I was an engineer in an earlier life and yes, a sphere is stronger than a cylinder, all other things being equal. A simplified way to describe it is that a cylinder has strength in only two dimensions whereas a sphere has strength in three. It would be interesting to test this concept utilizing braced tops.

Colin North wrote:
" I would hazard that a spherically convex top will move less than a cylindrical top with the torque at the bridge (both with the same radius)"

Bridge torque is not a major sound producer. Most of the actual power driving the top comes from the vertical component of the string motion relative to the plane of the top. The string goes up and down, and pulls the top along with it. This produces a loudspeaker-like motion on the top that effectively 'pumps' out sound. When I measured the actual forces at the bridge top, I found that the tension change that rocks the bridge is generally much weaker than the transverse force: it varies depending on the string but averages about 1/7 of the transverse force. Rocking the bridge fore and aft pulls part of the top 'up' and pushes part of it 'down', which tends to cancel out much of the sound output. Finally, we make tops so that they will resist this torquewise motion, since thats what ruins guitars, The twice-per-cycle tension change does produce some sound, particularly if the strings are very high off the top, since that gives that force more leverage. It's more a contribution to 'tone color' than actual power, though.

The curvature fof the top adds some stiffness, of course. I suspect that a cylindricaltop has somewhat different resonant mode relationships than a shpherical one. On violins different arch shapes produce different characteristic timbres to some extent.

Wasn't it Brondel (or Burton Legeyt?) who built his guitars with a cylindrical back? Seems the reasoning was that string tension, while compressing the top, would translate into tension along the length of the top, which could flatten the back. In doing so, the back would become longer, contributing to distortion in the body as a whole, leading to the need for a neck reset. I could be wrong. That happens sometimes.

Wasn't it Brondel (or Burton Legeyt?) who built his guitars with a cylindrical back? Seems the reasoning was that string tension, while compressing the top, would translate into tension along the length of the top, which could flatten the back. In doing so, the back would become longer, contributing to distortion in the body as a whole, leading to the need for a neck reset. I could be wrong. That happens sometimes.

The reason that a cylindrical top has less resistance to deformation from string tension is that the cylinder is flat in the direction of string tension.

This produces a loudspeaker-like motion on the top that effectively 'pumps' out sound.

Colin North wrote:
"I have read your analysis of sound production/loudspeaker analogy (several times)."

Sometimes I think I post some version of that somplace on line about once a week. I don't mean to come down on you, or anybody else, but that 'bridge rocking' model of sound production has been around a long time, and become a pretty well established myth. The only way I know to fight it is to put out the actual mechanism every time it pops up, so that folks who have not yet made up their minds have real information before the myth takes over. So I hope you can forgive me if I come across as the Department of Repetitious Redundancy Bureau from time to time.