Last year I needed to find out what pressure to use in a certain caravan tyre loaded at 60% maximum. I thought there would be readily available a formulae to calculate this; but I could'nt find it anywhere on the internet. I asked one of the major manufacturers, but they said it was "restricted information"!
The pressure to use at maximum loading for any tyre is easilly found, either from the data stamped on the tyre itself, or from various websites.
Eventually, I obtained the booklet "Tyre Tips for Caravan & Trailer Tents" from the BTMA*. This has tables for some tyre sizes showing pressures to use at loads below maximum.
So I plotted out a graph for each size, using % of maximum pressure as one axis, and % of maximum load as the other.
I found that all tyre sizes produced points on the same line (within about 2%), so I therefore had the formulae (down to about 40% load).
So, to replicate this, get a piece of linear graph paper with the axes designated 0 to 100 (%).
Label one % max. load, the other % max. pressure.
Put two points, one at 40% max. load, 30% max. pressure; and the other, of course, 100% both.
Draw a straight line between the two.
You can then relate this to your particular van.
Eg a 195/70R14 has a load index of 91 (615Kg per wheel), (at 36psi).
If on a van weighing 800Kg., load per wheel = 400Kg which is 65% loading. The graph shows 59% pressure = 21psi.
I submit this in good faith but without guarantee as to its "correctness".
If you have "solid" information that contradicts this graph, please post it.
Note the booklet pressure tables show AXLE loads, whereas the Load Index Table shows per wheel load.
*BTMA 020 7457 5040 (they also do a booklet for motorhomes), don't think you can download or order them online.