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Which launches faster: P85/19 or P85/21?

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I've heard that 19" tires have greater contact area. Does that mean that you get better launch from P85/19 over P85/21?
Not with stock tires, no. Equivalent tires, the same. The contact patch on the 19"s is a few percent larger, so there's not much chance of it being noticeable even with timing equipment. Given the 21"s don't slip when launching, the additional grip of the 19"s on equivalent tires doesn't buy you anything.

Equivalent tires, despite the smaller contact patch the 21"s will likely have a slight advantage in the corners due to the stiffer sidewalls. This will be offset by the higher unsprung weight of the 21"s, which is a big factor in how the car feels as it changes direction.

Finally, I didn't run the numbers but I'd suspect the staggered 21"s on the P85+ have a similar contact patch to the 19"s AND stiffer sidewalls, which would give them better performance both linearly and laterally.