If you use highschool physics to analyse the performance of slicks on the road, you'd expect narrow slicks to grip as well as wide ones. E.g http://www.stevemunden.com/friction.html
But they don't, because the physics of really pneumatic tyres is bloody complicated...
When you look at lateral grip other factors start to matter. The tyre develops side force because of the slip angle between the tyre and the road. This slip angle means the tread is being pulled sideways by the road surface. At the front of the contact patch the deflection is relatively small. As you move back along the contact patch the deflection increases steadily. At some point, the sideways forces in the tyre exceed the friction between the tread and the road and the tread starts to slip relative to the road. When the tread is slipping like this it produces less grip on the road...
...The longer the contact patch is, the more gradually break away occurs. If you shorten the contact patch, the break away occurs more abruptly but you get more absolute grip at the peak
I.e. if you imagine a really long contact patch in a fast turn, because of the variation of angle and speed across its length, some grip will be lost as rear parts of the patch skid while the front holds. This will happen less in a shorter but fatter patch.
Then it gets even more complicated because real road surfaces are rough, rather than the perfectly smooth ones you imagine in high school physics, and soft rubber tyres interact with this to give an extra source of grip besides simple friction:
If this logic is correct then increasing pressure in the tyre further improves grip, since more pressure = less contact patch area = shorter contact patch = better grip?
However more rubber on the road does help grip due to the hysteresis properties of rubber. As rubber expands to fill a depression in the road, it takes some time to do so. When a tyre is sliding (and due to the slip angle, the rear most portion of the contact patch slides at even low cornering forces), this means that the upward rise of the depression to which the tyre is moving has more rubber acting on it that does the upwards rise on the other side. This allows a pressure differential in the lateral plane, providing frictional resistance over and above that offered by simple friction. As the tyre vertical load increases, the rubber is forced more fully, and more quickly into the depressions, overcoming the hysteresis and reacting on both sides of the upward rise from the depression more evenly – giving less pressure differential and less grip.
So deciding the optimum pressure for a slick is really tricky if you want maximum grip...
Low tyre pressure is better for grip from deformation and hysteresis.
Tuning the pressure is about balancing the contact patch length (which is better as pressure goes up), and the contact patch pressure (which is better as tyre pressure goes down). Even though the optimum grip may be achieved at low pressures higher slip (because the hysteresis element is significant),low pressure increases tyre deflection, which increases heat (less even radius over longer contact patch). It therefore appears that the best way to increase grip is a wide tyre as this gives a shorter contact patch for the same inflation pressure.
Oh well - at least heat doesn't matter to us, but at least now I know that I'm not imagining with when I think Schwalbe Big Apples give insane levels of grip.
Source: I got this from a professional engineer's forum and the next post is from one of Dunlop's senior tyre designers for their motor sport team saying what a brilliant explanation it is...