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With a normal differential, the power goes to whichever wheel is easiest to turn. Under normal circumstances both wheels get power because there is not sufficient difference in traction coefficient between the tires to make one wheel easier to spin.
However, in the rain or snow, a normal differential will send power to only the one wheel.
A fully locked differential sends power to both wheels all the time. While this seems like a good idea at first, it is necessary for cornering for the outside wheel to turn faster than the inside wheel, which is not possible with a fully-locked differential since with a fully locked differential both wheels spin at the same speed all the time.
What a limited slip differential does is combine the two. Under most conditions, it behaves like a normal differential, allowing the outside wheel to spin faster in turns. However if one wheel spins faster by a certain percentage not encountered in normal cornering, the limited slip differential slowly begins to send more and more power to the wheel that is not spinning, giving the car more opportunity for traction.
This also helps in putting power down when coming out of a corner since the inside wheel typically has a much lighter load on it and tends to spin coming out of a corner. With a normal, or "open", differential, all power would go to that wheel and the car would lose momentum. With a limited slip, power is sent to the non-spinning wheel and the car maintains momentum.
Aaron
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Silver 1998 Volvo S70 T5 <- Daily (Anja)
Guards Red 1986 951 <- Seattle car (Gretchen)
White 1976 914 2.0 F.I. <- Prodigal car, traded away then brought back again (Lorelei)
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