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The sidewall is the max pressure that the specific tire manufacturer determined is safe. Basically the point where they shed liability if the tire blows up while you're inflating it up to 55psi.
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The offs of a blowout while inflating are quite low (unless you've got a old crappy tire).... It's more of a blowout when you hit a pothole. In any case, the max pressure is based off of a minimum factor of safety.
So I did a quick search... and found a patent for bias ply tires... It makes a reference that says the steel cord safety factor should range between 4 and 11, 7 being a target. Now that's not directly related to inflation pressure - but should be related to hoop stress (P*D/2).... Again, this isn't really an equivalent - and I don't know if the mentioned factor of safety applies to traditional radially belted tires... Really, I doubt I'll find the actual number anywhere as it's probably trade secret.
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Yes, the area will always be the same. The question is, how does the flexing of the rubber compare? The strain in the rubber is generally proportional to the energy loss. [Energy loss = (1-k)(strain energy) where k is the coefficient of restitution.]
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So that makes sense and all...
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A tall sidewall accomplishes the needed deflection (to make the flat patch) with much less distortion needed.
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However, (just thinking intuitively now) - shouldn't we be comparing the deflection delta? That is, a shorter (and stiffer) sidewall doesn't deflect as far when conforming to the road (stiff/bumpy ride) as compared to a larger sidewall with a lower k value...
I am also thinking of a case of a tire with wheel run out (out of round). So we basically have a tire in the shape of an ellipse (a very minute one though). The areas with the shorter sidewall will have more stiffness and translate that into the the vehicle suspension - as compared to the higher sidewall. So that, combined with the assumption that the normal force is constant leads me to the difference in taller versus shorter sidewall is the k. Thus the deflection for the stiffer (shorter sidewall) should be less than the taller sidewall...
So that paragraph above would mean that sidewall stiffness AND inflation pressure are variables that determine contact patch size (something tells me stiffness from the tire is much less than inflation stiffness)
Of course, this could be *** backwards - and x is constant and the force changes (although, intuitively - that seems wrong or I am missing a key point).
In any case, it doesn't matter for me either way. I have no intention to get a shorter sidewall

I just like this sort of discussion