Interesting article. Calculating the best grip conditions for a tyre is a subject of mechanical engineers master degree and it is modelized through differential equations. Something that is certain though, is that when fitting wider tyres, the contact surface does not change. It remains the same, if the tyre pressure is the same before and after. Increasing the tyre pressure (which is often suggested on larger tyres)
reduces the contact surface !
Lets say we have a 185mm wide tyre and lets say our car's weight is 1000Kg and that the front/rear weight ratio is 50-50. This means that each wheel gets 1000/4=250Kg of weight. Lets say that the tyre pressure is 28psi = 1.968 Kg/cm²
So the effective surface on which the weight will be distributed is
(250Kg) / (1.968Kg/cm²) =
127cm² ( pressure is force / surface )
Now lets say that we upgrade our tires with new, wider ones, lets say 205mm wide and we increase the tyre pressure to 30psi = 2.1Kg/cm²
The effective area that the same load (250kg) will be distributed is
(250kg) / (2.1Kg/cm²) =
119cm² which is SMALLER than before. This is because we increased the pressure while having the same vertical resultant of the forces ( = 250kg)
What happens in real ( in between limits ) is that the contact surface's width may have increased, but the "length" (the other dimension) gets smaller. If it wasnt, we would have different pressures on the inner and outter surface of the tyre at the contact area!!
Now there is another debate.. the physics say that the Friction is INdependent of the surface's size ( T = n * Fk , where n = coefficient of friction and Fk is the vertical sum of forces ). But it is generally believed that the wider tyre ( = smaller contact area since we usually increase the pressure) gives better grip !! Confusing ha? Well, what happens is that for some reasons the
n increases on wider tyres. This has to do with the rubber's better quality and different characteristics, which can only be modelised by tyre engineers, since it includes dynamic parameters that alter as the car moves and the tyre rolls.
Also the fact that the tyre construction combined with specific tyre pressures gives maximum grip at corners (where the touching surface changes shape and size) cannot depend on the tyre pressure only, because on such conditions the vertical forces are altered, so we cant know how much each factor affects the friction since we re talking on different speed, different turn curve etc.
Go figure