[mahout]

I don't know enough about tires on road to know if a tire on normal asphalt has a constant coefficient of friction but it isn't a violation of a law of physics for an increase in tire pressure to have no effect on braking or cornering as long as the tire hasn't lost it's grip.

First, the basic friction law F=uN is for non-deforming surfaces. Rubber doesn't fall in that catagory. Think of it as a deformable surface penetrating a non-smooth surface. Depending on the tread pressure (not the tire pressure) the deformable surface squeezes into the pits in the non-smooth surface, the tentacles in the road surface creating more than 1 g of 'adhesion' more like a gear than a fruction surface. (if you want a funny time research the argunments in drag racing prior to dragsters getting over 1 g acceleration, There were many proponents that dragsters could not accelerate faster than 1 g and opposed by those who took the side of rubber deforming into the pits and literally hooking up to get g forces as much as 3 or 4 to 1.)
When that Texas dragster ran a quarter-mile in less the 9 seconds at over 156 mph the argument was settled. Indy Cars and F! as well as dragsters depend on maximizing that pentetration with strong tentacles.

Second, its a big argument now whether tire contact surface change is directly related to tire pressure. I'm on the side that is doesn't because the structure of the tire interferes. When the tire pressure or tire structure changes the contact patch is changed but not directly related. An example would be supporting the vehicle on 2x4' or 2x6's. The load doesn't change but the surface pressure changes. A tire is more flexible than a 2x4 or 2x6 so there is an effect but not directly related. Thats why making suspension changes to suit weather or track is so diificult. Its one thing to change surfaxce pressure but another to maximize tentacles into the surface that are strong enough to hold without breaking,
PS changing tire pressures is mostly used not only to affect the road surace patch (hence the tentacles) but also to change the spring on the suspension. Drives NASCAR crew chiefs wild. And Goodyear techs.