Good grief - I keep saying that you can weigh your vehicle by using the foot print or contact area and psi for each tire. You just did it in reverse - weight and psi gives contact area. Pressure on an area gives the force -Okay, so as promissed.
Boeing Document #C1-APC-96-a072
Calculating Tire Contact Area
The tire contact area for any aircraft tire is calculated by dividing the single wheel load
by the tire inflation pressure. If the load is expressed in pounds, and the tire pressure in
pounds per square inch, then the area is in inches squared. The same thing works with
kilograms and kg/cm2 - the result will then be in square centimeters.
The shape of the footprint area is usually understood to be a 1.6 ellipse (as referenced
in the US Corps of Engineer's S-77-1 Report), wherein the major axis is 1.6 times the
minor axis. The calculation to solve for the minor axis is .894 times the square root of
the contact area. Note that the major axis runs parallel to the normal direction of motion
of the aircraft, and the minor axis is perpendicular to the major axis.
Example: 777-300 Main Gear Tire Contact Area
For this case, use the maximum taxi weight of 662,000 lbs configuration of the
777-300 as shown in Figure 7.2 “Landing Gear Footprint - 777-200/300” and
Figure 7.3 “Maximum Pavement Loads - 777-200/300.” Figure 7.2 provides the
main gear tire pressure of 215 PSI. Figure 7.3 shows the V(mg) per strut /
maximum load at the static aft center of gravity for this airplane configuration of
313,900 pounds. Given that the 777-300 has six wheels per main gear as shown
in Figure 7.2, to calculate the contact area first determine the load per tire
(313,900 / 6 = 52,317) then to calculate the contact area, divide the load per tire
by the PSI (52,317 / 215 = 243.3 in2 contact area).
The footprint area is a 1.6 ellipse determined as follows:
Minor axis is .894 x square root of the contact area (0.894 x sq root of 243.3 =
13.94 inches minor axis)
Major axis is 1.6 x minor axis (1.6 x 13.94 = 22.30 inches major axis)
So lets say we have Gladiator loaded to 6250lb at 30psi, 15psi & 8psi
6250lb / 4 tires = 1562.5lb per tire (yes I know, this is discounting weight distribution, go corner weight your own rig and do you own math)
1562.5lb / 30psi = 52.08333"^2 contact area
1562.5lb / 15psi = 104.1666"^2 contact area
1562.5lb / 7psi = 195.3125"^2 contact area
minor axis = .894 x sqrt (contact area)
@30psi = 6.451889052
@15psi = 9.124346372
@8psi = 12.49402982
major axis = 1.6 x minor axis
@30psi = 10.32302248
@15psi = 14.5989542
@8psi = 19.99044772
30psi = 10.32 X 6.45
15psi = 14.60 x 9.12
8psi = 20.00 x 12.50
That's a pretty dramatic increase in contact area that oddly enough has nothing to do with the actual size of the tire. Tire size and subsequent load rating should then be the determining factor for how long and how well any given tire performs in this situation. To take a look at it in very basic terms Load = Patch and Patch should be physically limited by tire carcass dimensions; you should not have contact patch wider than the physical tread width. Which is a long way of saying contact patch determines tire size and not the other way around.
Or even another way, load dictates how much air pressure you can tolerate via tire deformation; the larger the patch gets, the less sidewall you have supporting the load AND the more work an incorrect part of the tire is doing.