How does reducing surface area increase traction?

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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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Reducing the width of the tire (surface area) will increase the psi of the tire on the driving surface. Increasing the width will decrease the psi of tire on the driving surface. More psi on the driving surface equals greater friction. It’s important to match tire width to the weight of the vehicle as well as the use case and driving surfaces / conditions you expect to encounter.

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