Calculating string lift at 12th fret

[Phildo77]

Hi there,

has anyone used the Theorem of Intersecting Chords to calculate the string lift at the 12th fret as per book? (p4-91)

I have been able to calculate the curvature of the fretboard due measured neck relief.

However I am struggling to work out CX (string lift).

I know AX, BX and CD, but unsure of how to find CX (string lift).

If CD is 2x radius of curvature = 112m x 2 = 224m and CX=CD-XD (XD must be almost as big as CD in order to get an answer for CX of 0.5mm.)

I'm assuming the AX.XB=CX.XD equation is meant to be used, but can't find XD?

The relationship between neck relief and string lift seems to be a factor of 5, but I'd like to see how the Theorem is used to get this answer.

A worked example would great, apologies if I'm missing something very obvious.

Cheers

[Trevor Gore]

Just looking at the second part of the problem:

AX.XB=CX.XD (Equ. 1)

AX=XB= half the design scale length. As you point out, CX=CD-XD. Hence XD=(112-CX) (Equ. 2)
as CD=112 from the first part.

Substitute for XD (Equ. 2) in Equ.1 and solve the resulting quadratic equation in CX.

Get back to me if that still doesn't make sense.

[Phildo77]

Thanks Trevor, I originally tried substituting for XD and when I saw the CX^2 and CX thought I must have taken a wrong turn!

Have solved using the quadratic equation and got -0.515mm (25.34" scale length/0.1mm relief), which matches up with what you suggest in the book.

I'm a massive fan of the books and appreciate you taking the time to answer my question.

Cheers

[Trevor Gore]

Have solved using the quadratic equation and got -0.515mm (25.34" scale length/0.1mm relief), which matches up with what you suggest in the book.

Well done!