Chalk test, or classic formula for calculating pressure, works good when tires are 75 aspect ratio (or at least 70 to 80 aspect ratio) and the tire's section width is approx 2" to 2.5" wider than the wheel width.
This is one reason I like my tire/wheel size relationship to conform to what I said in first paragraph. For example, 225/75R15 on 15 x 7, 235/75R15 on 15 x 7, 30x9.5R15 on 15 x 7, 31x10.5R15 on 15 x 8, 245/75R16C (31x9.5R16C) on 16 x 7, or 265/75R16C (32x10.5R16C) on 16 x 8. There are larger examples too. All these have approx 75 aspect ratio and a tire section width 2" to 2.5" wider than wheel width. This works really good on and off road and gives a flat contact patch at street pressure. This is approx the formula used by engineers who set up stock SUVs, at least back in the day when SUVs were still made to go off road.
If you get outside that relationship, like a wide tire on a narrow wheel, or a tall skinny tire with aspect ratio larger than 80, you can't get a flat contact patch at a reasonable street pressure. So then you have to always air down for off road, then air back up for on road, and your on road pressure will not give a flat contact patch (until center treads wear down).
Guys set up for hard core rock crawling like to use wide tires on narrow wheels so they can use very low tire pressures without losing a bead. For other off road terrains it works fine if you air down. The wide tire, narrow wheel, combination is not ideal on road (because you can't get a flat contact patch at a decent street tire pressure.
If you had a traditional tire/wheel relationship (like I prefer), you wouldn't be setup for rock crawling, but you'd be set up fine for all other off road terrains and setup ideally for on road. Also, you wouldn't need to air down for off road, unless conditions were extreme. For most off road conditions I don't need to air down. My contact patch is flat at street pressure.
Since your tire/wheel relationship is non traditional, I assume you have a rock crawler set up (wide tire, narrow wheel). You won't be able to get a flat contact patch at a reasonable street pressure. You'll have to find the best compromise psi. When your center treads eventually wear down, you'll finally have a flat contact patch. It sucks, but that's what happens when you put a wide tire on a narrow wheel.
Other fellows with a wide tire, narrow wheel setup can help you figure out the best possible compromise tire pressure for your tire/wheel combo. I suggest follow their suggestions, and realize any psi you run is a compromise (when wide tire, narrow wheel).
Tires with aspect ratio larger than 75 (tall skinny tires on small diameter wheels) have similar contact patch problems at street presssures, especially when aspect ratio is larger than 80. An 85 aspect ratio tire like a 33 x 10.5 R15 or 255/85R16 (33 x 10 R16) will have similar contact patch problems at street pressures.
This is why I prefer a 75 aspect ratio tire that is 2" to 2.5" wider than wheel. It works good and has no contact patch issues. This set up corners good, gets decent gas mileage, and has good traction on mild to moderate off road conditions without needing to air down. For extreme off road conditions, air them down a little.
Warning: I often edit my posts a few times to get them complete or correct errors.