All guitars do this - they try to eat themselves through their own sound hole - unless they are so overbuilt that they are nearly silent!
Usually they stop after a few years, and then never (or rarely) get worse, unless they aren't strong enough to stand up to string tension. If you put nylon strings on this, there's a good chance it won't move any further.
There is little point trying to correct the dip in the top. Wood is a plastic substance, and takes on a set over time. A fix would involve removing the top, removing the bracing, building a mould of the desired shape, and then removing (or reducing) the deformation using heat and weighted bags (sand or lead shot) and re-bracing. So we can rule that out here, I suggest!
The normal fix is to re-set the neck so the plane of the strings is correct - with the action (height between bottom of string and top of fret) at the 12th fret around 3mm, the string should arrive around 3mm above the top of the bridge. This gives you 3mm of saddle projection, and you can take it down a little once strings are on as the top will probably rise around 0.5mm.
On a guitar like this, the easiest solution I can think of commensurate with its value is:
1. Drill a hole from around 2/3 down the heel from the fretboard through into the body of the guitar to take a bolt - 5mm or 6mm. Countersink the heel enough to get the bolt head below the surface of the heel.
2. Using a flush cut saw with a thin blade, cut from the bottom of the heel up to the bottom of the fretboard, protecting the sides with thin shim stock metal (or tape if you are prepared to keep replacing it). Nylon string guitars don't normally have truss rods, so there should be no metal in there. If in doubt, check with a strong magnet.
3. Get a scrap of something the same height as a fret and tape it on the fretboard next to the nut. Get a 3.5mm drill bit (or wrap a 3mm drill bit in tape until it is around 3.5 mm) - this will sit around 3mm above the frets. Tape that on the neck next to the 12th fret.
4. Work out where your saddle needs to go. Scale length = distance from nut to 12th fret x 2. On a nylon string guitar the saddle needs to be scale length + around 2.5mm on the low E, 1.5mm on the high E. If you are using a wide saddle, say 3mm, place its front edge at scale length + 1 mm and then you can file back at each string location to make the 12th note fretted exactly an octave above that string's note played open.
5. Fit your bridge to the top at that place (or you could fit it where the old bridge was, fill the saddle slot and cut a new slot at the right place). It needs to fit the curvature of the top via sanding (sandpaper taped to the top). Glue it on.
6. Take a straight edge, place one end on the spacer you taped at the nut and rest it on your drill bit - you want it to be 3mm above the bridge at the saddle location. It won't be, so ...
7. Use sandpaper with parcel tape on the back to floss between the heel and the body (push up neck, slide paper in, push down gently, pull paper out without rounding over the sides of the heel - repeat lots of times, remeasuring as you go).
8. Once the neck is correct, insert bolt, tighten nut inside, string up, shape saddle and play! If you want to touch up any chips and blemishes around the neck join, do this before you bolt it on.
9. Once you're sure that everything lines up nicely, you can fill the hole around the bolt head and do cosmetic work. Or leave it, as evidence of how clever you've been.
There are other ways of doing a neck reset, but they all depend on you knowing how the neck is attached and having skills (via practice) that the OP probably doesn't have.
Thanks. I think that I am going to have to read that a few times to visualize the instructions.
It's easier than it first looks. Basically three steps:
Glue the new bridge on in the right place.
Cut the neck until it's held on by just the fretboard, and sand the heel until the strings will arrive at the right height above the bridge.
Bolt the neck on securely.
Frank Ford's frets.com website will talk you through all of these, he is recognised as a world class repairman.
I think the bridge is the hardest part. A new bridge via eBay is cheap, and probably the same size. And you are right to fill the divots with filler to make all flat.
Your problem is that the distortion has moved the bridge footprint a few mm closer to the nut. So to play in tune, either the new bridge goes on maybe 2mm further back, leaving a visible old footprint, or you cover the old footprint and move the saddle back. Option 3 is to make the bridge yourself to fit the new geometry.
I should say I don't do many repairs, though I have successfully done all the things I list. But I've built 50+ ukes and guitars, and I read a lot!
There is one other option to correct the neck angle - release the back/body joint from heel to waist on both sides, clamp the neck in the right place, reglue the back/body joint. That's trickier than it sounds.
The method I outline is easier to get right. Go slow and careful and, apart from the bolt, it might be hard to spot that work has been done.
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