Calculating string lift at 12th fret

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Phildo77
Gidgee
Posts: 4
Joined: Thu Apr 14, 2011 3:27 pm

Calculating string lift at 12th fret

Post by Phildo77 » Sun Mar 01, 2015 1:35 am

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

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Trevor Gore
Blackwood
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Joined: Mon Jun 20, 2011 8:11 pm

Re: Calculating string lift at 12th fret

Post by Trevor Gore » Sun Mar 01, 2015 11:04 pm

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
Gidgee
Posts: 4
Joined: Thu Apr 14, 2011 3:27 pm

Re: Calculating string lift at 12th fret

Post by Phildo77 » Mon Mar 02, 2015 9:59 pm

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

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Trevor Gore
Blackwood
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Joined: Mon Jun 20, 2011 8:11 pm

Re: Calculating string lift at 12th fret

Post by Trevor Gore » Tue Mar 03, 2015 8:35 am

Phildo77 wrote: 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!

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