On car tires, shoes and other such items, having less of the material in contact with the surface underneath increases traction. Why is that? Isn’t friction a function of the contacting area and speed?
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Friction has *no relationship to contact area*, or to the speed of the materials.
What matters is what two materials are in contact.
Where surface area can start to have an impact in practice is basically the ‘probability’ that puts two two materials in contact.
Wide tires allow a tire a high chance of being in contact with concrete. Which has a high amount of friction with the rubber of the tire.
But some situations, like a wet road, a wide tire may not find the concrete. In some of those cases a narrow tire may be able to push one material (water) out of the way, to make contact with the concrete underneath.
To throw a complication on top of this, wide and narrow tires are typically made of different materials as well.
Wide tires usually have softer rubber and better grip. One reason they are wide is to reduce the pressure and wear on the softer material. Note that the width in this case is not to ‘improve grip’ directly. The width does allow the use of a material with better grip though.
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