I know enought physics to be dangerous, so here goes. [EMAIL PROTECTED] writes:
> Even with cushioned shoes, there is a force that is reflected back into > the foot. This force is dependent upon the coefficient of restitution > between the two materials. Could you please explain this idea more clearly? Suppose we take a temporal Fourier transform of the force applied to the bottom of the foot at landing, and inspect the power invested in each frequency. The most damaging frequencies ought to be those which correspond to the normal modes of the bones in the leg, which I'm guessing should be those for which the leg bones are a quarter wavelength. Determining the ratio of frequency to wavelength requires knowing the effective speed of sound: in air it's 330 m/s, in water 1480 m/s, and in bone up to 4200 m/s (the web is a fantastic thing!). I don't know which to use; taking air as a lower limit and bone as an upper limit, then for a 40 cm tibia, the damaging frequencies would then be those between 200 Hz and 2600 Hz--which is roughly the audio range. Now, high frequency audio oscillations are easily damped while low frequency audio oscillations can only be damped by sufficiently massive objects. A running shoe can't possibly be massive enough to damp a 200 Hz oscillation (can it?). So, I would conclude that asphalt is a better running surface than concrete if it turns out that asphalt is better at damping oscillations in the low audio range of perhaps 200 Hz (and if your body is so constructed as to be susceptible to damage by such frequencies--I'll bet some are, some aren't). The question now becomes, can one learn anything about the low frequency damping abilities of a running surface by, say, dropping a golf ball on it? I suspect the answer is yes, though I certainly agree with Christopher that a better test would be whacking the running surface with a sledge-hammer. A light golf ball falling on a surface generates much less low-frequency oscillations that a heavy sledge-hammer. Dropping a golf ball on a running shoe is irrelevant because we know a priori the ability of the shoe to damp low frequencies is much worse that its ability to damp high frequencies, because it is so light. For a running surface, there's at least a chance that the damping coefficient is independent of frequency. I await word from the list supervisor that political rants are to be preferred to faux physics lectures, Jim Reardon [EMAIL PROTECTED]
