Official Luthiers Forum!

Hi!

I have in my hand an article written by somogyi, talking about stiffness, density and modulus of elasticity(E).
I want to calculate the E of my tops and bracings. That could allow me to measure the stiffness of those whitout worrying about dimensions and thicknesses.

Here's my problem: I'm basically a french speaker, and I'm not sure about the definition of the terms of the formula.
Here it is:

E = (¼PL³) / (ybd³)

¼: Constant for center loaded beams
P: Load on the beam
L: Span of the beam
y: Deflection of the beam at its center
b: Beam's widht
d: Thickness or depth of the beam

I'm not sure what SPAN means; is it the lenght of the beam? On my jig, the braces are layed down on two metal rods, 10'' appart, then load applied at center. My guess is that span is 10''. Am I right?

I did the calculation this way, with an Adirondack brace.
3/8''x5/8''x10''
4.5lbs applied
.009'' deflection

(¼x4.5x10³) / (0.009x0.375x0.625³) = 1365333,33... psi
or E=1.3653
Am I right?

Thanks!
Francis

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Francis Richer, Montréal
Les Guitares F&M Guitars

Oui, span is the distance between the supports, so 10" for your case.
Using your numbers, I got the same E (1.36 Mpsi). That's on the low side for spruce, but it's probably reasonable for Adi.

Some suggestions for accurate experiments (you may know these already):
- Sometimes there can be extra deflection from parts settling in. First try applying a small load (1/2 - 1 lb) and then zero the dial indicator. This "tare load" will minimize any slop in the system. Leaving the tare load in place, next apply the main load and record the deflection as usual. I've found this method is often very important for tops (especially if warped), but it may not be needed for brace sticks.
- Flip the wood over and rerun the test; it should give the same E within 10%.
- Use planed surfaces if possible (sanding results in a layer of 'fuzzy' wood).
- Measure the height dimension carefully, since that number gets cubed.

Good luck!

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David Malicky

Thanks a lot David!

I run the test at least three times, setting all back to zero each time, and then make an average of the results. If there is too much difference between the results, I run more tests.

I measure twice the dimensions with a caliper.
I also weight them with a 0.01g precision balance, then calculate the density and also the Moludus of elasticity/Density (relative to water), than can show the stifness/weight ratio of different pieces or even between species.

Another question I have is about longitudinal/lateral/combinated stiffness, for tops.
''E'' is calculated basically with lenghtwise stiffness, If I understand good. So I can apply for longitudinal and lateral stiffness, depending on how you run your test (if the pivots are parallel or orthogonal to the grain) on a rectangular piece. But what about combinated stiffness? How could I apply or calculate the ''E'' on my shaped top deflection data? Here's how I run my test:

I have a outside mold, made or birch-ply, on wich I lay my top (I left about 1/8'' extra around the perimeter), then another plywood structure, same shape, go over it to clamp the top in place. My caliper take the deflection right on the bridge spot, and I put my weight just behind it (toward the neck).

The problem to apply the ''E'' formula seems to be that there's no ''span''.
A unbraced Adi top, 0.105'', OM shape, gives me, from memory, about 0.100'' of deflection for 2000g (~4.5lbs). The same top, braced, gives me between 0.007 and 0.008''.

Thanks a lot!
Franis

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Francis Richer, Montréal
Les Guitares F&M Guitars

Oh, also:

I debate I have with my self...

If my jig have a span of 10'', does it affect the results if the brace I put on it is 12, 15 or 20 inches?

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Francis Richer, Montréal
Les Guitares F&M Guitars

Francis, it's a long story! Put "Trevor Gore Guitar" into your search engine and you'll find that there's a book that has the answers to all these sorts of questions.

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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 believe one of the classical makers (Fredriech?) tested tops in a frame, clamping them at the edges (rectangular/guitar shaped?) and measuring deflection under load..
This would take MOE in all directions into account, and may minimise errors due to non-flatness of the board if averaged both ways.
I must add I have no experience of this, yet, but it may be a way round Trevor's method which requires more or less perfectly flat and even test boards, by doing several his way, and seeing if there is a relationship to testing them to the frame/clamping method.
Could save me throwing away (ebaying!) some tops.

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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.

Go ebay!

I've tried pre-loading twisted tops, testing them, then flipping them, pre-loading and testing again (static tests, of course). The differences I got between the two sets of results was such that I decided that I couldn't rely on any of them. YMMV. Mild twisting, no real problem, but flat is best. Bad cupping, forget it. If you can flatten them and they stay flat, you should be OK.

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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

Thanks Trevor!

I heard about your book a lot. It's in my plan to save some money to get it, or ask it for X-mas.
Yup, I'm a student, then, poor.

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Francis Richer, Montréal
Les Guitares F&M Guitars

I was thinking not about so much about twisted tops as much as ones with variations in "grain" and "quarteredness" across the board - what about bearclaw figures and also (live) backs when consistantancy across the board would rule out some interesting woods?

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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.

Yes, poor is never good for long. Stick with it and it'll change! Good luck with your testing. You're asking the right sort of questions, but the answers aren't always simple.


