Optimum thickness for red cedar soundboard?

[John LaTorre]

I'm building a 000 12-fret with a western red cedar top. It's currently just a shade over 3mm thick. I've gotten two conflicting opinions from luthiers about what the optimum thickness should be: one says 3.5 mm and the other says 2.5 mm. What has your experience been with this material?

[Stephen Neal Saqui]

It depends on the stiffness of the piece and intended string gauge....but generally 3 mm is safe.

[Mario Proulx]

How does it feel at 3mm?

Also, consider what string gauge do you anticipate running, scale length, style of playing, etc...

[Alan Carruth]

Right: the thickness would depend on the stiffness along the grain of that particular piece of wood. All woods vary a lot, so there's no substitute for an actual measurement. However, it turns out that the Young's modulus along the grain of ALL softwoods varies in the same way with density, with surprisingly little scatter for a natural material. Softwoods all have pretty much the same microscopic structure, and that probably accounts for the similarity. Young's modulus is a measure of potential stiffness: two pieces of material with the same Young's modulus will have the same stiffness at a given thickness. WRC is generally less dense than other top woods, and thus usually has a lower Young's modulus than the denser woods. At any rate, density is pretty easy to measure, particularly if you haven't cut the top to shape yet, and makes a reasonable surrogate for actually measuring the stiffness. For that matter, there are relatively easy ways to get the Young's modulus as well, again, if the top halves are still rectangular. If all else fails, I'd say that 3mm would be a decent 'safe' thickness: you might be able to go thinner, but would seldom need to go thicker than that with Cedar.

Be aware that WRC has relatively low surface hardness compared with spruce. Check for dents every time you pick the top up, and if you see one wet it to swell the wood out. The longer it stays dented, the harder it is to swell them out. Also, WRC has low peel strength, and I generally use a bridge with a larger 'footprint' on cedar tops to keep it from peeling up.

[John LaTorre]

Thanks for your responses.

The scale length is 24.9", and it's going to be a finger-picking guitar. I'll be putting either lights or extra-lights on it. As for the feel, I'm really not skilled enough to give an opinion, but it seems a little stiffer in flex than the spruce tops I've used before. I've taken those down to slightly below 3 mm, and they went on to OM or OO guitars. I've always wondered if I could have gone lower, but wanted to stay on the safe side.

Alan, I assume that measuring the density of the top involves calculating the volume of the wood, weighing it, and dividing the weight by the volume. That give me 0.35 grams/cu. cm., but that figure is fairly meaningless to me since I don't know how that translates into optimum thickness.

I've heard of other ways of calibrating flex, like supporting the soundboard on the edges and putting weight on the center until it drops a specified distance, but I don't know if red cedar deflection is equivalent to spruce deflection. And I've seen a few writers in the GAL magazine say that this isn't really an effective way to gauge optimum thickness anyway. My head hurts....

[Alan Carruth]

" That give me 0.35 grams/cu. cm"

If that's 'normal' wood, without a lot of runout or heavy latewood grain (reaction wood) that should give you a Young's modulus along the grain of about 8000 MegaPascals, plus or minus about 10%. I'd make that top about 2.8mm thick, so it looks like you're fine. An 'average' Sitka top, with a density of about .46 gm/cm^3, would have an E value around 14,000 MPa, and I'd make that about 2.4mm. The spruce top would be about 10% heavier at the same stiffness.

"I've heard of other ways of calibrating flex, like supporting the soundboard on the edges and putting weight on the center until it drops a specified distance, but I don't know if red cedar deflection is equivalent to spruce deflection. And I've seen a few writers in the GAL magazine say that this isn't really an effective way to gauge optimum thickness anyway."

That's about as good a way as any, but it has pitfalls, as any measurement does. One is 'cold creep'; the tendency of wood to keep deforming slowly under a load. The best way to get around that is to load the piece, zero the gauge, remove the load and read the spring back immediately. Hurd uses deflection measurements in his 'Left Brain Lutherie' , which I think you can still get. He talks about some of the issues, and how to get around them.

