Newton's Third Law and Treadmills
I have been told that running on a treadmill is less work
than running an equivalent speed over the ground, because the moving
treadmill does some of the work for you (by pulling your foot along
and back -- whereas over the ground you have to "push-off" of the
"stationary" ground to move yourself along.) Is this true? I would
think that it does not actually matter what is moving relative to
Earth's surface (you or the treadmill, as it is all relative, and if
we ignore details like wind resistance and the cushioning bounciness
of treadmills, etc., it should be the same amount of physical work.
If I am wrong, please explain to me what the key difference (or
benchmark?) is in running over the "moving" surface vs. the "stationary" one!
Amy - no further second-guessing - you are right,
and your thinking sounds like it validly covers the issue.
By the way,
given that work = force x distance,
it is pretty difficult to know the effective force when walking on open, level ground.
In principle the average force during a stride is zero,
since your speed is steady
and there is no portion of gravity in your direction of travel,
and your speed is low enough that air-drag seems negligible.
All the real work one does in this case is inherent within the stride itself,
a matter of force cycles and inefficiency.
I am not yet sure what values for work rate are used or how they would be estimated.
It may actually be good to consult diet or fitness information for calories per hour or mile.
Of course each "calorie" is 1 kilocalorie to a chemist, or 4.2 kiloJoules to a physicist.
Or one could try modeling the force cycles,
i.e., acceleration when the planted-foot is rearward and deceleration when the planted foot is forward.
or body mass being low when legs are apart and both feet are touching the ground,
then high when the legs pass each other.
And there is the work of re-accelerating each leg after it stops on the ground.
Also the motor efficiency of human muscles must be worked in somewhere,
and its percentage value will not be very well known.
Multi-part mechanical computer models have been done,
predicting energy use vs speed, for various animals.
Going up-hill makes the estimate of force easier, if it s steep enough that
the gravity clearly outweighs the stride losses.
A treadmill has the advantage that it can accurately measure within itself
the forces applied to the human subject and the effective distances traveled,
if the treadmill design is sophisticated enough.
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Update: June 2012