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BTW, with drag racing and reducing air pressure, there's more to it than just the contact patch. Air pressure is typically reduced to slightly lower than desired for optimal straight line traction, due the increase in pressure after the burnout. Also, a reduction in air pressure allows the tire/rear of the car to squat and the tire to wrinkle, allowing for optimal weight transfer.
The relationship of traction in regards to pressure and contact area is not linear, so one can't say that a narrow tire exerting x pounds of pressure will have the same amount of traction as a wider tire exerting lesser pressure.
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