Calculating Guitar Side Height

by Mike Doolin

Originally published in American Lutherie #75, 2003 and Big Red Book of American Lutherie Volume Seven, 2015



Back in American Lutherie #58 (Big Red Book of American Lutherie Volume Five), Jon Sevy published the article “Calculating Arc Parameters” which described how to calculate the radius, length, or depth of a curve. I’ve used these formulae extensively ever since for radiusing fretboards, making dished workboards, calculating neck angles, and even nonlutherie shop tasks. Recently it occurred to me that one could use them to calculate the height of a guitar’s side at any point. If the guitar has a spherically domed back, the back falls off from its highest point in an arc in every direction, as in the photo.

This “high point” is effectively the North Pole of the sphere from which the back arch is taken. If we assume a top whose perimeter is all in the same plane, as in Fig. 1, that plane intersects a line of latitude on that sphere. The high point is therefore the point on the back which is farthest from the plane of the top perimeter. All measurements of side height are then distances between that plane and the surface of the sphere of the back arch. I adapted Jon’s formula to calculate the falloff from the high point on the back to any point on the side: