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PostPosted: Fri Mar 10, 2023 1:20 pm 
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I have a theoretical question about difference in strength, if any, between a spherically convex top and a cylindrical top (both with the same radius) on a steel string acoustic guitar. Specifically, would there be any difference in resistance to deformation of the top behind the bridge under string tension assuming identical top/bracing between the two types of tops, or would it be a wash?

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PostPosted: Fri Mar 10, 2023 2:37 pm 
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I don't know the answer but that's a very interesting question!

Maybe Trevor Gore will chime in.


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PostPosted: Fri Mar 10, 2023 2:55 pm 
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I'm not actually a qualified engineer, but 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) on a steel string acoustic guitar.
Intuitively, an arch one way and flat the other is weaker than if it's arched both ways.
But if you increase the cylindrical radius, you could compensate for that loss of stiffness. How much? ask an engineer.....
My $0.02
See graph "Elastic Deformation of Curved Surfaces" on this page https://my.mech.utah.edu/~me7960/lectures/Topic7-ContactStressesAndDeformations.pdf
(I just googled "stiffness of a cylindrical radius plate vs a spherical radius plate")

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The name catgut is confusing. There are two explanations for the mix up.

Catgut is an abbreviation of the word cattle gut. Gut strings are made from sheep or goat intestines, in the past even from horse, mule or donkey intestines.

Otherwise it could be from the word kitgut or kitstring. Kit meant fiddle, not kitten.


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PostPosted: Fri Mar 10, 2023 3:32 pm 
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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.


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PostPosted: Fri Mar 10, 2023 4:01 pm 
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Barry Daniels wrote:
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.


That makes intuitive sense to me, especially for a downward load perpendicular to the top. I'm wondering if it would be any different in this case where the load is almost tangential to the surface and aligned with the cylindrical axis. Bridge rotation seems like it would be a factor too.

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PostPosted: Fri Mar 10, 2023 4:19 pm 
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Just wait fellas, my conical-topped guitars are gonna blow some minds.



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PostPosted: Fri Mar 10, 2023 4:57 pm 
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A spherically CONCAVE top would theoretically be the strongest top geometry, but would sound terrible. Essentially the same principle as a domed roof in architecture.

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PostPosted: Fri Mar 10, 2023 5:36 pm 
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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 tansverse 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.



These users thanked the author Alan Carruth for the post (total 3): bionta (Sun Mar 12, 2023 11:41 am) • joshnothing (Sat Mar 11, 2023 5:16 am) • Colin North (Sat Mar 11, 2023 5:01 am)
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PostPosted: Fri Mar 10, 2023 6:31 pm 
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The advantage I have found with the cylindrically arched instruments I have built, is that you can arch the plate more strongly than you can spherically arch a plate. This additional arching can create added stiffness which can help the top support a greater down bearing force with the types of bridge/string systems traditionally found on archtop guitars and violin type instruments. It gives a different sound - a stronger attack, but still have a reasonable sustain. It also seems to improve the headroom which allows the instrument to be played loudly. It works well for bouzoukis, citterns, and octave mandolins.
Presently I am working on an L0 shape body with cylindrical arching.


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PostPosted: Sat Mar 11, 2023 5:16 am 
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Alan Carruth wrote:
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.


I have read your analysis of sound production/loudspeaker analogy (several times).
I was merely answering the question in the OP - "any difference in resistance to deformatiin of the top behind the bridge under string tension "
As an aside, I remember Laurent Brondel did a "twin build", one with spherical top, the other with a cylindrical top for comparison and posted soundclips to get people's opinions.

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The name catgut is confusing. There are two explanations for the mix up.

Catgut is an abbreviation of the word cattle gut. Gut strings are made from sheep or goat intestines, in the past even from horse, mule or donkey intestines.

Otherwise it could be from the word kitgut or kitstring. Kit meant fiddle, not kitten.


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PostPosted: Sat Mar 11, 2023 10:02 am 
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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.

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PostPosted: Sat Mar 11, 2023 10:45 am 
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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. If you turned the cylinder 90 degrees so it went side to side then it would have more resistance.


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PostPosted: Sat Mar 11, 2023 11:10 am 
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Pat Foster wrote:
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.

Not sure which one (maybe both?), but that's part of my reason for using them.
CF along the marriage strip may help too.
Also more comfortable under the arm if you use enough radius on the back, more than 3/4" narrower at the lower bout than the tail depth in my builds.

