** I say 'directs torque away from' rather than 'limits torque to the lesser of' simply because I prefer to see it that way, and can understand better what I see happening. I believe the result is the same regardless of how defined. Personally, I believe that without resistance to torque, there is no torque other than in a theoretical, potential sense, and would rather describe open differential performance in terms of available traction rather than available torque. Drive lines don't produce torque, the engine does. The drive line only transmits it. Even when there is no available traction, there is still available a rather large amount of torque potential generated by the power plant, so saying that the differential limits torque to the amount at the free wheel rather misstates what torque is and how it is made, in my opinion.
Useful that you made that point explicitly. Torque is the "twisting force" on a shaft, and is the
product of what the engine/transmisson produces, and the
resistance provided by traction. Without traction, there is no torque (as would be demonstrated by putting a suitable strain gauge on the relevant half-shaft, and measuring it). In other words, torque is produced by the engine
and by traction, together - and the driveline, as you say, merely transmits it.
For our purposes, we can assume that the engine can potentially provide as much torque as could possibly be needed, and therefore, the torque on any shaft will be dependent entirely on the traction at that wheel. Also, we're only discussing the torque required to move the vehicle, rather than bothering about accelerating an already moving car, etc. So traction is indeed usually a proxy for torque.
In fact, though, the real issue is the force actually exerted between the ground and the tyre, which is the "motive" force that makes the vehicle move. Usually, this would just be equivalent to the torque - indeed, the torque is
generated by that resistive force working against the engine. But as soon as we add the use of brakes into the equation, then we have resistance (and thus torque) that is
unrelated to the motive force. A differential responds to torque, and not motive (tractive) force. What you have said so far shows that you clearly understand this, but it's worth saying explicitly, to distiguish between torque produced by brakes, and torque produced by traction.
One might try a simple experiment. In two wheel drive in a vehicle with an open differential, jack one drive wheel off the ground. Then start the vehicle and try to drive away. The lifted tire will spin and you won't go anywhere. While the tire is spinning, tap the brakes and see what happens. If BTM simply does not work, nothing will happen. If it does, your vehicle will probably come down off the jack.
Funny you should say that!
I have previously described just such an experiment, and the results I got:
Here's one of the simple experiments I did, with a series Land Rover, in 2WD, and then the same with a Disco 1 (centre diff unlocked):
I jacked up one of the back wheels, using a trolley jack with casters, on a smooth concrete floor. Then I just put the car in various gears, and experimented with different brake/throttle techniques.
Result?
The Series truck didn't move at all. If there had been any positive effect from the BTM, it was completely offset by the front wheels being braked at the same time.
The Discovery jerked a little bit back and forth on the castered jack. I doubt it would have fallen off its own bottle jack, except perhaps on some of the more extreme wheel-spinning/slamming-on-the-brake attempts. (Incidentally, I also tried this with a front and a rear wheel up on castered jacks, and the centre diff both locked and unlocked).
This was more or less in line with what I would have predicted. Certainly there was no significant or systematic increase in driving force induced by BTM, else the car would have been driven forwards quite easily. I attribute the rocking/jerking to uneven braking forces and some internal friction in the diffs. Subsequently Rob pointed out that the rocking would have been caused by the inertia of spinning up the heavy wheel under acceleration, not braking. The inertial resistance created torque which would have been balanced across the open diffs to the other wheels.
The good thing about this experiment is that it is easily repeatable. If anyone is interested, by all means try it for yourself.
Most of us see and use science in out lives without understanding just why or how something works as it does. So, whether we can formulate a clear explanation for something is less important, in my opinion, than being able to demonstrate that something actually works. If someone has actually used BTM to get a vehicle moving again, why deny them their point of view or reduce the importance of their perspective simply because they can't put into words why and how that something really worked? Not saying you did say that or even suggest it, of course. Only suggesting that even without science on one's side, if they have used BTM to get moving again, it probably does work whether or not we understand why it should be so.
I like other people having a point of view, (though I do have a philosophical aversion to perpetuating a belief in things without foundation). And the fact that so many other people claim to have had amazing success with BTM is the very reason I am trying to understand the mechanism. Given the experiment I've done, it's now also not just a case of trying to understand a possible mechanism, but also to reconcile claims of BTM working in the "real world", and not working under controlled conditions.
I can't think of
any other driving technique or piece of hardware where the principles behind it are not understood. BTM with a LSD? I get that. Spinning a wheel in mud? Clears the tread. Using "fiddle" brakes? Raises the torque on the spinning side of the diff by means of braking, therefore raises torque on the side with good traction too. Keeping revs down? Takes advantage of static friction being higher than dynamic. Etc.
A lot of people who have earned wide respect (including mine), have said BTM works, but even on this forum where there is a huge wealth of knowledge of mechanical engineering and physics, no-one's come up with a consistent explanation of why
equal braking across an
open differential, should increase the
force between the tyres and the ground.
It may also be that brake force evenly applied nevertheless has a differential effect on the two wheels in a stuck vehicle situation because with one wheel spinning freely (or at least faster than its partner), there is more area swept and more brake force generated on the spinning wheel, sufficient that it might shift the traction balance back towards the middle, and allow the wheel with traction to at least turn over and get you moving again.
The "bigger swept area" is intriguing possibility - though I can't really see how that in itself makes the braking
force (and therefore the torque) higher on that side. (The energy absorbed is higher, but in principle that's a function of the same force being applied over a bigger distance). Unless, possibly, the brakes get hot on that side, and somehow bind more?
(I'm also still left with the issue of why it doesn't work in the controlled experiment).
Related: I did think at one point that maybe BTM works with drum brakes because the "leading shoe" effect only comes into play when the wheel is turning, so the spinning wheel is braked more effectively than the stationary one. But as many of the proponents of BTM are driving disc-braked vehicles, that doesn't seem satisfactory.
