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I'm hoping someone out there can correct my understanding or help me understand better of how an open differential distributes power to the wheels of a vehicle.

So picture a RWD vehicle that has one of it's back tires lifted off the ground, if it has an open differential; the tire in the air gets all the power, leaving the other drive wheel and the vehicle stuck on the ground.

Now imagine the same vehicle driving along a boundary of two surfaces, the one side being on ice, and the other dry pavement. Both wheels are heavily loaded and have sufficient contact with the surfaces they are touching. Does the same thing happen as if the wheel was in air? i.e. Does all the power from the engine go straight to the wheel on ice?

Is there a general rule for how it would distribute the power? I can't help but picture it being almost like a linear relationship, i.e. if the force going in to the differential was 900N, and the one tire had 2 times more friction (not sure if that is the correct term in this context, but imagine a brake rubbing against the side of the wheel), then it would receive 300N (half as much as the other side). But this doesn't make sense at all, as the gears are free to rotate there must be a point where they only transmit power to the one side (i.e. when the tire is in the air), or am I wrong here?

Or does it behave like an on/off switch, where each wheel gets equal power up until a point, and if so is there a way to calculate that point?

I only have a high school education in physics, so I'm hoping the general solution is simple enough for me to understand.

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Yes. If one wheel is on ice (or in slippy mud) and one wheel on rough tarmac, the ice-contact wheel will spin. This is why off-road vehiles have a diff lock. Note however that the spinning wheel is not receiving very much power as it is doing no work. The better concept here is torque.

It's really no different from you standing on ice and pushing on a tree. By Newtons' third law you are pushing on the tree with the same force that the tree is pushing on you, yet your feet will slip and the tree stay put. Similarly the differential is applying an equal "rotating force" or torque to both wheels but the one easiest to move is the one that spins.

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  • $\begingroup$ Does this mean the wheel with the least amount of force required to move it is what determines the amount of force the differential applies to both wheels? For example, say one tire requires 100N, and the other requires 105N. Does the differential only apply 100N and thus the one that requires 105N wouldn't even move? $\endgroup$
    – Buretto
    Commented Aug 19, 2019 at 16:48

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