How important are the tyres in this case (snow, gravbel, etc)?
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Very important. In general smaller and with a v shape is always better for snow. Better to push the snow out from under the tire.
Are you sure about that graywolf? If that's true then ABS is very close to the optimal brake performance. When ABS was introduced I think they alternated between completely locked wheels no brakes at all. The ideal brake assisting system would use the technique Wide and I has described. If that's what a modern ABS does between the locking it's great, but the car industry is scared by the thought of having a computer controlling such vital functions of the car...
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May be that's the Electric Brakeforce Distribution (EBD) instead of the basic ABS system?
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So if you manage to brake as hard as possible without locking the wheels,
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To clarify what I said earlier. ABS works by keeping the tires operating at as high a force as possible without locking. (what I meant by optimal brake force) That is it's sole purpose. ABS can and does do this better then any human can (if it is setup properly.) The abs system uses a speed sensor in the wheel to detect at what point the wheels are decelerating faster then the tires can cope for. At this point they begin to pump the brakes. On each pump they give just enough force to equal the friction of the tires(when setup properly). Then they let off.. then they hit it again. In this manner they don't stop the wheels from spinning completely or to a point where they are spinning to slowly which would cause lockup. Remember a wheel is a spinning object. Brakes effect the spin of the wheel before they affect the lateral acceleration. The reason abs is better then a human when properly setup is because a human simply cannot pump brakes as fast as a machine even if they know what they are doing.
EBD shares the same parts as ABS but is different. It varies the force based on where it is needed. As such it can move brake force foreward or aft.. left to right.. depending on which wheel needs it most.
On a side note abs is not going to help you for turning as much as people here seem to be pushing it. As you turn the force your tires can handle is equal to that of lateral grip+braking+accelerating. As such while abs is better for turning, under heavy braking it is ebd that will save you from spining.. Not abs.