Here's my take on tire pressures with our Fleet on the Tacoma.
Starting with the original tires from Toyota:
Toyota's placard pressures for the P rated tires are 30psi, front and back. The
empty weight of our truck, fully fueled with two people (we weight 160 and 120 lbs) was
2700 lb front, 2000 lb rear.
Max axle weight per placard are
2910 lb front, 3280 rear.
So why does Toyota recommend 30 psi for all four tires? No idea, but a couple ideas are they are trying to keep it simple, optimize for gas mileage, braking performance, traction, etc. Let's say the truck is loaded with 800 lb over the rear wheels and the passengers weigh 100 lb more than we do. Then both axles have 2800 lbs. This makes my thinking easier. It seems like a typical scenario that Toyota's engineers may have assumed.
The Kevlar tires that came on the 2018 truck are rated for speed T, 112 load index which is 2469 lbs/tire at 35 psi, max 51 psi. There are no table values past 35 psi. For trucks, P rated tires are to be derated 10%. Per
https://www.toyotires.com/media/2125/application_of_load_inflation_tables_20170203.pdf (apparently Toyo tires are sized a little differently, so I did a little interpolation) the tires are
rated at 30 psi for 2275 lb each tire.
Derating by 10% reduces this to
2068 lb/tire.
So if we load the truck to 2800 lb/axle, and have the capacity of 2 times 2068 lb/tire, then the tires have a "
safety factor" of (2*2048)/2800 =
146%.
Overloading the truck and using E rated tires:
So then we got a camper, loaded it with water and camping junk, etc. and our axle weights went to:
2800 lbs front, 3600 lbs rear. Front is ok (max axle capacity 2910 lbs), rear overloaded (max axle capacity is 3280 lbs). We added Sumosprings which leveled out the truck and it seems to work well on and off pavement. We bought BFG KO2 tires, E rated which have tougher/more plies, and should use higher pressures.
I never found out why E rated tires need higher pressures. Perhaps the more plies create more heat. I've read that heat really damages tires, so under pressurizing is bad news.
After reading the toyo tires link above, it appears the basic method for E rated tires is to keep a similar safety factor. So I ran these numbers for the E rated tires in the same document, derating by the 146% factor. Their method is worded differently, where they ask you to use the rating at a certain load, but I think it amounts to the same thing. Maybe I'm interpreting this wrong, but it seems to match other methods I've seen mentioned*.
So I took the line for the LT265/70R16 Single tires, multiply by two tires per axle and divide the capacity by 146% for the same safety factor, and get this:
psi 35 40 45 50 55 60 65 70 75 80 Wheel weight (lb) 1,820 2,000 2,170 2,335 2,500 2,655 2,835 2,955 3,105 3,195 Axle weight (lb) 3,640 4,000 4,340 4,670 5,000 5,310 5,670 5,910 6,210 6,390 146% 2,267 2,491 2,702 2,908 3,113 3,306 3,531 3,680 3,867 3,979
So I weigh the axles and pressurize according to this chart. For mine it's 45 psi front, 65 psi rear. The 65 seems too high, so getting emotional about it and worrying about too harsh a ride, I use 45/55! That's the illogical conclusion. But I've only been on one long trip so far and will try the higher pressures next trip. Off pavement, very rough roads we've had success with 15 front /20 rear psi.
By the way, your flatbed with extra water, etc probably weighs more than ours. We've removed some stuff to lighten the load too, like the bed extender, not-full tanks most of the time, and lightweight backpacking gear.
*Other methods include:
http://www.fourwheeler.com/how-to/wheels-tires/1801-the-pressure-where-should-you-run-your-tires/
and lots of anecdotal ramblings you find all over on line that are not scientifically based. One was from a tire dealer that made absolutely no sense! Lots of people on line say "I've always done such and such, and it's the only way to go", but I didn't find the reasoning very compelling.