The Cantenary Arch

The main arching of a violin, viola, cello, and this Archtop guitar is formed on the inside with catenary arches.

A catenary arch is what you get if you stretch a chain out, and let it dangle:

That is what it is, but what we are really thinking about is the other way around; like this:

You see it all the time on concrete overpasses.  I see it on the steel truck beds.  They are almost flat when loaded down, but rise up like this photo above when they are empty.

A catenary curve is very strong.  We don't want violins and guitars to be VERY strong.  They have to vibrate.  But the stronger we design them, the thinner the wood can be.  This makes the response faster.

Of course, wood choice has a lot to do with this as well.  The bellies usually bring much more to the table sound wise than the backs do.  The Euro Sycamore, Acer, that I'm using for the back is just starting to have some sound to it.  It is still quite thick, especially around the edge, but now I can get a series of ring tones that were suppressed by the wood itself before.  The curly redwood belly is as thick as can be right now, and it shakes with resonance.

Everything on the inside is checked with the chain.  Just a 2 foot chain from Walmart.  The ends are set in from the edges.  Further in on the lower bouts, and closer at the middle.  There is more recurve on the lower bout than the middle.  It helps to draw it out first.  With violin posters it is easy to do.   This one is another story.  I carved inside and out until I had an idea, and then I went with it.

There is a full diagonal cross arch from the bass top to the treble bottom.  The diagonal cross arch from the little wing to the bass bottom is broken up.  They meet at the point where the first diagonal arch went.  The top end is deeper, giving a very curvy, stiff area.  The other end is more like the arch on the other side.

There is also the same kind of arch down the centerline.

The cross arches go through the diagonals, and end at the centerline.  But at the top things are different.  The cross arches there start out perpendicular to the diagonal arch.  They go from edge to edge, and through the diagonal.  The small wing is almost centered on the diagonal, and the diagonal is the deep point.  The bass side isn't, and the deep point is further towards the neck.  When the cross arches get past the area where they go from end to end, they gradually change to cross arches from the side to the middle.

It reminds me of the line pictures you see of finite element analysis.  Each design constraint pulls on the other, and the final shape is the smallest way that the surface can be draped around the form.

On the outside I mark the point of inflection.  The outside can be roughed really close to size across the middle, and fairly close up to the point of inflection.  I have this down to about 4.5 mm or so at most of the inflection line; except for the ends.  From there the thicknesses taper to 6 -7.5 mm in the middle.  That's about as far as you can go until you define the finished outline, and cut the recurve on the inside in.

The part at the top will have to wait until the recurve is cut in.  It seems to be a lot more complicated.

Yes, I am going to have a tapered Guadagnini button.