Official Luthiers Forum!

I bought Trevor Gore's book set a couple of months ago and thought I'd give his method of dynamically testing wood a try.
I've been doing deflection test for years on my wood, but Trevor has some pretty slick formula for top thicknesses based off of tap frequencies.
Anyway, I was pretty happy to discover that his method of dynamically determining the modulus of elasticity returned the same number I get with my deflection testing. There's no reason I suspected it not to, I was just pleased when it did. The numbers matched pretty exact. I also got the same numbers using Audacity and Visual Analyzer, I've seen a little discussion on this too.
This is an easier method as there's no fixture to set up.
As a side I think the books are a nice complement to the Somogyi Books.

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Jim Watts
http://jameswattsguitars.com

Answers all the questions Somogyi's books only raise...

Jim, that's nice to know.

Trevor is a big advocate of VA but as a MAc user Audacity is a much easier route. Do you find any significant differences between them that are likely to impact the general testing problem? I know Trevor had mentioned that it is far easier to capture multiple tap events in VA and average the spectra.

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Jim Kirby
kirby@udel.edu

Jim, I don't find much difference between the two myself. I think Audacity is a little easier for me, perhaps it's just what I'm use to.
I record my taps using a Zoom h4 recorder. I capture 5-6 taps into a file and then open the file in Audacity, I then average those taps with the analysis function.
That's probably more than you wanted to know, but the bottom line is I got the same answer with both.

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Jim Watts
http://jameswattsguitars.com

No, that was good to know too. Thanks.

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Jim Kirby
kirby@udel.edu

Why do the extra step of recording, just record with Audacity. I create a project file and record and label each series of taps for every guitar at all steps of construction.



I have to agree with you there, Somogyi gives his feelings about the science of the guitar while Trevor proves his theories with math and measurements. Whether we agree or not the proof of what he is doing is there to read.

Fred

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Fred Tellier
http://www.fetellierguitars.com
Facebook page http://www.facebook.com/pages/FE-Tellier-Guitars/163451547003866

+1 on that. Gore's books provide the substance that Somogyi's books sadly lacked.

Because my zoom has better mic's in it than my computer and I save the file for future reference. It only involves hitting a button.

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Jim Watts
http://jameswattsguitars.com

If they are like me, I don't have room for a computer in my shop. I use an H-1 to record my taps, when I record them. Mostly I build by ear.

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Waddy

Photobucket Build Album Library

Sound Clips of most of my guitars

I agree on the the quality of the computer mic's but whether I use my laptop mic or my Zoom as a USB mic the readings come out the same as for as frequency peaks but I prefer the Zoom as a Mic.

Fred

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Fred Tellier
http://www.fetellierguitars.com
Facebook page http://www.facebook.com/pages/FE-Tellier-Guitars/163451547003866

Good to know that the physics still works!

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Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

I also have nothing but praise for Trevor's books and wood testing techniques. Much easier to
do a quick dynamic test on VA holding the wood and tapping than to do either the static
testing or the dynamic testing with a loudspeaker. I just have to remember it's best done
before I join the plate halves.

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Gene

Politicians and diapers must be changed often, and for the same reason- Mark Twain

+100

I know it's early, but I nominate this for comment of the year anyway.

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Bob Garrish
Former Canonized Purveyor of Fine CNC Luthier Services

Except in the middle of Black Holes - still some work to do there

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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

I just have to remember it's best done
before I join the plate halves.

Huh? I don't have "the book", but why would we want to test plates in the raw, before even being joined?

To determine the modulus of elasticity as an aid to making decisions on plate thickness, or whether you even want to use that particular soundboard at all.

Not quite raw, you want to have a smooth surface not rough sawn and it is a lot easier to get results from a single side than a wide glued up soundboard

To determine the modulus of elasticity //snip///

Really? Is there a limit to the size of the piece of wood? Trevor, would this method work on a 1-1/4" thick plate, like we'd use for a carved instrument(violin, cello, mandolin, archtop guitar, etc...), for example? And what about a wedge cut plate? And lastly, could your method determine if a raw billet, and even a whole log, is worth slicing-up or not? Without revealing anything you don't wish to, does your method "scale" up and down, or is it based on a given thickness for the raw plate?

Trevors method determines long grain, crossgrain and shear modulus from taps wth a rectangular board supported in three different positions.
Whist I have done a joined soundboard, the note produced in crossgrain testing does get rather low and harder to determine.
Rectangular,uniform thickness boards only but not a standard thickness or size

Physics is physics, so carries on working within its prescribed limits.

So what are the limits?

First there are differences between "plates" and "bars". e.g. a half soundboard blank is a plate, a fretboard blank is a bar; basically an aspect ratio thing. Easy to get E long for both, harder to get E cross for bars, different formulae for each, both in the book.

