not using a air compressor. i want to install a air tank under my van to fill a flat tire LT235/75 R16 to 85 psi. what size air tank in cubic feet and at what psi will fill the tire.
I'll take a stab at actually answering the original question. A BFG AT KO 235/85R16 is 31.7" tall and 9.2" wide in section. Ignoring the thickness of the rubber, that cylinder has a volume of 7,215.26 cubic inches. A 16" x 6.5" wheel (I guessed, used BFG's "measured rim width") has a volume of 1,286.80 cubic inches, so we'll subtract that from the tire and get 5,928.46 as the volume of the tire itself and that's 3.43 cubic feet.
Assuming you've started at 0 psig (14.7 psia), you need a tank of at least 6.86 cubic feet at 85 psig to inflate 1 such tire from 0 to 85 psi. That's over 51 gallons. Larger than the typical residential water heater. Double the pressure and you can halve the volume, so 3.43 cubic feet at 170 psi. That's asking a lot of an air tank. This number is optimistically low, since it treats the wheel as a simple cylinder, and it isn't. The wheel has a dropped center between the tire beads which increases air volume inside the tire.
The tank capacity must be at least double that of the tire and/or the pressure must be higher, or you'll reach equilibrium at less than your desired pressure. A higher starting tank pressure can allow a smaller tank to fill the tire just as well but honestly most air tanks suitable for vehicle mounting are gonna max about 125 psi and that's MAX, so don't go inflating your tank to 125 cold then drive out to the desert. Now for a more realistic scenario, you're probably airing down to 20 or so psi offroad then back up to 85 to hit the highway, which requires only 77% as much air, or 2.64 cubic feet per tire, 82.28 gallons for 4 tires. So basically, a 100 gallon air tank at 100 psi will air up all 4 tires from 20 to 85 psi once. That's a big air tank, like, REAL BIG, as in, very doubtful you'll get that under your van at all. Keep in mind the shape of air tanks; they're cylinders, not rectangles, etc. The 80 gallon tank on my compressor is about 40" tall and 30" in diameter, so laid on its side, it would not even come close to fitting under my van.