Green machine, Great job with that. I do have one question about your explanation. My understanding of and experience with open diffs (principally on Porsches) includes a subtle difference from your explanation. When one wheel has zero traction it receives 100% of the motor's torque. In other words, all torque is still made by the motor, and that torque seeks the path of least resistance; if one wheel (speaking of a 2WD axle now) has less traction than the other but still some traction the torque will go in inverse proportion to the low-traction axle. Which means that if that wheel has zero traction, 100% of the torque will go to that wheel.
To see this in action, get your open diff Jeep or car stuck in snow. Then put a traction block of some sort under one wheel, giving it adequate traction to back the car up. When you apply torque to the rear axle, one wheel stays perfectly stationary, and one spins furiously. This works in a manual gearbox as well as auto, and there is no torque converter in the manual to absorb a small amount of torque (such as when you sit at a light with an automatic, the engine is turning but the car is not moving; the torque at idle is being absorbed by the torque converter. But a manual doesn't do that; it would stall the motor if even a tiny amount of torque goes through the gearbox but is unable to spin a wheel.)
So what I'm saying is, the "small amount of torque, let's say 15 ft/lbs" that in your example was making its way to the wheel with traction, couldn't be doing that in a manual Jeep -- that 15 ft. pounds has to spin something, there's no slop in the system to absorb it. So if it were going to the wheel with traction, and that wheel weren't spinning, the motor would stall.
Another way of looking at it is this: You indicate that the torque will always be 50:50, and that if the spinning wheel only requires a small amount of torque, the other one will also only get a small amount. But the reason that can't be is the motor will make whatever its rated torque at a certain RPM is. It cannot make less torque just because a spinning wheel doesn't require much torque. So let's say that in trying to unstick it you run the motor up to 3000 rpm, and it makes 240 lbs-ft at that point. It has to send that torque out through the gearbox to the diff, and in so doing, to the wheels.
The open differential chooses to send 100% (240 lbs-ft.) all to the spinning wheel, since that is the path of least resistance.
But with BLD, the fact that you begin "adding traction" to the spinning wheel (at least in the "mind" of the open differential) means that it begins handing some torque back to the wheel with traction, since it's suddenly equally hard to spin the spinning wheel. And so it goes back to 50/50, as long as the BLD is willing to apply brakes hard enough to even it back up.
It still may not get you unstuck, of course, if the wheel that used to have traction finds that it doesn't really have enough traction to handle the 120 lbs-ft of torque it's now getting, and starts spinning also. When that happens, whether you have open diff, LSD, or lockers you're SOL, cuz none of them manufacture traction.
To see this in action, get your open diff Jeep or car stuck in snow. Then put a traction block of some sort under one wheel, giving it adequate traction to back the car up. When you apply torque to the rear axle, one wheel stays perfectly stationary, and one spins furiously. This works in a manual gearbox as well as auto, and there is no torque converter in the manual to absorb a small amount of torque (such as when you sit at a light with an automatic, the engine is turning but the car is not moving; the torque at idle is being absorbed by the torque converter. But a manual doesn't do that; it would stall the motor if even a tiny amount of torque goes through the gearbox but is unable to spin a wheel.)
So what I'm saying is, the "small amount of torque, let's say 15 ft/lbs" that in your example was making its way to the wheel with traction, couldn't be doing that in a manual Jeep -- that 15 ft. pounds has to spin something, there's no slop in the system to absorb it. So if it were going to the wheel with traction, and that wheel weren't spinning, the motor would stall.
Another way of looking at it is this: You indicate that the torque will always be 50:50, and that if the spinning wheel only requires a small amount of torque, the other one will also only get a small amount. But the reason that can't be is the motor will make whatever its rated torque at a certain RPM is. It cannot make less torque just because a spinning wheel doesn't require much torque. So let's say that in trying to unstick it you run the motor up to 3000 rpm, and it makes 240 lbs-ft at that point. It has to send that torque out through the gearbox to the diff, and in so doing, to the wheels.
The open differential chooses to send 100% (240 lbs-ft.) all to the spinning wheel, since that is the path of least resistance.
But with BLD, the fact that you begin "adding traction" to the spinning wheel (at least in the "mind" of the open differential) means that it begins handing some torque back to the wheel with traction, since it's suddenly equally hard to spin the spinning wheel. And so it goes back to 50/50, as long as the BLD is willing to apply brakes hard enough to even it back up.
It still may not get you unstuck, of course, if the wheel that used to have traction finds that it doesn't really have enough traction to handle the 120 lbs-ft of torque it's now getting, and starts spinning also. When that happens, whether you have open diff, LSD, or lockers you're SOL, cuz none of them manufacture traction.
