Does anyone know the equation used figure out the hole size/placement and length of an instrument as compared to the width and shape?

Example: Flutes with wider bores would have to realign the placement and size of the holes and also the length to make the flute's scale in tune. What equation are the makers using to do this? Or is this one of those things only mathmaticians know?

The reason I want to know is because I was thinking of learning how to make my own instruments(like fifes and ocarinas).

Thanks

Benade's book, Fundamentals of musical acoustics has most of the formula's

If you want to get started practically. Pete Kosel's flute-o-mat has the formulas for design in a Java program. I've made quite a few whistles and fifes using his handy designer.

http://www.cwo.com/~ph_kosel/designs.html

There are links to Peter Hoekje's spreadsheet with the formulas located here also

and the flute-o-mat design page

http://www.cwo.com/~ph_kosel/flutomat.html

Joe B

Of course for flute-like instruments we could go back to Boehm:
"Die Flöte und das Flötenspiel" (The Flute and Flute-Playing) is avaiable translated.

http://www.midi-classics.com/p1513.htm

" In it he covered the acoustics of the instrument; the technique for establishing its proportions ....."