Ok Duders...
This is a Turtle back...sorta like a bowl back but way way different.
Bowl backs have each stave identical...well most of them... and the staves have one curve in them.
Well a Turtle back has no 2 staves the same...other than left and right...and looks like a Turtle
shell . Staves are all different lengths, and different arcs bent in to them and a twist into the stave on both ends.
They are compounded curves...first the arc and then the twists.
This instrument is gonna be an 14 stringer, a Sympatar, 7 above the finger board starting with a low C string and 7 sypmathetic strings under the fret board and tuned to A at 435 hz. So chew on that for a while. Gee me might even fret the sucker...just for to make it easier to play
I do trial and error, scribe, cut and fit and fidget around. Wouldn't have a clue how to do a drawing that someone could follow. I ain't got the grey matter to figure out the maths but I suppose it is possible.
Here be drawing.

Here be pic of standard bent stave on right, then a twisted stave and the one I am holding shows the twist and the fact that the glue edges are not at a 90 degree angle to the face and so the two edges and two sides form a parallelogram.

Here I have taped on two sticks and taken the shot from end to end to show the extent of twisting on some of the staves.

a bent stave

the first stave has no twists...it starts on stave 2 and 3 and then it really starts on the 4 and 5 - right and left side which you can see in the upper left of the photo.

the 4-5 and 6-7 stave are pretty much the same....but with staves 8-9 the arc takes a recurve cure at one end ...gentle at the wide point and not at the base of the instrument.
Here is blank unbent stave #8 with its penciled in ark

Band sawed and being bent on a BBQ starter shoved into a 2 inch exhaust pipe. Works great!

Next shot is the start of the test fitting and shaving by shoot edge on plane and bending and twisting and shooting the edge until it fits .

Rough fit

see where the ends have to now get the twist bent in


As it is impossible for me to calculate the maths for a compound curved edge curfing...the kurfed linings were installed a half inch proud of the rib and then are carved and filed for each individual stave.

Takes about 1-2 hours to hand scribe, bend, twist and fit a stave to the previous stave and on to the rib before it can be glued into place.

The next photo shows the recurve starting between stave 7 and 8.


The next three pics should make it easier to see.



Here you can really start to see the turtles shell. This was taken looking down the neck from the back of the nut.

So there you have how to bend up a turtle back. Believe me, it ain't no piece of cake. However if approached with the right attitude and patients is not all that hard. Medium to advanced bending skills and edge jointin ~ shooting the arc on that bent stave ....simply because the staves start to show more and more end grain and end grain is easy to shoot a joint in one direction and a real challenge in the other.
.
So here is the Turtle back off its work board.
The overhand has been rough trimmed.
Next I will continue to sculpt the back of the instrument with scrappers.



Removing the weight by trimming the curfing back. I over installed the kurfed linings in order to have some meat for trimming and scribe fitting each stave to the rim.



Conclusions on staving. Well first thing noticeable is the weight is much light than the first bowl back of a few years ago. I am very pleased with the seams...came out much better than I had hoped for...bliss...near perfect... only one small spot showing light that maybe a sliver of wood or filler will take care of. Some of the curves are a bit drastic but they still work and can be worked down more gracefully with a scraper. The bulging back and the recurve actually tilt the instrument so that the fret board is quite visible without tilting the instrument or learning forward...you know "guitar neck" The shape is interesting. Don't know if I fancy it. On the next one I will start the twisting on the second and third staves, use narrower staves and lessen the recurve, this will allow for a slightly larger volume enclosed and a more graceful curve to the back.
Ok, on to figuring out some sort of top for it.
======================================================================
Two years later....
So me pulled out a lutz top of some flavour or other a Mario DaCosta special from Sprucetonewood.com, glued her up and thicknessed it.
This morning me finally resolved the rosette for it. It is based on one of my old mandala paintings.
see mandala painting

see resolved rosette.

Me just printed it out, shellacked the sound board and gonna glue her down in a few more min.
Is gonna be a fun carve...stick around for the ride.
blessings
duh Padma