Walking Speed

A persons natural walking speed is a result of the natural frequency of movement of their legs. We can treat a persons leg as a pendulum and find its natural frequency. The period of a pendulum of length  
\[l\]
  is  
\[T=2 \pi \sqrt{\frac{l}{g}}\]
  so the frequency is  
\[f= \frac{1}{T} =\frac{1}{2 \pi} \sqrt{\frac{g}}{l}} \]
.
If someone with a leg of length  
\[l\]
  takes  
\[f\]
  strides per second, swinging their leg through an angle of 30 ° each time, then the distance moved in one stride is  
\[d=l \theta\]
  and the distance moved in one second, the speed, is  
\[v=df=l \theta \frac{1}{2 \pi} \sqrt{\frac{g}{l}} = \frac{\theta}{2 \pi} \sqrt{lg}\]
.
The length of a leg is about 0.9m and a person may swing their leg through an arc of 39&deg' or  
\[\frac{\pi}{6}\]
.
\[v=df= \frac{\theta}{2 \pi} \sqrt{lg}=\frac{\pi/6}{2 \pi} \sqrt{0.9 \times 9.8}= 0.25 m/s\]
.
This is only an approximation. A comfortable walking speed is about 3 miles per hour or  
\[\frac{3 \times 1609}{3600}= 1.34 m/s\]
.

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