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Wouldn't the area of tire deformity be equal on both? A wider tire has more area than a skinny one, but less of it is in contact with the ground at a particular moment.
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For any given moment, yes. Per mile however, the fatter tire has a larger square footage making and breaking contact with the road. That square footage has to deform over every imperfection in the road. Visualize a roll of toilet paper unraveling. The fatter the roll, the more square footage it's going to cover per mile of length.