You got me interested. That's always a bad thing
I worked out a way to estimate the volume mathematically.
I doubt there's a way to get an exact figure except empirically due to differences in tire designs (thickness) and rim shape. A calculation can be made by thinking of the volume of the tire the revolution of an ellipse. A revolution is the volume created by a 2D shape being revolved about an axis. A
torus is the revolution of a circle. Calculating the volume of a shape like that would require Calculus and aspirin
However shape created can be thought of as an elliptical cylinder bent in a circle til it's ends touch. The volume of that can be easily calculated using the volume formula for an elliptical cylinder is V=(pi x R1 x R2 x length)/4. The pi x Radius1 x Radius2 part is the surface area of an ellipse. Multiplying that surface area by the length and dividing by gives us the volume of the cylinder. Using the variables below the formula is V=(pi x W x H x L)/4
The two radiuses we need for the ellipse come from the tire width and height. Now that tire code gives the tire width and the rim diameter (13.6 x 16 respectively). It doesn't give the tire height which is required for this calculation. You should measure it (top of the rim to the top of the tire) but for the sake of example I'll assume it's 12 inches. Thus W=13.6 and H=12
To get the length of our cylinder we need to get the circumference (the distance around a circle) of a circle that runs through the middle of our ellipse (black circle). Circumference is just pi x diameter. To get that we take average of the diameter the tire and the diameter of the rim and then take the circumference of that.
So the inner diameter (Id) is the rim size, 16 inches, and the tire's out diameter (Od) is the rim diameter plus 2 times the tire height (Od=2 x H + 16) giving 40 inches. Taking the average of the two gives us the diameter of the black circle (Id+Od/2) gives us 28 inches. It's circumference is the length number we need thus L=28 x pi=88 inches.
Punching our numbers into the formula we get V=(pi x 13.6 x 12 x 88)/4which gives us a full tire volume of 11279.6 cubic inches. 231ci per gallon so 49 gallons per tire if filled to the top. Normal fill is only about 75% so about 37 gallons per tire.
The whole thing ready to dump into a calculator
like this one: (((pi*W*H*(pi*((2*H+2*Rd)/2)))/4)/231)*.75 (Rd is rim diameter). A simplified version: (pi^2*H^2+pi^2*Rd*H)*W/1232
It's a rough estimate due to the odd shape but that's how I'd go about doing it. I'd bet that's within 5 gallons of the actual number. Though it may be a bit high as I'm not accounting for the volume the actual tire takes up so you may want to subtract 0.5-1.0 inches from the H and W numbers.
Well that took longer than I planned on. Whether you end up using it or not I enjoyed working it out.
Matt
EDIT: Hummmmm cross referencing with the numbers on Lil Foot's table the agri tires come out pretty close when the height is slightly less than the width sounds about right. But that doesn't work at all for the turf tires. I'm not sure why.
