alright guys, I know some of you are very intelligent engineers, so this is something that's been puzzling me for a while, please help:
Everyone knows that widers tyres = more grip....or does it?
Frictional force is found by the following formula
F = (mu) * N
where F = friction force
(mu) = coefficient of friction
N = normal reaction force (for our purposes, just assume this = weight force)
so what this means is that friction force is proportional to coefficient of friction between the two surfaces, and also proportional to weight force on the surfaces.
it's also worth pointing out that friction is a reactive force, ie this figure above is the maximum friction force a system can generate in reaction to an opposing force trying to accelerate the object, not a constant force.
Anyway, here's a simple thought experiement:
1. Take a block of steel, with a weight of 100 Newtons (that's about 10kg mass)
2. On the bottom of the steel block, affix a large piece of rubber
3. Place the block on smooth asphalt, rubber side down
4. Attach a rope to the steel block and pull with increasing force until it moves - let's say it takes X amount of force to move it.
Now, take an identical steel block, with rubber on the bottom, place it next to the other, and repeat the experiment. We now have twice the weight, 200N, and as you can obviously imagine, the force required to move them would be 2X
So what this all means, if you look at the formula from above:
F = (mu) * N
with our values from the first experiment, we have
X = (mu) * 100
so (mu) = X/100
from the second experiment we have
2X = (mu) * 200
or (mu) = 2X/100
which is the same as
(mu) = X/100
also from this relationship we can see that if we had 2 steel blocks of only 50N each, the force required to shift them would be half as much as 2X, so again we would have (mu) = X/100
so what this shows is that the coefficient of friction has not changed whatsoever, despite the fact that the contact patch has doubled from the first experiment to the second, and therefore the larger contact patch has not given us any increase in maximum available friction force....
so, does a wider tyre/larger contact patch really give you more available friction force?
(please don't answer this by saying you put bigger tyres on and got more grip, because that's not what I'm trying to establish)
Anyway, one reason I can think of for the apparent increase in traction when you increase tyre width, is that you're also increasing the mass moment of inertia for the wheel/tyre (basically the rotational equivalent of the linear value of mass), which means if you apply the same amount of torque to the wheel, the angular acceleration will be less because:
M = I * (alpha)
where M = moment (torque)
I = mass moment of inertia
(alpha) = angular acceleration
and btw M = I * (alpha) is the rotational equivalent of Newton's 2nd Law, F = m * a (force = mass * accelertion)