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The name catgut is confusing. There are two explanations for the mix up.

Catgut is an abbreviation of the word cattle gut. Gut strings are made from sheep or goat intestines, in the past even from horse, mule or donkey intestines.

Otherwise it could be from the word kitgut or kitstring. Kit meant fiddle, not kitten.


Last edited by Colin North on Sun Mar 12, 2023 5:28 am, edited 1 time in total.

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PostPosted: Sat Mar 11, 2023 1:01 pm 
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Pat Foster wrote:
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.


I'm pretty sure Laurent makes his guitars with a cylindrical top and back, similar to Sobell. My tops and backs both have compound arches with flat rims (not including a longitudinal body taper, also on both).

I do make the upper bout of my backs flat to resist deformation (or the flattening of the arch, as you noted) there affecting the neck angle. The body taper (more like a crease near the waist) allows that flat plane to rise and meet a 10' radius of the third back brace so the lower bout has a fairly extreme arch.

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PostPosted: Sat Mar 11, 2023 1:35 pm 
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Barry Daniels wrote:
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 is exactly what I was wondering about.

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PostPosted: Sun Mar 12, 2023 12:17 am 
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Alan Carruth wrote:
This produces a loudspeaker-like motion on the top that effectively 'pumps' out sound.


I’m telling you guys - conical tops :D


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PostPosted: Sun Mar 12, 2023 10:16 am 
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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. ;)



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PostPosted: Sun Mar 12, 2023 11:25 am 
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Keep preaching it, brother Al.


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PostPosted: Sun Mar 12, 2023 1:57 pm 
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I spherical top distributes forces in all directions. Seems that is a desirable thing with guitars. Yes, I am an engineer who took strengths of materials in pre and post graduate studies. But that does not mean I am qualified to answer this question. All I can do is rely on my background and intuition. Plus, they just look so dang good.

Mike


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PostPosted: Sun Mar 12, 2023 2:43 pm 
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Alan Carruth wrote:
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. ;)

No forgiveness required Alan, certainly no offence taken, and apologies if I sounded miffed.
I am in fact an avid reader of anything you have written, and have your DVD on plate tuning.

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The name catgut is confusing. There are two explanations for the mix up.

Catgut is an abbreviation of the word cattle gut. Gut strings are made from sheep or goat intestines, in the past even from horse, mule or donkey intestines.

Otherwise it could be from the word kitgut or kitstring. Kit meant fiddle, not kitten.


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PostPosted: Sun Mar 12, 2023 4:25 pm 
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Second try at posting this.

I have a plan of a Ramirez classical that seems to show a cylindrical (or similar shape) lower bought. Ramirez is long considered one of the finest sounding classicals. I concur with the suggestion above to just try different shapes. The subtle differences cannot be figured out by pondering. There is more to it than using the strongest shape.

Building with a spherical board and uniform thickness plates has to be one of the simplest methods. Yet many of the finest builders still use tentalons because their top design is so complex that tentalons are the best practical way to attach to the sides.

retired engineer


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PostPosted: Sun Mar 12, 2023 5:14 pm 
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According to Eugene Clark the 'normal' Spanish method was make the upper and lower edges of the rim flat. Tops were domed by gluing the fan bracing on in a shaped solera, and various makers had different ideas about the 'correct' shape. Backs used a non-uniform three dimensional dome so that the center line of the back was more or less uniformly curved. It's tricky to do this without ending up with 'dimples' in the waist. The edge of the rim on the back is very slightly beveled to match the angle formed by the dome. Torres apparently did it by gluing the back braces into inlets aroud the edge that brought them proud of the edge by the right amount, and then planing them off to the right curve. The back was then glued to the braces. Clark was adamant that this was the only proper way to make a Classical guitar, and thoroughly execrated spherical doming.

One top scheme, used by Greg Byers, is to dome the top upward in front of the bridge, but make the surface more or less level behind the bridge. The torque of the strings would push the dome downward in front, and pull the top up behind, eventually producing a uniform dome, at least in the lower bout, but the rim edge itself in level, so far as I know.



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PostPosted: Mon Mar 13, 2023 12:49 pm 
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Just for interest Nigel Forster build some models with a very tightly radiussed cylindrical top. If you have a good search of his website you can find some pics.

Cheers Dave


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