Hello all. I’m hoping you can help me with a semantic issue. It involves off-road driving and the distribution of torque.

Question 1: Imagine you have a vehicle with 3 locking differentials. And all three are locked. And the surface that you are driving upon, at the current moment, provides traction to only one wheel. All three diffs are locked and there is no wheel spin. Do we say that 100% of the torque output is going to the one wheel with traction? If not 100% then how much? (Let us discount mechanical losses and other inefficiencies.)

Question 2: Now imagine the same question - all three differentials locked – but now two wheels have traction. Does each wheel receive 50% of the torque? Or do both wheels still get !00% of the torque, or is the torque split based on the weight distribution of the vehicle across both wheels, or what? This is relevant in terms of evaluating how much stress is being put on various components, so damage can be avoided.

Let’s leave it at those two questions for now. I have others, but depending on how these two get answered the others might answer themselves.

I know locked center full time 4wd/4H part time 4wd is 50/50 but I'm not sure if it's 50/50 again at the diff meaning 25% to each corner.

In the case of all axles locked, 1 wheel on the ground, torque is distributed 50/50 front and rear to each locked axle, but 100% is getting applied at the one wheel with traction.

Your scenario is faulty. You can't really have only one wheel with all the traction (the vehicle can't "stand" on one wheel like a unicycle). Gravity will pull it down one way or another until at least two wheels are on the ground. Granted, each of those two wheels may have different amounts of traction (one on hard surface, the other in mud), but each of those two wheels will give some force to move the vehicle proportional to the amount of traction each has.

A better way to look at this is to keep in mind that with all differentials locked, all wheels are forced to turn at the same rate, period. Those that have some contact with the ground, will propel the vehicle in proportion to the amount of traction they have. Those wheels that don't touch the ground will simply spin in the air at the same rate as all the other wheels -- the differentials are locked.

Question 2: Same rules apply -- all wheels are forced to turn at the same rate. Those that touch the ground will provide some force to move the car; the ones in the air contribute nothing to moving the car, even though they are spinning at the same rate as the others.

Torque is a force. You cannot apply torque to a wheel unless there is a resisting force (traction due the the wheel touching the ground). This physics rule applies here: for every action (force/torque) there is an equal and opposite reaction. If a tire is in the air, there is zero torque going to it even if it is spinning madly.

Another way to look at it is from a "work" prospective. Work is done if energy is transferred from one thing to another -- in a car case, energy from the engine is used to move the car.

Ok, for you semantic purists, it is possible to have only one wheel with traction if the car is high centered: one wheel touching the ground and all the others dangling over huge holes in the ground.

But the same rule applies: with all differentials locked, all wheels are forced to turn at the same rate. The wheel that touches the ground will provide some force to move the vehicle. The others will just spin in the air and provide no motive force.

Let me propose a slightly different, real world scenario, that actually happened to me a few times, and I'm sure a lot of other drivers that go off road.

The SR5 4Runner does not have locking differentials from the factory, but it does have a transfer case that locks the front axle to the rear axle, forcing the two axles to turn at the same rate.

Suppose that you come to two pot holes that leave diagonal wheels off the ground, one front wheel and the diagonal opposite rear wheel. If the car is fairly balance, it can rock back and forth supported only by those two wheels. I call that the "teeter-totter" mode. Since the axles are forced to turn at the same rate, the wheels over the holes will spin and no force is transferred to the wheels touching the ground; the vehicle doesn't move.

Two ways to get out of that predicament:

1. Have the passengers move around until a third wheel touches the ground. Really hard to do and scary as hell if the holes are really deep, necessitating rocking at a sharp angle to one side.
2. Fortunately, the SR5 has a nifty "Atrac" button that engages the traction control system. In Atrac mode, the spinning wheels will be braked, allowing some energy to go to the wheels touching the ground. Attention Required! | Cloudflare

This actually happened to me on Imogene Pass is western Colorado. We sat there for several seconds, not knowing what to do, wheels spinning in the air. Fortunately, before I realized I could use Atrac, the car very slowly tilted to one side until a third wheel touched the ground, then off we went.

This.

Fully locked (Front, "center", and rear) - every wheel gets 25% of the torque regardless of what is on and off the ground.

Open - the wheel that requires the least amount of torque to spin will dictate the amount of torque being applied to all other wheels. It takes say 20lb/ft of torque to move a wheel in the air so in that case, if you are completely open, you would only be getting that 20lb at the others (regardless of what your engine makes) and it isn't enough to actually move you.

ATRAC just uses the brakes to increase resistance on that wheel that is spinning so more torque can then be applied to the wheels on the ground.

This is my point exactly. This sounds good to me, but I think it’s wrong.

As an aside, I read that when the Limited’s center diff is unlocked the torque split front to rear is 60/40. I couldn’t understand how it could be that the front and rear prop shafts could turn at the same speed but deliver different torque. After a lot of research I learned that the reason has to do with the gear ratios in the planetary gear set in the center differential. When the center differential is locked, then the torque split is 50-50 front/rear.

Thanks for that reply. Could you explain a little further? 100% is getting applied? 100% of 50%? Or 100% of 275 ft-lbs coming off the crank shaft? (Again, let’s not concern ourselves with mechanical losses etc.)

The motor is supposedly putting out 275 ft-lbs of torque. In the scenario I outlined I think the single wheel with traction is getting most of that torque, and not ½ or ¼. No?

It’s a hypothetical. A framework in which to discuss the use of the term “torque”.

After someone educated me and after some reading, that 60/40 is not a constant but a max variance value when there is slip.

It is my understanding that the Limited 4Runner has a Torsen (Torsen - Wikipedia) center differential. The Torsen differential is a right down weird device that can send most torque to the wheel that is NOT spinning.

Many full time AWD cars are noted for having Torsen center differentials, including Subaru, Audi, and my VW Passat 4Motion (AWD).

Torsens are probably the most interesting design. Just gears based on the interaction (or lack of) between worm gears and sprocket gears. Almost no maintenance totally gear driven and doesn’t take any input to activate or deactivate and you can choose a bias ratio that suits your application (obviously Toyota chose it)… would make sense to use in an AWD center. I think they used to be in more than just the limited IIRC

As previously mentioned, torque cannot be applied anywhere that no other force can be applied. If all diffs are completely locked, then all power would be going to a completely fixed drivetrain and yes 100% of torque would be applied at the single wheel where it has traction. the rest of the drivetrain would not apply any force except drivetrain loss since they are spinning freely.

Transferring the torque to where traction is, is the concept of how a-trac works by applying opposing forces to the free spinning wheel(in the form of braking) to transfer power to where traction is.

Yes. If you open the Wikipedia link I gave above and scroll down, it says they were used on these Toyotas:
Toyota: 4Runner (All 4WD 4Runner from 2003-2009) and 4Runner Limited (2010 to present), FJ Cruiser 6-speed manual, Toyota Landcruiser 200, Toyota Landcruiser 120/150, Toyota Fortuner, Toyota Land Cruiser Prado, Toyota Sequoia, Toyota Celica GT-Four/All-trac ST165, ST185, ST205, Toyota Caldina GTT and GT-Four