The formulae I quote in the book are for accurate rectangular cross sections and rectangular plan forms (e.g. a rectangular half guitar plate of uniform thickness). Essentially, the vibrational frequency is related to EI (Youngs modulus and the second moment of area), so it's theoretically possible to modify the formulae for any prismatic section and outline shape, but you will likely only readily find formulae for e.g rectangles (which is all you get in the book), cylinders, maybe I-beam sections and maybe hex bar. I've not come across one for wedges or triangular sections, but it should theoretically be possible. Most engineering books presume homogenous materials (metals), but wood is orthotropic and very few references deal with that.

The problem with measuring a joined guitar plate at close to final thickness is that some of the frequencies you're trying to measure are pretty low, e.g. 10-20Hz and it just gets impractical to measure that accurately with inexpensive gear. But because the physics "scales" you can get the data you need whilst the plate is still thick, but it has to be of uniform thickness and rectangular profile because that's the formula I'm using.

So, to your questions:

Not really. You have to have a formula for the shape you've got, you have to support the sample in such a way that you excite the mode of vibration that the formula is for and you have to have resultant vibrational frequencies and amplitudes in a range that can be measured. So that lot imposes some practical limits on what you can easily do.


It would work fine for rectangular section plates, but if wedge shaped you would need to find the appropriate formulae. There might be something in Carleen Hutchins' publications; Al C. would know.


If the billet is dry and rectangular section etc., you should be able to determine the material properties and make a decision based on that, so I don't see why not. Obviously, wood properties change a lot through the drying process so you would have to take that into account. I once saw a reference with a pic of a guy measuring the speed of sound in a standing tree with the object of inferring wood properties (speed of sound and elastic properties are related, of course) but no idea, now, of where this was, or even if it worked.
Yes, it scales up and down, as above, and that's why it works.

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Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

The late, great Oliver Rogers worked out a computer program that would return the various engineering constants for a violin wedge. I don't have it, but at least it _has_ been done.

Most of the fiddle folks would test offcut strips from the plates. This has drawbacks, of course. One is that, with the small pieces, measurement errors get to be a real problem. Mort Hutchins, Carleen's husband, used a lab balance to weigh things to the hundredth of a gram so that he could get enough significant digits to be useful. You also need to use a micrometer to measure the thickness and width in that range of sizes. There is also the issue of consistency: the strip you cut off the outer edge of a top may not be representative of the wood in the middle. On the whole, measuring the properties of offcuts is probable better than no data at all, but one has to wonder by how much.

There's a shortcut if you want to know the Young's modulus along the grain: it tracks the density pretty nicely for all softwoods I've tested, with the exception of Eastern Hemlock. The relationship is linear, and something like 2/3 of the samples I've run have been within 10% of the predicted E value. This is not foolproof, but, again, it's better than nothing. I work in metric units, so density is in kg/meter^3, and Young's modulus is in Pascals (or megaPascals). Softwood with a density of 300 kg.m^3 will have a Young's modulus along the grain of about 6000 mPa, while softwood that has a density of 500 kg/m^3 will be closer to 16,000 mPa.

One advantage of this is that you can usually calculate the density of a fiddle wedge. It's even possible to find it directly: weigh the thing, and see how much water it displaces. Some of the fiddle folks will wrap it in a plastic bag before immersion, which is probably a good idea.

I'll note that, in a series of articles in the old Catgut 'Newsletter', McItyre and Woodhouse discussed the ways of finding the engineering constants for wood. They pointed out that the usual formula for finding E based on the mass, dimensions, and lowest bending mode frequency of a bar, is only accurate to within about 10% anyway. The math simplifies out some things in the interest if tractabilty. They discussed the possibilities of using computer programs to make corrections based on the other modes of a rectangular plate, which depend more strongly on the things the usual math leaves out. That was before most of us has access to reasonably powerful computers, and they didn't go into sufficient detail for dunces like myself to get very far with it. My feeling is that, given measurement limitations, plus or minus 10% is probably about as good as you're going to get anyway. That's only a 3% difference in thickness, for example, and most of us can't measure or work any closer than that anyway at the normal thickness of guitar plates.

Fascinating!
Wish I finished physics so I know how you come up with all this stuff!

I have a question about the use of Young's Modulus in lutherie. I am an engineer by trainging, so I know what the modulus is and how it can be useful in structural and mechanical calculations. Are luthiers performing these calcs? Do you try to calculate how thin a top can be based on the load due to the strings? Or do you just use the modulus as a reference point? As in, "Guitar 123 had a top with a modulus of X, and it sounded great. The top for guitar 124 has a slightly higher modulus, so I will go slightly thinner."

I use the modulus along the grain to calculate the thickness of the top, based on past experience.

