Liutaio Mottola Stringed Instrument Design



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Calculating Bridge Height of the Flattop Guitar

American Lutherie #111 featured an article I wrote about all of the properties of the geometry of the flattop guitar that combine to determine the total height of the bridge and saddle over the surface of the top of the instrument.1 That article included a number of diagrams and all the math needed to make bridge height calculations for most styles of flattop guitar. This page includes a calculator that will do all of those calculations for you - you just fill in the blanks and press the Calculate button. For the most part the descriptions of the parameters here are self explanatory, but for all practical purposes you'll need to reference the article for its diagrams and terminology before using this calculator.

Initial appearance: Spetember 9, 2012
Last updated: November 25, 2017



The formulae for caclulating bridge height as a function of the construction geometry of a flattop guitar are:

Calculating Total Bridge Height

h a = 2 s

h b = b n + f

h t = b n - b e l ne * l

l jb = l 2 n / 1 2

h n = sin a π 180 * l jb

i = r t - r t 2 - l jt 2 2

d = i + r t 2 - l jb - l jt 2 2 - r t

l r = l - l 2 n / 1 2 - 0.056 l 2

r r = s r 2 + l r 2 2 s r

h r = r r - r r 2 - l - l jb 2

h = h a + h b - h t + h n - d + e - h r

where:

h = total bridge height (calculated);
ha = the part of total bridge height attributable to the action (calculated);
hb = the part of total bridge height attributable to the total thickness of the fretboard and frets at the nut end (calculated);
ht = the part of total bridge height attributable to longitudinal thickness tapering of the fretboard (calculated, subtracted);
hn = the part of the bridge height attributable to neck angle (calculated);
The part of the bridge height attributable to arching of the top (calculated);
The part of the bridge height attributable to elevation of the fretboard (calculated);
hr = the part of total bridge height attributable to relief (calculated, subtracted);
s = action, measured at the 12th fret;
bn = thickness of the fretboard only, at the nut end;
be = thickness of the fretboard only, at the body end (not needed unless fretboard has longitudinal thickness taper);
lne = length of the fretboard (not needed unless fretboard has longitudinal thickness taper, but specify it if you know it);
f = height of the fret crowns above the fretboard surface;
l = nominal scale length of the guitar;
n = the number of the fret at the neck/body join;
a = the angle between the nominal plane of the top and the underside of the fretboard, in degrees;
d = height of arching of the top at the bridge, measured from the nominal plane of the top (Use zero (0) for a truly flat top. Leave blank if you want the calculator to calculate this value for a spherically domed top.);
rt = radius of the top doming. Leave blank if a value for d above is specified. Note that this must be in the same units as all the other values;
ljt = length of the top along the centerline (not needed if a value for d above is specified, but specify it if you know it);
e = overstand, elevation of the fretboard (zero (0) if no elevation);
sr = relief, to be measured between the first fret and the fret at the neck/body join;
ljb = distance from the neck/body joint to the nominal bridge position along the fret plane (calculated partial result, not shown);
i = height of the apex of the top arch (in the center of the body, which is not usually where the bridge is located) (calculated partial result, not shown);
lr = half the distance between the first fret and the fret at the neck/body join (calculated partial result, not shown);
rr = radius of the relief curve of the fretboard; (calculated partial result, not shown);

If values for lne and ljt are specified, the calculator can check for collision between the top and the underside of the fretboard. Note that a collision or a lack thereof is not necessarily a good or bad thing, but must be accounted for in the construction of the instrument. Again, see the referenced article for more information about this.

References and Suggestions for Further Reading

  1. Mottola, R.M. “Fretboard/Top Plate Geometry of the Flattop Guitar” American Lutherie, #111