If looking in general at handling balance in the case of tyres, the cof drops off as you increase the weight on the wheel and you can tune a car's handling by adjusting the anti-roll bar.
The bigger the contact patch the more grip you can get. In a drag race, dropping the tyre pressure increases the contact patch area and increases grip.
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. As the slip angle increases the sideways deflection builds up quicker so the front of the contact patch works harder. But more and more of the back of the contact patch is sliding and losing grip. At some point you reach a maximum point where more slip angle means less side force because you are losing more grip at the rear of the contact patch that you are gaining at the front.
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 as there is less variation in sideways distortion between the front and back of the contact patch, more of the contact patch reaches maximum grip and starts to slide at the same point.
When you fit wider tyres the contact patch wider and shorter for the same tyre pressure. This means you get a more abrupt breakaway but more grip right on the limit.
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.
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.
However tuning the handling balance using tyre pressures, appears to be a combination of trying to match front and rear slip angles, ultimate grip at the limit, and effect of heat which may effect inflation pressure and tyre compound?
