i dont see any evidence given to support the
15 percent is optimal
claim

the fact it is a round number suggests that
it was chosen arbitrarily

and while there is a caveat that
rough rides need more and smooth rides need less
the idea that one magic amount of drop
is best for all tires
is a bit hard to swallow

however
it probably gets people closer to the mythical
optimum pressure
than guessing and squeezing the tire with the thumb

also
when i find my tire sizes and approximate wheel loads on the chart
it is pretty close to the pressures i like to run at
based on experimentation and personal preference

to the op
good job on the forumla

try to also
derive a formula
where nominal tire diameter
and desired drop
are entered

that would cover the weakness i see in your forumla as written
there is no compensation for wheel diameter
which should change everything as the length to width ratio
of the contact patch changes
and
it only works for 15 percent drop