I would like to know what the largest size tire I can but on a 15" GTU rim. I've got a TII and have 225/50 16" on the stock rims, but I don't want to use my street tires on the autocross track. What size will give the best preformance?

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Typically, you don't want to put a tire on that's more than 1" wider than the rim, otherwise you get bulges in the sidewall and it might not seat against the bead properly.

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SuperchargedRex
New name, same old knucklehead
Supercharged '88 SE -> The Ultimate Sleeper