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The problem is with the variance in outer diameter, the differentials could detect the difference in wheel spin (the worn down tires have faster rotation and engage) - burning the differential out. This is the problem with AWD or 4WD and having different tire sizes.

I don't know your specific tire size but for the sake of argument lets say 265/60R17. A nice SUV/CUV sized tire.

The outer diameter would be 29.52 inches X 25.4 = 749.81 MM.

The three tires that are worn down we need to remove 8mM, remember, for outer diameter you need to include it twice, one for one side and one on the other. So the od on the other tires is 741.81 MM, or 29.21 inches.

The difference is total od is .31 inches.

The new tire will travel 92.73 inches in a single revolution.

The older tires will travel 91.76 inches in a single revolution.

This thankfully is close enough for math to call it one inch.

At 60 MPH, driving for an hour you will travel 3,801,600 inches.

Your new tire will revolve 40,996 times to "roll" 3,801,600 inches.

Your older tires will revolve 41,430 times to "roll" 3,801,600 inches.

The difference is 434 less revolutions on the new tire, per hour at highway speed. That is about 7-1/2 revolutions per minute.

Now here is the magic question after all that math - is that variance enough to make the differential engage? To make the system think three wheels are slipping and the fourth wheel has better traction. If the answer is yes - it is going to get expensive when the differential overheats and eats itself.

The one assumption in this math is the tire size. The bigger the outer diameter, the bigger the difference 4MM makes. The smaller the outer diamater, the less difference 4MM makes.
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