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Shoulda' paid attention huh!

Two converging lines, the edges of a neck or fingerboard. You know the length and distance apart at both ends. If you pick spots along the way, such as the fret locations or say every .25 inch or so, how can you calculate or mathematically describe the distance from one line to the other?
TIA again

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Tickle your guitar daily, and it'll tickle you back.

John,

If it's a fretboard say, and the width at the nut is a, the width at the soundhole end is b and the length from nut to soundhole along the centre of the fretboard is c, then at any distance l from the nut measured along the centre line, the width of the fretboard (perpendicular to the centre line) will be given by:

width = a + l*(b-a)/c

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Dave White
De Faoite Stringed Instruments
". . . the one thing a machine just can't do is give you character and personalities and sometimes that comes with flaws, but it always comes with humanity" Monty Don talking about hand weaving, "Mastercrafts", Weaving, BBC March 2010

FWIW, I agree with Dave's calculation. The important thing is that you MUST measure "l" from the nut (as he noted above) for the width to be correct for this equation.

Joe

FWIW this equation has one less thing to measure

if you have
y=1/2 distance at nut
L=relevant length of fingerboard down centerline
B=angle between angled edge and witdth
then the witdth is equal to

2(L*tanB + y)

plus it has trig in it which makes it cooler

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"Anything that happens, happens. Anything that in happening causes something else to happen, causes something else to happen. Anything that in happening happens again, happens again. Though not necessarily in that order." Douglas Adams

Thanks David, just what I needed.

_________________
Tickle your guitar daily, and it'll tickle you back.

John , looks like we need to send you the life and work of Pathagreous for your Holliday reading pleasure Just teasing

That would be Pythagoras' dyslexic brother

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Dave White
De Faoite Stringed Instruments
". . . the one thing a machine just can't do is give you character and personalities and sometimes that comes with flaws, but it always comes with humanity" Monty Don talking about hand weaving, "Mastercrafts", Weaving, BBC March 2010

"dyslexic" Fine

John for you work shop wall if you wish. View it and save picture ase then you can print it if you wish

Every thing you wish to know about right angle triangles but were afraid to ask.

Dave White's solution is the best as it involves distances that are easy to measure accurately. Measuring the angle accurately is almost impossible. You'd have to calculate it from the length and the width at each end, which rather defeats the object.

Is that in reference to my posting RT formulas? If so I will disagree as you need not work with nor or measure the angle of the taper to use one of thes formulas but rather you just need to know the hypotenuse and one other leg length. You know the nut length; You know the length from the nut where you want to find the width, you them measure the length of the hypotenuse to the intersection you need to know the width of. So you solve to find the short leg. Short leg times 2 plus nut length is the width of the fretboard at a given long leg dimension. You can measure the hypotenuse as accurately as you can measure any other measured length.

Yes, I really didn't want to go there.

Michael, I do remember some of that although I remember my math teacher calling it the "Square Garage Door Theorem".

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Tickle your guitar daily, and it'll tickle you back.

No Peter, my comment was with reference to J Jones formula which simply used 'tanB'. In this case there's no need for trig, as it's simply a case of proportions, as Dave's formula shows.