Why has the max angle of the slope not been mentioned? Wouldn't that be part of the equation?
My understanding was, maximum slope with a wheel tractor is around 18 degrees. With boom mowers and stuff you can radically change that, or with articulated tractors you can negotiate steeper slopes obviously, but as a general rule of thumb, 18 degrees start engaging the "pucker factor".
But even here, loaded rear tires is not a huge part of the equation. Again it is physics...
The limiting factor of a tractor tipping over is the amount of angle the FRONT AXLE oscillates. Sure, we have al side loaded the bucket, stopped quick, the tractor came up on three wheels, but never went over.
Why?
It rolled easily to that point because the front axle pivoted until it hit the frame. Again, physics: three points in space make a plane.
The second that happened though, now the tractor has four points to overcome to keep going over, and unless excess speed, or a loader bucket is up to high, or a down hill tire hits a gopher-hole, the tractor has to do A LOT to flip over.
Loading tires does not really help with the center of gravity because those fluid-filled tires are tilted at 18 degrees or more too. Remember: if your front axle is hitting the frame, then your front axle has stayed level with the terrain (18 degrees), but if your high, rear tire is off the ground, your rear-end is going to be several degrees steeper than the hill you are on. That means the fluid at the top, on both tires, is located DOWNHILL by 18 degrees or more. So some of that fluid filled weight is working against you, not for you, in trying to force the tractor to roll over.
But it takes an awful lot to roll a tractor once that front axle hits the frame. A whole new set of physics takes over.