[John LaTorre]

Thanks for your response, Alan. I'm going to go for 2.8. If it ends up thinner than that by a wee bit, I can always make the braces a little taller. In fact, that might be the way to go, since I can always modify the bracing when the strings are off at string changes, reducing their height if the board turns out to be too stiff, whereas I'll be pretty much stuck with whatever thickness it turns out to be.

[Alan Carruth]

In my work I try to get some sort of balance between the top plate stiffness and the braces. At least, that's one way to interpret the Chladni patterns. I generally use a 'tapered' profile, and sometimes they get pretty low at the lower ends. Everybody has their own way of doing things, and they all seem to work when you get them right. All I can do is tell you how I do it, and that may not be your cuppa.

[John LaTorre]

All I can do is tell you how I do it, and that may not be your cuppa.

Good enough for me.

[Alain Lambert]

" That give me 0.35 grams/cu. cm"

If that's 'normal' wood, without a lot of runout or heavy latewood grain (reaction wood) that should give you a Young's modulus along the grain of about 8000 MegaPascals, plus or minus about 10%. I'd make that top about 2.8mm thick, so it looks like you're fine. An 'average' Sitka top, with a density of about .46 gm/cm^3, would have an E value around 14,000 MPa, and I'd make that about 2.4mm. The spruce top would be about 10% heavier at the same stiffness.

Alan are you targetting a specific Young's modulus for your tops?

[Alan Carruth]

"Alan are you targeting a specific Young's modulus for your tops?"

No: I measure the wood and figure out the thickness to use based on the Young's modulus. Depending on what the guitar is supposed to sound like I might use denser wood with a higher Young's modulus, or less dense wood that's not as stiff at a given thickness. Lower density gives you a lighter top if it's following the usual rule relating density and Young's modulus, and that will tend to result in a more 'responsive' and powerful top. Denser wood seems to give more 'headroom' all else equal. Thus I tend to save the lower density tops for Classicals, and the denser stuff for steel strings for heavy strummers. There's more to it than that (as usual) but that's the short answer.

[Doug Shaker]

Alan-

What is the relationship that you look for between the measured Young's modulus and the target thickness? It doesn't appear to be a linear relationship.

[Doug Shaker]

Just fishing around with the numbers it looks like you want the thickness in millimeters to be the cube root of 190000/[Young's modulus of the wood].

[Alan Carruth]

I'm using a somewhat simplified model which disregards the cross grain stiffness. That seems to be important acoustically, but does not seem to help structurally in the long run due to 'cold creep'. In that case you can look at the top as a collection of parallel beams of different lengths. The stiffness of any one of them will vary as the cube of the thickness, and the stiffness of the whole top is just the sum of all of those. This has lead me to a simplified 'index number' system that seems to work pretty well for the way I make guitars.

Suppose you made a guitar with a top of known stiffness and thickness that worked out well; it sounds good and the top seems pretty stable. You'd like to duplicate that success with a different piece of wood. As an example I'll use a recent OM with a Sitka top. The wood had along-grain Young's modulus of 11,900 MegaPascals, and the average thickness was 2.7mm. 2.7^3 = 19.683, and that times the E value (19.683 x 11,900)=234,000, so that becomes the 'index number'. Let's say I want to make another OM with a cedar top that has an E value along the grain of 8,000 MPa. I'll take the index number and divide it by the new E value (234,000 / 8000) = 29.27. The cube root of that is 3.08, s that's the thickness of the new top in millimeters.

The new Cedar top won't sound like the Sitka one: the damping factor is probably much different, and the cedar top will probably be a bit lighter in weight, but STRUCTURALLY it should work as well, and that's what this is about. IMO it really doesn't matter if the guitar sounds great if it falls apart too soon, and if it's too heavy structurally you've probably sacrificed some sound, so anything that can help hit that 'sweet spot' is good.

Note that this is not written in tablets of stone. Ideally any such system is something you fine tune with more experience. I use a different index number for Classical guitars (180,000 or thereabouts), and it's likely that you'd want to use a different one for an 0 than a Jumbo or Dread. It's also likely that different brace profiles would call for some modifications: I use 'tapered' bracing (tall at the bridge), and a scalloped profile might need some other number to really work right.