Assuming you're trying to make the lightest possible top that will be durable enough, it's plain that the limit to how thin you can go is set by provision of 'enough' stiffness to resist bridge torque over the long term. It seems to me that cross grain stiffness contribute little here _in_the_long_run_, as cold creep allows the top to deform irreversibly. At any rate, leaving out consideration of cross grain stiffness simplifies things, and does not seem, so far, to have made much difference.

We know that the stiffness of the top as a beam will vary as the cube of the thickness if the E value remains the same: it will be proportional to E*h^3, where E is the Young's modulus and h the thickness of the top. What I've done is simply to come up with an 'index number' by multiplying E in megaPascals times the thickness of the top in millimeters, cubed. Thus, if the top on a guitar that worked well was 2.8mm thick, and the E along the grain was 12,000 mPa, the index number for that top is 263,000, more or less.

The next top I take off the rack is much less dense, and has a lower E value; let's say it's 7000 mPa. I can divide 263,000 by 7000, to get 37.6, and the cube root of that is 3.35, which is the proper thickness for that top in millimeters.

I realize this is probably 'way over simplified. OTOH, it seems to work out well in practice. Obviously, there are a lot of refinements that can be incorporated, such as scaling the thickness up or down when making different body sizes, bridge heights, and number of strings. I use an index number of 250,000 for steel strings in the 000/Small Jumbo range of lengths, and 180,000 for classicals. Structurally at least, this has worked well enough. Obviously the guitars will tend to sound different due to the differences in thickness and mass of the tops, but that's not the purpose here.

Both David Hurd and Trevor Gore have written up much more exact methods for calculating the correct top thickness based on these measurements, and I'm sure Trevor will be along any time now.

Thanks, Alan. I think that approach probably makes more sense than trying to calculate the required stiffness, especially for the small shop builder. You could determine the required stiffness for a given acceptable bridge rotation angle, and apply a safety factor. But I expect that the design of the guitar has probably evolved over time to a pretty good stiffness anyhow which balances the risk/reward relationship involved. I suppose doing the measurements and calcs can get you that last bit of available mobility for each particular top. I don't have any feel for how much that might be or how it might impact the sound.

Does anyone test bracewood stiffness as well?

Hmmm. Must be getting far too predictable...

Note to Al: in SI ( Le Système international d'unités) milli is m (10^-3); mega is M (10^6) and giga is G (10^9) Hence GPa, etc.. Might help avoid some confusion down the line for the less experienced with these units...

Some of us do, certainly.

There are two main issues regarding top design; the static and the dynamic. You want to be strong enough and stiff enough to survive the torque due to string load over the long term (the static problem) whilst being able to vibrate with sufficient mobility and with a preferred set of modal vibrations to get a great sounding guitar (the dynamic problem). Obviously, it is difficult to separate the functions on a real guitar, but, simplistically, the static issues are mostly about the bracing, because that's where most of the stiffness is (for SS guitars) and the dynamic issues are mostly about the top panel, because that's where most of the mass is. Modal resonance frequencies are related by SQRT(K/m) where K is the equivalent stiffness of a mode of vibration and m its equivalent mass, whereas a top's mobility is proportional to 1/(SQRT(K*m) which is a measure of loudness and responsiveness.

Alan's explanation directly above addresses mainly the static issues, because he is measuring and adjusting for stiffness without a specific relationship to mass, so (and I'm sure Al will step in here if I'm selling him short) there's no direct relationship to modal frequencies, which ultimately determine a guitar's sound. Al has other ways of dealing with that.

My methods comprise measuring the elastic constants of a top and back panel (long, cross, shear moduli) then using those to compute a panel thickness that will give a target vibrational performance when used in combination with a normalised bracing design. I use CF in most of my bracing systems so that I don't have to put in extra wood to get the long term creep resistance. CF, well applied, is pretty creep resistant. Of course, this "dead reckoning" approach only gets you so far, but always close enough so that you can trim the built guitar to a specific set of low order modal resonant frequencies using a combination of "tuning" techniques applied once the box is closed.

Hard to get your head around initially, but actually quite easy to do in practice (or maybe just I've had a lot of practice!). A good number of people have followed the process now and I get frequent emails telling me how pleased they are with their results. You don't need extensive gear to do this stuff; a mic, a sound card in your computer and some free software, so no additional expense for most people.


Remember that the predominant driver of SS guitar evolution has been the corporate profit motive; very little to do with sound. The last time I was analysing a corporate's QA performance, less than 1% returns were to do with sound. That's not because their guitars sounded good, (they sound acceptable), it's because most people buying in main street shops haven't heard a good guitar. So sound quality is sacrificed for "gloss" and structural integrity every time. And when factory guitars are measured for mobility (a measure of responsiveness and loudness) they come out only about half as good as they could be and that measurement series included most of the big name makers. And yet many builders aspire to make a guitar as good as a M____n. The corporate bar is really pretty low.

Note to self: must stop ranting...

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Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au