length serving as base units; conventional units are shown (left-hand axis)
for convenience. Data shown are mean ± S.D.
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was defined relative to vertical, and torque T due to muscle force
was defined as positive in the same direction as 
. We assumed a
relatively constant moment arm for muscle force. Torque and rate of work
requirements increase with the square and cube, respectively, of swing
frequency f (Hz) or 
(rad s-1) above the natural
frequency, fn or 
vs frequency of leg swinging f, showing metabolic rate
increasing approximately with f 4 as predicted by
force/time hypothesis (Equation
12). Data shown are for all frequencies applied, but the curve fit
was only performed on data for fast leg swinging. (B) 
