The subject of this made me think of something that's useful to keep in the back of your mind... The OP titled it "Working tire pressure = Contact area ???"
I know after reading what he was asking, but I'll add some other useful info, as I deal often with maximizing vehicular mobility in general over rough terrain...
On ANY tire, you can equate tire pressure to ground contact pressure, as long as you're on a semi-hard surface. So if you have 80psi in your truck tires, the tire is touching the road with roughly 80psi of contact force. (averaged over the entire contact patch.) If the surface is softer, and cannot support a contact pressure corresponding to tire pressure, the surface will deform until it has achieved a lower contact pressure by increasing the contact area. Any time surface deformation needs to happen, traction suffers. A good example of this is wheel hop in softer conditions... Wheel hop is the result of the surface not being able to hold the contact pressure, and deforming to achieve a contact pressure that can be supported. You'll find that as you lower tire pressure, the surface will need to deform less, and wheel hop is reduced. If you lower pressure enough, wheel hop will be virtually eliminated, and you'll notice that your tracks don't appear to deform the surface much at all.
(climbing onto my soap box...) For CUT tractors, which often do much more loader work than "ground engaging" work, I find that tire sizing is completely wrong... We really need larger tires on the front to carry the weight better. With ground engaging work, like plowing or discing, the 3pt pulls down, weighting the rear tires and de-weighting the fronts, so small front tires are fine. Since typically, that's what tractors did, it became the norm. But with increased loader work, and decreased amounts of ground engaging work that most CUT's perform, it makes no sense to have small front tires... For the scenario common to most CUT users, similar size tires front and rear would make much more sense. I realize that turning angle would be obviously limited as the front tires get too large, but but most CUT's could easily have been designed with front tires several sizes larger, and at least closer in size to the rears, which could often be smaller and would still work fine.
The worst example of this that I can think of is the LS 3xxx series tractor. I referred to it as the "T-rex" of tractors when I was looking. The rear tires are HUGE compared to the tiny front tires. Why?? No good reason, I assure you. Search for stuck pics of this model, and you'll almost always see the front buried. Tires too small for the load they're subjected to on soft surfaces. This is an odd contrast to the 4xxx series, which has much larger front tires relative to the size of the rears.
Running either end at full pressure all the time is akin to running all four of your truck tires at full pressure. Tire wear suffers, traction suffers, surface damage suffers, ride suffers, and they become much easier targets for punctures. There is NO REASON you should be doing this on ANY tractor.
OK, I'll climb down. Please use tire pressure to your advantage. You'll find much improved traction, and mobility, and you'll ease the work for your tractor as well, particularly in soft conditions. Meanwhile, I'll continue to watch for a more reasonably designed CUT to come out.
Oh, and rest assured that tire pressure does not significantly change the revolutions per mile of any tire. You can run the front's nearly flat, and the rears at max pressure, and not affect the drive ratio by enough to even notice. It has to do with the fact that the same amount of "belted" rubber has to contact the ground. You'll find people saying differently, but in the tire industry, those people are called "the uninformed".
I wish you all success in your quest for better mobility!!
