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A wider tire that has the same height as a narrow tire, has less pressure on each square inch of the tire because your spreading the same weight over a wider area. The Narrow tire will bulge more to support the same weight, and lengthen the contact patch. Tire width does simply just change the shape of the contact patch. Sidewall stiffness and tire pressure will change the contact patch size, but with the same tire pressure, load, and sidewall stiffness, the contact patch size will remain the same with wider and narrower tires.
It is also true that a longer contact patch will grip better in a straight line than a wider contact patch, this is because straight line traction depends on traction along the tire.
A wider contact patch will grip better in corners because your applying lateral force to the tire that requires traction across the tire.
Tire compounds, sidewall stiffness, tire pressure, and suspension set up will have the greatest effect on achieving a particular performance.
Tire width has more to do with tire temperature control, a narrow tire will run hotter because of increased pressure applied. A wider tire will have less resistance, but they are typically heavier making the rest of the car work harder to accelerate, stop, and turn.
Drag racing is a little different because you run low tire pressures and soft sidewalls to increase contact patch, also the suspension is set up to transfer weight to the rear tires for increase pressure on the tire.
If you wanted more straight line traction without a suspension set up that could transfer weight, you would want a taller/narrower tire.
When I use to drag race my 280ZTT with the stock suspension and simply firmer springs and shocks to handle the power, I ran a 6 inch wide racing slick and ran 10.08@ 140 MPH in the 1/4 mile. The same diameter slick in a 8 inch wide tire was almost 1/2 a second slower.
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10:58:09 12/28/12
