Q7.13 Swinging leg (T)

Estimate the swing frequency of a disembodied (human) leg, suspended from one end. Hence estimate a comfortable (human) walking speed .
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Hint

The second part supposes that the leg is appropriately attached.
 

Solution

Reveal
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Solution

Let us estimate the length of the disembodied leg as L=1 m. If hanging freely from one end (not a pretty sight) the result of the previous question shows that it will oscillate with a period of about T=1.6 s.

Now imagine the leg reconnected to its owner. One might imagine that, in walking comfortably, the owner will swing each leg so it moves much as it would if it were swinging freely. Then one pace would take a time t=T/2. Estimate a pace as d1 m. Then the associated walking speed is

\[ v= \frac{d}{t} = \frac{1}{0.8} = 1.25 \, ms^{-1} \]
In more familiar units, this is about 5 mph, which is a bit fast, but not bad given the crudity of the model.