Everywhere I read on tire pressure for bikes I hear that lower pressure gives you increased control and climbing traction. Lower tire pressure gives you more surface area between your tires and the ground. Whatever the frictional coefficent may be of the surface you are riding on (and your tires), the frictional force (traction) is independent of the surface area, correct? Your tires should slip under the same force no matter what the tire pressure is according to classical physics right? (This of course is not intuitive and I am not sure I belive it) This is because the Normal force increases on each individual particle as surface area is reduced and decreases on each particle as surface area is increased. So the product of force and particles is always the same for almost all material.