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why not start a fresh and make a new one.
is that the neck end or the box end in the picture?
personally I would scrap that piece of wood because your never going to be happy with it.
it is already giving you grief and more,just put down to lesson learnt
I'd make a new neck(for what it would cost! a new piece of wood.)
you could knock up a new neck in an hour or two and if the box is buggered to make a new one too.
as for your friend tell him sorry things haven't worked as planned and that your going to make a new one.
so that is only option and easiest thing to do.
once you've sorted the guitar,go back to the 1st cock up and see where you went wrong.
no doubt the penny will drop.
in time of desperation and rushing, believe it or cock ups go hand in hand.
take your time and think things through.
take it from me your not the 1st nor will you be the last.
a small rabbit at the top of the fingerboard will hold the bolt.
No the drawing is not mathematical, it is a quickie sketchto show the strings going down into the headstock, like on a classical guitar in the other picture I posted.
Here's another pic to illustrate, a double bass has a severe break angle, and uses tuners where the capstan is parallel to the nut, and does quite well with it.
check out this headstock by another member, http://www.cigarboxnation.com/photo/cigar-cask-3-str/next?context=user
So here is a basic drawing to depict a bolt on style neck. I switched to this style because of all the challenges to get a "neck-thru" to work. Especially if one plans to include magnetic pickups...in which case, the neck thru needs a chuck cut out of it to get the mag pup installed...which makes the neck weak. That's just one reason for me, since I primarily use mag pups.
So in the drawing, the box profile is the black line (this varies depending on box). The tan is the neck blank, the dark brown is the fretboard. Notice the FB is a little higher than the top of the box.
The orange section are two pieces of wood. The longer one runs from tail to front, inside the box. This provides a solid foundation for the bolt on neck, and when paired with the smaller orange piece, a place for a tailpiece for strings, and a foundation for the bridge are created. Plus it gives all the structural strength needed to deal with the pressure of strings pressing down on bridge/box top...i.e. no more crushed box lids.
There is still enough box lid left to "resonate". The only cut needed on the box will be a slot 3/4 inch deep, and as wide as your neck (likely 1.5"). * (note: the long "orange piece" that the neck bolts to will need to be tall enough to reach the bottom of the cut out on the box that you make for the neck.)
It's really easier than it looks. I just picture the box as if it's the body of a solid body electric guitar, like a Stratocaster, etc. I carefully measure and mark where the box will be cut, and use a sharp Exacto blade to make as much of the cut as possible. Especially on the box top, for a clean seam. A good box dimension for this style of build is where the depth of the box from the inside surface of the bottom of box to the top of the lid outside measures close to 1.5".
This means that the slat of wood (the longer orange one in the drawing) which is 3/4" thick, paired with the 3/4" thick neck without the fretboard attached, brings the surface of the bare neck flush with the box top. So then when you attach the fretboard, the finished neck rests 1/4" above the surface plane of the body. This results in a string height over the body of approximately 5/15" to 3/8", depending on scale and action you create by the type of bridge you use. This string height allows for a good playable string height over the body. One bonus to this design, is that magnetic pickups have plenty of space inside the box, without the need to cut into a "neck-thru" designed neck, which later requires extra bracing and headache.
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