Another Method for Calculating the Area of a Plate

by R.M. Mottola

Originally published in American Lutherie #70, 2002 and Big Red Book of American Lutherie Volume Six, 2013



There are a number of reasons to calculate the area of the plate of a stringed instrument. The area of a flat plate can be used to determine the volume of the instrument by simply multiplying the area by the depth. This value is useful in the design of electric guitars and basses to determine the weight of the body of the instrument before it is built. This info can aid in the design of an instrument that balances well when hanging from a strap or sitting on the leg. In the design of acoustic instruments, the volume can be used to calculate the nominal Helmholtz resonance of the soundbox, which may be useful in the tuning of the resonance characteristics of the instrument.

The technique specified here will work for any arbitrary shape and is both simple and relatively quick. It is the essential algorithm of a CAD script I use, and is based on a computer graphics rasterization technique. Modified and simplified for use with pencil and paper, it yields a good enough approximation of the area of a plate for the purposes outlined above.