Originally posted by A.B.:
IMHO Limited slip differentials are of great benefit when driving in sand especially when crossing dunes, extracting another vehicle or starting to move from a stop in soft sand. With an open differential, the instant a tire looses traction it will start to spin and dig itself in, as the open differential will transfer all the engine torque to the spinning tire. That’s what it’s designed to do; send all the torque to the tire that rotates faster. A limited slip will make sure that some of that torque goes to the other wheel, which might still have some traction. A locker does even better since it splits the torque right smack in the middle between the 2 tires.
I've read many of your posts, and given your excellent grasp (and experience) of things 4x4, this is a rare opportunity to, ahem, correct you on a fairly crucial factual point. :-)
If an open diff did what you describe above, I would agree that a diff lock (or lsd) would make a significant diffrence to traction in sand.
However, an open diff doesn't send all the torque to one side. In fact, it always
torque on each side. It allows one side to rotate faster than the other, but the torque (and hence the motive force) on each half-shaft will be equal. The torque on the shaft is a product of the driving force from the tranmission, meeting a resistive force from the ground. If one wheel is on (say) ice, the resistive force on that shaft will be very low (not high), and the wheel will spin. An open diff is incapable of supplying more torque to one shaft than the other, the torque on the other wheel will be limited too, even though it is on firm ground with a high tractive resistance. The torque on the "good" side will fall to the same level as the wheel slippery side, and it may stop turning.
Even though it may be stationary, that wheel is still contributing the same amount of forward motive force as the spinning wheel. (Just as a person pushing a vehicle may be contributing even if he is not actually succeeding in moving).
Hence, with an open diff, both wheels always contribute the same motive force.
If you lock the diff, then the only limit to the torque on a sideshaft is the resistance from the wheel (assuming you have plenty of power from the engine and gearbox). Each shaft has a different torque. The one on the ice is still low, but the other one is no longer limited to the same low figure. It will rise until either the vehicle starts to move, or that ground also gives way, and both wheels are spinning.
The important part of the above is that a diff lock only adds torque to one of the wheels, and it often only adds a very small increment.
Two examples to illustrate the extremes (using a 2WD with a diff lock, for simplicity):
1) Assume the vehicle needs a total torque of 1000Nm to start to move up the slope.
* Left wheel on wet ice, maximum of 100Nm of torque supported before the wheel starts spinning.
* Right wheel on good rough concrete surface, maximum of 2000Nm of torque supported before the wheel starts spinning.
Open (unlocked) diff: torque on left wheel 100Nm, torque on right wheel, 100Nm, Total 200Nm, vehicle stuck.
Locked diff: Torque on left wheel 100Nm, Torque on right wheel 900Nm (then the vehicle starts to move, so no increase in torque). Total 1000Nm, vehicle moves.
Here, where there is a big difference in the traction conditions, a locker increases the torque by a big amount - from a total of 200Nm to a potential total of 2100Nm (though not needed).
2) Assume same total torque requirement of 1000Nm
* Left wheel in sand, ground supports 400Nm before giving way.
* Right wheel in slightly firmer sand, ground supports 500Nm before giving way.
Open diff: torque on left wheel 400Nm, torque on right wheel, 400Nm, Total 800Nm, vehicle stuck.
Locked diff: Torque on left wheel 400Nm, Torque on right wheel 500Nm, Total 900Nm, vehicle stuck.
With the small difference in the traction, a locker increases the torque only marginally - from a total of 800Nm to 900Nm. Obviously I chose the specific figures to illustrate the point, but notice how in the second example there is only a very narrow range of traction conditions where the diff lock would make a difference.
With just a bit
more traction under the left (spinning) wheel (100Nm extra), the vehicle would have driven out even without a diff lock, because the total torque would increase on both
wheels - i.e. by 200Nm.
This may seem over-technical, but the salient points are that a locker provides the SUM of the two torques, whereas an open diff provides twice
the LOWER torque. Therefore a locker offers a very small advantagee when the traction under both wheels is similar, and a great advantage when there is a big difference in traction condtions.
For the record, I have lockers in my vehicle, and have occasionally found them useful in sand. But they are much more value in mud, and absolutely indispensible in rocks or axle twisters, where wheels lift off the ground.
Anyway, like too many of my posts, I have rambled on... sorry! :-)