Let me show you how this simple result and a little more scaling analysis
can be used to derive an interesting and surprisingly simple
result about walking. Walking is the most economic way for humans and
animals alike to move themselves. To minimize energy consumption in walk
the legs swing at their natural pendulum period. This is quite different from
running where muscles drive the legs back and forth at greater speed
and cost in energy than is the case in walking. The time taken in two steps
corresponds to one period of oscillation. Thus two steps take
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Here I am using
since the leg is hardly a simple pendulum
so while we should expect the same scaling properties the different mass
distribution should be expected to yield a different numerical pre-factor.
The distance covered in two steps will grow with the length of the
legs,
ie.
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From these equations we derive that the walking speed varies as

This is a simple yet fascinating expression. It tells you why
astronauts on the moon walk so slow. The acceleration of gravity
is approximately 10 time less there so relaxed walking speed is three
times less. The expression also seems consistent with the general relaxed
walking experience. However to really check this out
I would be delighted if one of you working on Zoology could plot
the squared walking speed for a bunch of animals versus
their leg length. Our expression predicts that you should get a straight line.