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Is a locking differential the recommended approach to a steep slippery climb situation? Seems it wouldn’t be the recommended approach to a slippery boat ramp where you need the front wheels to stay dry or end up on YouTube. The driveway would have to be unevenly iced with no stretch of ice under both rear wheels for a locker to work.....
You're right, a rear locker won't help much at all with both back tires on ice. What a lot of people don't understand about open diffs is that they always drive both tires equally. People see only one tire spinning and assume the diff isn't sending any torque to the other tire. But it's getting the same amount of torque the spinning tire is getting.
All a locker can do is give you the additional torque that the non-spinning tire can support. Sometimes that's a LOT. Like when one tire is in the air and the other is stuffed into a rock. But when both tires are on ice they are both getting about the same traction, so you don't pick up much more out of the other tire.
With a locker spinning both tires you will be less stable. A spinning tire doesn't care which way it moves, so a locker will let the back end slide around side-to-side more than an open diff.
So is a locker the recommended approach to a steep slippery climb? It will help some, but probably not a lot. Better tires or better weight distribution will usually help more (although a van's weight distribution isn't that bad). Putting a barrel of sand beside the driveway might not be a bad idea either!
All that said, it will help some, and if there are ice patches where only one tire is losing traction, then it will help a lot.
Ah yes, moving sideways. Like when you opt for cheap ladder snow cables with those crimped on thingies that prefer to roll than break ice, rather than proper diamond pattern snow chains.