So to help out a bit.....and we don't really have all the information we need to do the approximation.... Take a tape measure, measure from the center of your wheel to the middle of your sidewall...this is big R. Then measure from the middle of your sidewall to the edge of the tire (no air in the treads so don't count them) and this is equal to little r. Square little r then multiply by pi (3.1415926535.....) squared...multiply by R and times by 2 ie 2*pi^2*R*r^2 depending on how you measured your tire this will likely give you the cubic inches of air in your tire
If you don't want to do this much math (It works for a torus, but even a torus is not going to be "right", just close...), there's a mechanical way too.
The torus assumes the cavity of the rim is a round concave shape, and that the tire over the rim is a round concave shape, so that the mounted tire forms a cylinder wrapped around the rim.
As the volume of the tire includes the volume created by the rim cavity, but the above calculation uses the sidewall edge, that will leave out that extra volume, and essentially measure a cylinder that ENDS where the sidewall ends, instead of the full volume, etc...
The mechanical way should be pretty darn close for tire filling volume estimates.
Get a tank of water, the kind of tank you dunk a tire into to see if there's a leak.
Mark the level of the tank, with a sharpie, or scribe, etc....to show the water level.
Put the tire (on the rim) into the tank....completely submerged.
Mark the new water level.
Take the tire out.
Use something with a known volume, like a graduated bucket, etc (Marked in gallons/Oz, or whatever...), and add water to the tank until you reach the water mark left by the tire....noting the amount of water you added.
That's the volume of the tire, plus the rim,
Rims are not that voluminous, but, all you do then is dump the rim in w/o the tire, and mark THAT new water line...
...remove the rim, and pour in enough water to bring the water up to THAT level....and that's the rim volume.
Subtract the rim volume from the rim+tire volume, and, THAT'S the volume of the tire.
It of course is the displaced volume, so the thickness of the rubber, etc...will make it off a bit still, but, you'll be seriously close.
Even just doing the tire on the rim ALONE gets you closer than a torus calculation, as you can't measure the inside of the mounted tire for that either...and the mounted shape IS different from the unmounted shape...a LOT different.
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The next thing, if planning on FILLING the tires, is to remember 14.7 psi.
That's the pounds per square inch at sea level that the atmosphere presses down on us with...known as one atmosphere, or, 1 atm.
For every atm of psi, you need ANOTHER air volume equal to the tire volume.
If you figure out your tire holds 4 cubic feet of air (A random #), and you want to fill it to about 29 psi, that's 2 atm....
...meaning, you need TWO 4 cubic foot volumes to DOUBLE the atmospheric pressure.
If you have a 4 cubic foot air tank, pressurized to 14.7 psi, you would not be able to fill this tire to 29 psi, just to ~ 7.35 psi...
as half would go to the tire, and then the tank and the tire would be equal, and so no more air would flow from one to the other.
So - you need enough stored air to not only equal the volume the tire needs, but to FORCE that air INTO the tire....at the PSI you want.
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A gallon is only about 0.13 cubic feet.
One cubic foot of air is about 7.48 gallons.
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A 4 gallon air tank only holds about 0.53 cubic feet of air.
:wink-big:
