not sure if this info will help you Bob, but in 15 years of oval racing, we were restricted to mandatory open rear diffs in one of the divisions i built cars for, so we had to figure out how to apply upwards of 300 horsepower to the rearend, all the while maintaining minimal wheelspin and maximum forward momentum. not an easy thing to do, especially when required to use a bias-ply tire, which when heated grows like a pimple on prom night.
you need to take into consideration the amount of downward force applied to each tire contact patch(static weight), the difference in circumference between the rear tires (stagger) if any, the approx. radius of the turn, and the crossweight percentage change relative to the amount of static caster setup in front wheels.
an example, we were required to weigh no less than 3400 lbs., with a max. 54% left side, 49% max rear weight.
ideally, we would use the crossweight to load the left rear/right front tires, atempting to get as close to 1000 lbs of static weight on the left-rear. by doing this, and also by adjusting the pre-load using shims, we were able to manipulate an open rearend to act like a locked rearend, driving both wheels with what seemed nearly the same force. now had we not attempted to force so much static weight on the left rear, wheelspin would result, regardless of the amount of pre-load in the diff.
no this is not a mathematical answer, but maybe the example will help you reach your destination......