The Stovebolt Site Forums The Parking Lot Big Bolts tandem axle power divider

Hi all. I'm new here, posting because the "mental puzzle" aspect of this is something I've always appreciated. My short answer is that the original poster is totally correct about the "torque" being equal on both sides of an open differential (whether an inter-axle differential or any other of an open design). Note that this is not the same as power distribution, and all statements about "power" distribution are actually not addressing the question. Since an inter-axle differential is functionally the same as the differential between right and left wheels, let's use the differential in a single-axle truck to decribe what's going on.

Example #1:
Say for example that a single-axle truck is stationary and 450 pounds of "push" from the wheels is necessary to get it moving. One wheel is on hard ground and has far more traction than what is needed, but the other wheel is on snow or mud and can only generate 200 pounds of traction when spinning "uselessly". In this case, the truck is stuck and it won't move. While the one wheel spins, what's the other wheel doing? It may not be spinning, but it IS supplying traction, 200 pounds worth to be exact, just like the spinning wheel. The nature of an open differential is that the torque output on both sides is always the same, no matter what (ignoring the small amount of friction losses within the gear system). That's why it's misleading to talk about where the "power" goes. Sure, the only place power is being used in this case is where the spinning tire contacts the ground (the power in this case is only being used to generate heat, rather than move the truck), but the total tractive effort is 400 pounds, shared equally by the right and left wheels. Since the truck needs 450 pounds of traction to move, a person pushing on the back is all it takes to get it going. However, IF the stationary wheel were indeed accomplishing nothing, as so many people believe, the truck would be stuck much worse instead of "just barely".

In summary, the wheel that doesn't turn in this situation DOES have torque applied to it, and it's the same amount of torque that's applied to the wheel that's spinning on account of having too-little traction. BOTH wheels are pushing even if only the one with poor traction is spinning. Their combined effort in that case just isn't great enough since the wheel with good traction can never push any harder than the wheel with poor traction, or more accurately, both wheels always push with the same force because the TORQUE on the two axles is always equal.

Example #2:
Imagine a truck with a locking differential with one wheel on very slippery ice and the other on hard ground. A truck with an open differential would be terribly stuck in this case, but when the right and left axle shafts are locked together by the locking diff, both wheels turn together and the truck gets moving easily. In THIS case, the torque applied to each wheel is not the same (there's almost no torque applied to the wheel with almost no traction), but contrary to what most people think, the power is not shared equally between them either. Nearly all the work being done to move the truck is performed by the wheel with good traction. Power is mathematically related to the work being done, so where the work gets done is ALSO where the power is expended (to illustrate, note that you can't measure the horsepower of an engine unless you provide an opposing torque). Thus, if traction is unequal between the two sides of a locked differential, power application is unequal as well. It is incorrect to say that the power is distributed equally when the differential is locked.