Tuesday, September 23, 2008

How do people walk?

How do people walk (with their legs)?
(K's Answer: "Put one foot in front of the other.")

Okay. There are two parts to this question. 1) physics 2) biology
I'm only going to answer the first part (and really only one very small but important part of that) tonight. I'll try to get to the biology part later in the week.

Basic physics of walking:
1) You all know that we need friction to get anywhere. The ground exerts a frictional force against our forward foot, causing it to stay put while we swing our rear foot around the pivot (hips), advancing our center of gravity; this movement is very much like a pendulum, which I'll get to later.

We can actually write a little expression for the (approximate) minimum coefficient of friction required [linky]:

m = v /[6gL / p2 - v2]1/2

Where m is the coefficient of friction, v is your speed, g is the gravitational acceleration Earth exerts on you (9.8 m/s2) and L is the length of your legs. So, for someone like me who has, ~1 meter long legs, moving at ~2 m/s (4.4 mph), the minimum coefficient of friction required is about 1.4.

That's a unitless number that basically tells you that the frictional force stopping my foot from moving must be 1.4 times the force gravity exerts on me. This is not strictly correct, but I don't have the space to go into it; suffice to say that the amount of force you apply in the opposite direction of your movement must be no larger than the frictional forces. The coefficient of (static) friction only makes sense in this context: when the frictional and applied forces are perfectly balanced, just before your foot slips.

As I try to go faster, I exert greater forces that attempt to cause my feet to slip, and I need a greater coefficient of friction (or more appropriately, the frictional forces need to be higher to keep my feet from slipping, which requires a greater coefficient of friction). If I try to walk on ice, I cannot move very fast because the coefficient of friction is so low that the forces required to move my feet faster tend to easily overwhelm the frictional forces attempting to keep my foot from moving and I slip (and then I usually fall).

I'll talk about the pendulum-like behavior of our bodies next time, when I also get to the biology of walking.

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