Power and Friction

Period of Legs: T = 2pi [2L / 3g]^1/2 (Physics for Scientists and Engineers: Pg. 405)

g=9.8 m/(s^2) and is independent of walking speed.
pi=3.14
L=length of a person's leg

Walking Model

Note: Energy is lossed during the rise and fall of each step

Power(walking) = (mg / pi) [3gL / 2]^1/2{1 - [1 - pi^2v^2 / 6gL]^1/2}: Joules/s

Running Model

Note: Energy is lossed during the rise and fall of each step.

Power(running) = mgv / 4 : Joules/s

Example:

Power consumed for walking and running as a function of speed 'v' for an individual with m = 100 kg and L = 1 m.

Running: Linear increase of power with speed increase
Walking: Quadractic increase of power with speed increase

Power: At 2 m/s the powers consumed in walking and running are about 500 Watts for a 100 kg person.

Graph courtesy of http://sprott.physics.wisc.edu/technote/walkrun.htm

Jog or Walk: If two people weighing over 200 pounds were moving at the same speed below 2 m/s, the person jogging would be getting the better work out! Their roles would change, once they increased their speed beyond 2 m/s.

Friction Requirements

m=coeficient of friction.

Walking: m = v / [6gL / pi^2 - v^2]

Running: Force occurs over a short time interval and is much larger than the person's weight.

Note: To launch the person at a 45° angle requires equal vertical and horizontal forces. Running then requires m = 1 to be independent of speed.

Results:

Coefficient of friction as a function of speed 'v'.

Walking: At slow speeds, the coefficient of friction is small. This greatly increases above speeds higher than 2m/s due to the constant force being applied to the ground.

Running: The mimimum coefficient of friction when running is constant, and smaller than for walking at speeds above 2m/s

Graph courtesy of http://sprott.physics.wisc.edu/technote/walkrun.htm

Run or Walk: If a student is late for class, and the trails are icy, what should that person do? Walking is the safest way becuase the coefficient of friction is the highest, but if they start moving faster than 2m/s, the safest thing and easiest thing to do would be run, rather than walk.

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Shoes and Support
Force and Efficiency
Bibiography