Coefficient of friction (µ) of tires on a dry, clean and smooth tarmac or concrete surface. Contact your tire supplier or look on the Internet for specific values regarding the coefficient of friction of your tires. Figures can vary from 0.7 or 0.8 for good "summer" street tires, via 0.9 or even 1.0 for "extreme performance summer" tires, all the way up to 1.4 or higher for dedicated race rubber.
Tires have the highest friction (on a dry, clean tarmac/concrete surface) when they experience approximately 6-8 % slip.* This is in contradiction with most other materials/objects, that experience a decrease in friction when slip starts to occur. In other words: static µ is usually higher than kinetic µ (also called dynamic µ), but not so with tires.
Friction force Ff ("grip") between objects is the result of the product of friction coefficient µ and normal force FN (force perpendicular to the friction surface). So the size of the contact area is irrelevant. Examples are brake pads rubbing against brake rotors, a chair on a wooden floor, etc. All (relatively) solid objects on a solid surface.
With tires however, things are more complicated. Some of the additional factors that can make a difference are for example: Width of the tire, inflation rate, temperature of the tread, tread pattern and flexibility of the side wall. Unfortunately, these factors are not independent variables that can be be plugged into a simple formula.
In general, a heavier vehicle needs wider tires (everything else being equal) to reach the same grip level as a lighter vehicle.
In general, the wider tire needs a softer compound to benefit from it's greater width, everything else being equal.
A wider tire (same rubber compound), could benefit the cornering g's, but harm the brake g's.
Increasing tread width only increases "grip" up to a point (for a given vehicle/road condition). This point could be very close to the "starting width".
On Oct. 5, 2013 I got an e-mail from Joost de Winter (co-author of "An Isomeric Braking Task" and many other scientific papers). Here are some of his interesting thoughts about this subject:
> Wider tires (of the same diameter) do not necessarily provide a larger area of contact. While the contact patch is wider, it also is less deep.
On Nov. 16, 2013 I found a short and simple explanation by Jason Cammisa. Definitely worth reading!
> Wider tires do not necessarily provide more grip per se. Grip comes as a function of (among other things!): tire width, rubber compound, road condition, tread design, inflation pressure, normal force on tire (vehicle weight, down force, weight transfer during braking), etc.
Daryl Garner, M.S., Physics teacher at the Mac Arthur School in Lawton, OK explains it as follows:
It is true that wider tires commonly have better traction. The main reason why this is so does not relate to contact patch, however, but to composition. Soft compound tires are required to be wider in order for the side-wall to support the weight of the car. softer tires have a larger coefficient of friction, therefore better traction. A narrow, soft tire would not be strong enough, nor would it last very long. Wear in a tire is related to contact patch. Harder compound tires wear much longer, and can be narrower. They do, however have a lower coefficient of friction, therefore less traction. Among tires of the same type and composition, there is no appreciable difference in 'traction' with different widths. Wider tires, assuming all other factors are equal, commonly have stiffer side-walls and experience less roll. This gives better cornering performance.
Since I don't see a way to incorporate tread width into the equation of this brake calculator, for optimizing the deceleration of your vehicle I would recommend tires that have the same** or slightly wider tread as the OEM tires, and the highest friction coefficient you can afford, or follow the rule book of the racing organization that oversees your car.
* This is measurable with an accelerometer and two speedometers, one connected to a wheel that brakes and one to a wheel that freely rolls with the speed of the vehicle. An example of slip: while braking in a straight line, 8 % slip occurs when the circumferential speed of the tire tread is 92% of the speed of the vehicle. 100% slip occurs when the vehicle moves but the tire does not rotate. Slip = (Vv-Vt ) / Vv ( Vv= speed of vehicle; Vt= circ. speed of tire)
**Except for vehicles that came equipped with narrow "economy" tires. These can surely benefit from a wider size, since the corner stability of narrow street tires is just not very good thanks to high side walls that flex a lot, also resulting in deformation of a relatively big portion of the contact patch.
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