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Longitudinal grip - used when you're accelerating or braking (tire length)
Lateral grip - used when you're turning corners and steering (tire width)

Below is an example of some common tire sizes and their respective contact patches for the Hellcat.

It takes into account a 4439 lb curb weight (~ 954 lb load per rear tire), 20x9.5 (for 20 in tires) and 18x10 (for the 18 in tires) and also accounts for various tire size load indexes:

275/40/20 (106Y)
285/35/20 (100Y)
295/35/20 (105Y)
305/35/20 (104Y)
305/45/18 110V

Here are the results:



Of note, a larger contact patch increases the chance of making ground contact while a stickier tire and load (weight) on that tire will increase the coefficient of friction with the ground. A general indicator of a stickier tire is a lower wear rating (e.g. All Season is 400 vs. Summer is 220).

http://www.drivingfast.net/car-control/grip.htm
 
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