Propeller pich adjustment

Hi guys,
Is there any empirical equation for calculating how much the propeller pitch should be decreased or increased to fit the target RPM?
For example:
A boat on WOT is performing 3900rpm with propeller of 23" of pitch.
As the engine nominal (max.) power is achieved at 3600rpm, I`m wondering about how much should the pitch be decreased to achieve this 3600rpm as engine working point?!
I`m not talking here about the rules of thumbs because they are well known (200-300 rpm change for 1" of pitch or 1" of diamater means 2" of pitch):idea:, I`m wondering here if there are any formulas to be more accurate in predicting this change.

If there are no such an equations, in which way would you try to calculate this?!

I`m asking that beacuse when you send a propeller to some offical propeller workshop (Proposcan or some using Hale MRI) they say that according information about the present engine rpm, they can calucate how much the pitch should be changed in order to fit the target rpm.

Regards
Bojan

 

Formula is simple:

dP=P*(1-RPM0/RPM1)=dD

dP - change of pitch;
P - existing pitch;
RMP0 - required RPM;
RPM1 - reached RPM;
dD - change of diameter;

Formula is valid for +/-10% changes after trials.

 

What is the manufacturer's recommended maximum RPM of the engine - 3600? In a fully loaded state, fuel, people, etc., if you are still getting 3900RPM, I would consider it a long-lived engine and keep the thing running easy. No simple formula to get it exact other than rule of thumb with too many variables. The guy with the prop calculator can get it pretty close with enough information (hull, transmission, engine, weight, etc.) Probably want no less than 3,700 RPM fully loaded.