And the advantages of he concave style would be.....?
Background into the design philosophy (from my end). First off, I can never tell the difference between concave and convex so I will use my language of cove vs. quarter round. Not suggesting that one is better but instead that each has its particular application. I designed the cove to 1) maintain surface area for gluing surfaces 2) minimize weight 3) improve (in my eyes) aesthetic appeal. The soundboard face glueing surface is maximized. The side face glueing surface is maximized. Weight is reduced by removing material from the areas which are not attached to or used as glueing surfaces. The disadvatage/expense of the weight removal by using the cove, as opposed to the quarter round, has already been addressed in your previous post. So both the cove and quarter round are successful in 1) Maintaining surface area. 2) The cove has an advantage over quarter round in weight as it weighs less (assuming the design philosophy that lighter is better. 3) What looks better is subjective. I personally like smooth curves more than straight lines (triangle kerfing) and in my eyes the quarter round goes the "wrong way" with the natural shape of the instrument so I feel the cove is more aesthetically pleasing. Other's may disagree on this and that is okay. Also for those who believe that round surfaces help the sound more than straight/square surfaces both the cove and quarter round are successful in accomplishing that.
I see the cove design's biggest advantage if being used on an instrument back that has no purfling (binding okay with some minimal modifications to the thickness of the coved kerfing) because it is visible through the soundhole and no concerns about purfling in that scenario. If the cove design is used on an instrument back, it maximizes all of the advantages and none of the drawbacks (assuming no purfling is being installed on the back).
The picture I included in the original thread, looking through the soundhole, was strategically chosen because I felt that it showed the coved kerf design in it's optimal location, optimizing strengths and limiting weaknesses. With that said I'd use something besides the cove on the soundboard because it's less visible and no one will see it so the only advantage of the cove design in that scenario would be the weight savings but at the expense of function for binding/purfling install which for that tradeoff is not worth it.
All of these comments are based on me spending the last 5 hours in the shop working on different designs and trying to improve on the design based on Chuck's and other's comments and my own thinking by experimenting with kerf heights, widths, etc. No pictures yet, but lots of sawdust and kerfing on the table.
Open to further critique and constructive criticism
Thanks for asking Chuck. This helped to make things in the design explicit. As I was writing I realized some of those things might not be obvious. I sometime forget that other people can't see inside my brain
We have not discussed the issue of lining/kerfing stiffness but that conversation has a lot of assumptions that would need to be laid out first.
donovan