I just put some new tires on the rear of the Kart. The tire shop set the tire pressure at 38 PSI -way, way too high. I proceeded to air down the tires but then wondered, "what SHOULD it be?" I've never taken the time to decide what the correct pressure should be on the Kart now that it weighs over 1000 lbs less than it did from the factory. Previous tires, I didn't GAF about so didn't take the time to think it over, but they were ~25 lbs. Ride and handling were fine.

Without the engineering resources, testing time and facilities, and relationship with "my OE tire provider", I decided to use the stock tire pressure and car weight as a starting point, and try to match the results that it provides. The stock car weighed about 3300 lbs, and was about 50/50 F/R so ~825lbs on each wheel. The stock recommended tire pressure is 35 lbs.
825lbs/35 lbs/in² = 23.5 in² contact patch. Knowing that the Kart has ~400 lbs on each rear wheel, quick algebra shows me that 23.5in² *x=400, x=400/23.5=17.0 psi. 17 lbs (about 1/2 the pressure) to achieve the same 23.5in² contact patch with about 1/2 the weight on the tire -that jives.
In reality, the Kart tires are bigger than the stock car's tires were: 285/40R18 on the Kart, vs 275/40R17 originally. So, the larger tire should be able to carry the same weight with less air than the stock tire, but I'm going to ignore that to err on the side of more air pressure.

All that being the case, anyone see any glaring issues with this method?

 

Use the tire temp method. Take it for a drive, measure temps across the tread, take notes. PSI is right when temps are even across the top

 

Great idea. Will do Thanks!

 

You can also use a chalk line as a reference for how much sidewall flex / contact patch you're getting.