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There's been a few discussions concerning the effect of what various radii mean to guitar tops lately.
I ran a few models in an FEA package this morning to give people an idea of how the various radii effect the stiffness of the top.
Please note: These are not design guides or an actual guitar. What it is, is a representation of an unbraced top constrained at the ribs with a virtual thumb pushing down on it with 10 lbs of force.
So here we go...
250 ft radius ( very flat) - .250 inches of deflection
25 ft radius ( pretty standard) - .189 inches of deflection.
20 ft radius - .169 inches of deflection.
15 ft radius - .139 inches of deflection.

Hopefully you can gain some concept of how the various radii effect your top.

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Jim Watts
http://jameswattsguitars.com

thanks, this is an interesting visual insight into one of the aspects i found (and im sure many others) most confusing when i first got interested in luthiery. much appreciated

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"Anything that happens, happens. Anything that in happening causes something else to happen, causes something else to happen. Anything that in happening happens again, happens again. Though not necessarily in that order." Douglas Adams

JIm,

What does your model say happens to each of these different radii tops when you take the virtual thumb off having deflected them?

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Dave White
De Faoite Stringed Instruments
". . . the one thing a machine just can't do is give you character and personalities and sometimes that comes with flaws, but it always comes with humanity" Monty Don talking about hand weaving, "Mastercrafts", Weaving, BBC March 2010

Wood can take a set...so there would probably be some permanent deformation. Jim's FEA model won't really tell you that though (unless you know the stress levels required to permanently deform the top).

Here's some related stuff I have been playing with...I calculated the reactions at the bridge glue up surface. The string tension resolves into a vertical force component (pressing down on the body), a horizontal component (trying to slide the bridge off the guitar), and a torque compoment (which tries to twist the bridge off the top). Here are how these things look for a generic acoustic:



It might be interesting to plug some of these conditions into an FEA model and to try to optimize neck angle & saddle height in terms of the reaction loads on the body...with the goal being to minimize the tendency of the top to go concave.

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http://www.PeakeGuitars.com

Good job at showing the affect of compression loading of various spherical radii domes in a guitar shape. It would be even more interesting to carry the exercise to the actual rotational forces that the dome would see, as apposed to the straight line compressive load.

Parser, is the "neck angle" in the equation the saddle height? Or is the saddle height a constant and the neck angle an expression of the string angle to the plane of the top.

I'm assuming you're changing the saddle height because that's the only way I can see the vertical force going to zero.

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http://www.chassonguitars.com

Jim, that's interesting. Thanks for sharing. Parser too.

Parser, I was wondering basically the same thing as Kent too, only I was more curious if the saddle height or bridge height was changing.

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Mike

"The Dude abides. I don't know about you but I take comfort in that. It's good knowin' he's out there. The Dude. Takin' 'er easy for all us sinners. Shoosh." The Stranger

Dave, Parser is right in my model it'll just come back. But in reality it will take some time to recover, and maybe never fully recover depending on the time period the load has been on it.

Parser, that looks great man. I also assume your using the neck angle to drive the saddle height.


Thats pretty much what I've been doing on designing some new tops for myself.

Thanks hope some people have been able to glean some information from it. It may help explain why the sound of a guitar changes with the change in humidity. The stiffness of the top is changing as the radius is rising and falling. Just a thought.

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Jim Watts
http://jameswattsguitars.com

Jim,

I wasn't thinking so much about the long-term impacts of a constant load but more the short term dynamics of loading the bridge area and then taking the load off, and how this different for different top radii. I was thinking that this is more like what happens when the strings are plucked but I could be wrong. Deflections are static measures - the dynamics are when it gets interesting

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Dave White
De Faoite Stringed Instruments
". . . the one thing a machine just can't do is give you character and personalities and sometimes that comes with flaws, but it always comes with humanity" Monty Don talking about hand weaving, "Mastercrafts", Weaving, BBC March 2010

Ahh, well in that case Dave, the resonant frequency goes up with the stiffness of the plate.
but probably not a lot. If memory serves me right, and it seldom does, the resonant frequency is the square root of the spring constant divided by the mass.

