Nothing to do with contact patch. It has to do with air volume. 17" wheel has less air volume than a 15" wheel of the same size tire and would need higher psi for the load capacity part.
That being said, load carrying capacity is only one of many factors that go into the recommended tire pressure for a specific vehicle. The general rule is don't go lower than the door placard but you may need to go higher if the load capacity requires it.
Just a few things besides load carrying capacity that tire pressure affects- rollover tendency, stability, spring rate, hydroplaning, steering, ride quality, tire heat buildup, etc etc. The engineers take this all into to account in addition to just the load carrying capacity.
You will notice most all vehicles have a tire pressure of at least mid 30's even though that load capacity far exceeds what is needed and that is not by accident.
Interesting stuff. So, if I run my 30x9.5 Load Range C tires at 29psi, how would I go about determining the proper pressure if I moved up to a 31.5x9.6 R17 tire?
