It is hard for me to see how this can be done with math. But those who do it that will say I am wrong.
I won't disappoint: You're Wrong!!! :-)
Actually, I misread his post -- I thought he wanted to know where to put the CG on a ship that's built, not how to design the ship so that, once built, it'll be right.
A long time ago there was an article or two on designing stunt ships. What it said in its most basic form was to measure the distance between the LE and the spinner back plate. Then you use that measurement between the flap and the leading edge of the stab. But I could be wrong about that. It might have said to measure from hinge line to hinge line. If I was going to do what your talking about I would get out a set of Nobler plans and measure the moments of it. You know nose length and hinge to hinge. Using these dimensions you will be in the ball park.
... and you'll just be building a Nobler with different aesthetics.
The reason the math part is wrong for me is I do not know how to do it. Besides that it is subjective. The weight of the wood finish etc are all unknown. I think that is why so many ships are an evolution of several models.
Not so much subjective, as subject to guesswork. You can estimate the weight of the finish, and for the rest of it you can monitor where your center of gravity is going to be as you build. I've done pretty good that way -- with some spectacular flubs along the way.
Just find the point where you want the CG, calculate all the moments around that point, and make sure they add to zero. It's easy as pi (calculating pi, that is), except where you estimate the finish weight wrong...
This I do know. The Cg should be at the thickest airfoil section at the wing root. Forward of this is stable aft of it is unstable.
Half of that is half wrong, but the last half is right.
Where the CG lands depends on the planform of the airplane -- that's what the article that I quote goes into.
Most stunt planes are designed so that the CG should be somewhere around 25-30% back from the leading edge of the wing, and
most stunt wings are designed with the thick point there, too. But that relationship is largely coincidence. Use a funky airfoil with the thickest point ahead of or behind the 25% point and you'll still need the CG to be around 25% -- it won't change at all with the airfoil change. On the other hand, make the stabilizer really, really big and you'll be able to move the CG back (in fact you'll have a wider range of good CG locations). Rip the stabilizer off and you'll still have a plane that can be made stable and fly -- think flying wing, or combat ship. Build a canard, and the CG will be in space, between the two wings.
Etc.
(make your stunt ship so weird that the CG doesn't land somewhere fairly close to the 25% point, and see if you have a chance to make it fly nice...)
Another thing to remember is that the finish process ads weight to the aft section of the model more than the forward part. I hope by jumping in here and making some statements others will also jump in and agree or disagree and the end result will be good information for you.
I check the CG before finishing, to see if I can lard up the tail or if I have to make it really light.