How is “correct” tire pressure related to tire volume?

I have a unicycle with a Surly Endomorph 26"x3.7" tire, and I've discovered that this tire rides best at significantly lower pressure than smaller tires.

Even though I weigh ~110 kilos, I can ride this 3.7" tire at 12psi without pinch flats.

Previously I rode a 24"x2" Nokian tire that required at least 40psi.

Is there some known relationship where higher tire volume encourages lower tire pressure?

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Presumably you ride the uni less aggressively than say an MTB. On another point, Schwalbe's Snakebite Protection maybe makes the tire walls significantly harder and P = F / A no longer holds. – Vorac Dec 17 '14 at 15:29

If you ignore the strength in the tire walls (pretty much zero for bike tires) then the pressure (which = force / area ) multiplied by the contact area of the tire on the road must be the force you are putting on the road (ie. the weight of you and the bike).

So for a large tire contact patch you need a lower pressure to support your weight, for a small area narrow tire you need a much higher pressure

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Is there any way to estimate contact patch size given tire size plus tire volume and rider weight? – shapr Feb 2 '11 at 5:49
@shapr You would need to know the strength of tire wall – Greg B Feb 2 '11 at 14:59
@shapr: You can get a rough estimate in square inches by dividing the total weight (rider + bike + stuff carried, all in lbs) by the tire pressure (in psi). Divide by the number of wheels to get the contact patch for each wheel. – darkcanuck Feb 3 '11 at 16:03