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Jim Watts
http://jameswattsguitars.com

Hey guys, the neck angle is the pitch of the strings relative to the top. The minimum saddle height is actually variable based on the neck angle. At 2 degrees, the saddle is much higher than you would want it...but that doesn't count deflection of the top.

So I guess these #'s I put together really address 2 aspects of design:

1) neck angle - higher neck angles yield more downward pressure on tops
and
2) saddle height - higher saddles yield more torque on the bridge.

Both of these observations seem to be pretty widely accepted among builders. I just ran some #'s real quick on a spreadsheet to get an idea of how one compares to the other. When I get a chance I will run some basic deflection calculations in order to determine how much of an effect the reaction moment has versus the effect that the neck angle has in deflection of the top.

As for all that dynamic stuff that happens when the strings are plucked...I think that really gets into the topic of soundboard tuning. I always figured that the goal of building a top was to make it pump as much air as possible out of the soundhole, without sacrificing structural integrity. I don't know if this is right...but it's my best guess!

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http://www.PeakeGuitars.com

Parser,

Yes but given the debate about building with flat tops, 25-28' spherical tops and tops with more radical arching (and all flavours in between) and their impact on a tops dynamic behaviour and response, it would be interesting to see what a model like this would say about the differences in dynamic response of the unbraced tops with different radii. Then you can think about the impact of bracing from there. I'm not sure it's all about the "quantity" of sound - it's a quality/quantity balance.

I don't know much about these model systems so forgive me. Do they allow you to examine dynamics or do they just give you a series of static snapshots for given specified parameters that help you visualise things better?

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Dave White
De Faoite Stringed Instruments
". . . the one thing a machine just can't do is give you character and personalities and sometimes that comes with flaws, but it always comes with humanity" Monty Don talking about hand weaving, "Mastercrafts", Weaving, BBC March 2010

Thinking about it, if you just push it down it will just come back up. I'm thinking of the model showing the dynamic impact of say tapping the top in the middle of the bridge area with say a 20lb force - like one string's tension.

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Dave White
De Faoite Stringed Instruments
". . . the one thing a machine just can't do is give you character and personalities and sometimes that comes with flaws, but it always comes with humanity" Monty Don talking about hand weaving, "Mastercrafts", Weaving, BBC March 2010

Are you able to add braces to the model?
I think it will significantly change the results by narrowing or eliminating the differences.
What edge support conditions have you allowed for?

Jeff,
Yes, I have tops that are fully braced in a variety of styles, and loaded completely different than the above. it's quite the interesting exercise. The top is attached to the ribs and the ribs are fixed for the constraint.
This exercise here was meant to be nothing more than an attempt to provide some basic data for others on the effect of increasing the radius of the top. The load is totally unrealistic to an actual guitar top, but is effective at demonstrating the effect of varying radii.

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Jim Watts
http://jameswattsguitars.com

Jim Watts wrote:
" It may help explain why the sound of a guitar changes with the change in humidity. The stiffness of the top is changing as the radius is rising and falling."

I suspect that changes in the frequencies of 'air' and 'wood' resonances would be more important. Wood becomes denser and less stiff as the R.H. rises, so resonant frequncies drop. The speed of sound in air is determined by the average molecular weight, and since water vapor is lighter than either nitrogen or oxygen molecules, as the humidity rises the speed of sound goes up, and so do resonant frequencies. The sound of the intsrument is determined in part by the interactions of these resonances, and with them shifting around in opposite ways, those can change quite a lot.

Jim,
If you Have a model with bracing, can you repeat this exercise with different radii.
perhaps with a load that produces deflections of the magnitude of 1mm or so.

Jeff,
I can do that, but it's not really going to tell you anything as it will have properties tailored to the last set of wood I built with. Wood properties can vary as much as 100% maybe more.

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Jim Watts
http://jameswattsguitars.com

If you kept material properties and bracing the same and just changed the radii then did the deflection test above, it would show how stiff the whole combination is with varying radii.