[Doug Shaker]

Alan,

Thanks, interesting. Thank you for the detailed explanation. As always, well thought-out and impeccably reasoned.

What method do you use to measure Young's modulus? Or do you estimate it from the density?

[Alan Carruth]

I measure Young's modulus by a vibration method, using top and back halves. Gore talks about doing this using a recorded tap, and spectrum software to pick out the resonances. I've been using a signal generator to do it for years, since I already have one, and feel that it's a more accurate method, at least in principle. I'm actually working on a post about it for another list, and could put it up here if I ever get it in shape. As always, there are pitfalls no matter how you do it, and no measurement is ever totally accurate. Still, it's good enough to be useful.

The density/modulus relationship is something that showed up when I charted out the data I had on a bunch of tops. Other folks have noticed it. When I discussed it on another list with some experienced researchers they thought it made a lot of sense. All softwoods share a very similar microscopic structure, and the similarity in properties follows from that. There's still enough variation that it's much better to make actual measurements, but in a pinch you won't be too far out most of the time using density as a proxy for long grain E. Hardwoods vary a lot more, both in structure and in properties.

[Doug Shaker]

I've been using a signal generator to do it for years, since I already have one, and feel that it's a more accurate method, at least in principle. I'm actually working on a post about it for another list, and could put it up here if I ever get it in shape.

Well, I will be interested to see your method when you have it written up. Thanks.

[Trevor Gore]

I'm building a 000 12-fret with a western red cedar top. It's currently just a shade over 3mm thick. I've gotten two conflicting opinions from luthiers about what the optimum thickness should be: one says 3.5 mm and the other says 2.5 mm. What has your experience been with this material?

As other have said, there is no single "right" answer as it depends on what sort of sound you like. For the 000 sized guitars I do, from my data for WRC, ave. Elong is 6.6GPa, density 336kg/m^3 and top thickness is 3.2mm. The range is from 2.9 to 3.4mm, depending on the stiffness and density of the piece. I use a formula that combines the elastic constants and density so that I get the target vibrational frequencies I want from the panel, irrespective of the wood properties. Seems to work, because I always get the mode frequencies I want on the finished guitar!

Suppose you made a guitar with a top of known stiffness and thickness that worked out well; it sounds good and the top seems pretty stable. You'd like to duplicate that success with a different piece of wood. As an example I'll use a recent OM with a Sitka top. The wood had along-grain Young's modulus of 11,900 MegaPascals, and the average thickness was 2.7mm. 2.7^3 = 19.683, and that times the E value (19.683 x 11,900)=234,000, so that becomes the 'index number'. Let's say I want to make another OM with a cedar top that has an E value along the grain of 8,000 MPa. I'll take the index number and divide it by the new E value (234,000 / 8000) = 29.27. The cube root of that is 3.08, s that's the thickness of the new top in millimeters.

Alan's formula is a short form of the formula for flexural rigidity, E * I (Youngs modulus multiplied by the second moment of area, which for rectangular sections is proportional to the thickness cubed). And as Alan says, that should give you a standard resistance to static bending deflections. What it doesn't do is say much about the mode frequencies, which is what you hear. For that you have to include the density as the mode frequencies are proportional to SQRT(stiffness/mass).

I measure Young's modulus by a vibration method, using top and back halves. Gore talks about doing this using a recorded tap, and spectrum software to pick out the resonances.

In my tests, static deflection methods of measuring Youngs modulus correspond very well to the result gained from dynamic testing. (Without looking it up, better than 1%, iirc). I've tried using speaker excitation like Alan, but found that tap testing is much quicker and gives sufficient accuracy to deduce the target panel thickness for that particular piece.

Works for me and seems to be catching on!

[Trevor Gore]

Just fishing around with the numbers it looks like you want the thickness in millimeters to be the cube root of 190000/[Young's modulus of the wood].

Needs some work on the decimal point .

[Alan Carruth]

Those pesky decimal points....