Yes, backs can be problematic, especially panels that come to you "coffin" shaped. I've handled these in that past by making whatever measurements I can, relating them to previous measurements, then allowing room for adjustment once the instrument is boxed. Best to gain experience with "simple" wood first.

Grain drifting off-quarter slightly across the board has never presented me with a problem. However, soundboards where the off-quarter keeps reversing never seem to make great guitars. IMO, those are the ones to avoid if you can.

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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

Well, personally, I don't look to maniacally precise measurements. I don't want to build a ''scientific'' guitar, only basing myself on deflection or resonance tests or on formulas and mathematical theories. What I'm looking for is to have a minimum of information on my materials then I can compare more objectively my instruments. If I build two guitars of the same model, using the same woods, same thicknesses and bracings, and then one ends more deep or boomy than the other one.... Well, If I don't have any information on the raw materials I use, I could not say where the difference come from. But if I have deflection datas of my top, my back, my main braces, and all the masses/weights, then I can have a better idea.

It could also help me to reproduce a sound that I liked on one guitar, or also to make a more 'selective selection' of my materials prior to build.

Well, all that to say: I'm just trying to know what I'm doing.
Francis

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Francis Richer, Montréal
Les Guitares F&M Guitars

If you test your tops in guitar shaped form as you are talking about, you are going to get a mix of long grain and crossgrain stiffness,effects of load width, variable span etc.
It might be ok for comprarison purposes but will not give you objective material properties
You can do deflection testing as you have done on your braces while the unjoined plate is rectangular, preferably with a greater span and using a narrow load at the centre across the full board width.
This will enable you to calculate along the grain E

I will do this for the next one, for sure.
But still, my top will ends in a guitar shape, so I think it's relevant to measure the ''mixed'' stiffness, no?
I know I can't measure the ''E'' pretty exactly this way, because of the span that is... well, hazardous, but I'm wondering if I could use a theorical span (let's say the lower bout widht). It won't gives me the right E, but, if I always use the same number, on the same jig, for the same shape, it could give me a reference value, that is not ''correct'', but that would allow me to compare the tops between them. Maybe i'm wrong...

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Francis Richer, Montréal
Les Guitares F&M Guitars

It looks to me that you're on a great track and asking important questions!


Great techniques!


Yes, it's good to find both E_longitudinal and E_lateral, tested as you describe. E_long is certainly important for structure, as it is oriented to best resist the string torque. Very generally, E_lat might be more relevant to tone, as it is the weaker one. The ratio of the 2 modulii is thought to be important; it typically ranges from 10:1 to 20:1. Many luthiers find a high ratio produces a poor instrument. E_long is pretty well correlated to the wood's density. E_lat is very sensitive to how close to quartersawn the wood is. Alan Carruth has some good posts in the archives on those. David Hurd's site has a plot of E_long vs density.


It's good you aren't sure how to calculate E for this case, since it can't be calculated (at least by any simple formula)! We can easily calculate E for uniform shapes and simple loads, but once the top is cut into a guitar outline, there is no practical formula. As Jeff said, that test involves a mix of both E's and variable spans. Here's a useful distinction: E_long and E_lat are material properties, while the overall stiffness methods you describe produce a structural property (dependent on both materials and the design of the structure). So, the stiffness number (deflection at load) you find is a very relevant measure for that structure.

There are ways to calculate the structural stiffness of a "T" section (a brace with a strip of top glued to it); I have some spreadsheets for this if of interest, or see David Hurd's site. Trevor takes the structural stiffness measure a step further in calculating the monopole mobility.

Some thoughts on measuring technique:
- The way the perimeter is clamped will affect the structural stiffness. There are two classic cases: fully clamped (aka "fixed") and completely able to pivot ("pinned"). Either case is fine, but a mix of the two can give confusing results. If clamping the perimeter, make sure it is indeed clamped securely and uniformly all around. Possibly, that might require more than 1/8" of extra wood, and maybe lots of clamping points.
- I'd try to load the top right where the saddle would go, and measure deflections there or just behind it (toward the tail). That duplicates the load point, and puts the measurement closer to where the top is most acoustically active.


Nope, those extra lengths won't have any practical effect on the measured E. The small weight of the cantilevered portions will add a tiny torque to the wood between the span (and bend the center very slightly upward), but the deflection due to the 5 lb load will be the same. I.e., by zeroing the dial indicator after the wood is placed on the supports, any effect due to the cantilever portions is cancelled out.

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David Malicky

It looks like you may have been referring to my post.
Sorry, I didn't make my thinking clear.
It was to test plates as per Trevor Gore's book, and obtain parameters for MOE cross and long grain from his methods.
Then to clamp in guitar shaped frame and measure deflections, for comparison to see if there is any correlation.
This might let me estimate final thickness for plates which the book's methods are "meaningless", i.e. those with inconsistancies over the board which appear to interfere with the book's methods, but which might be useable.
It was just a thought, would not take much time, and could be interesting.
Just trying to collect as much data as possible.
Sorry for butting in, if you were not referring to my post!

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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.

No I was referring to Ti-Roux's post where he was considering whether he bould derive an E value from loading a guitar shaped top at the bridge location.
For a large variety of reasons that is not possible.
Testing in this manner after bracing and with bridge attached is another matter and can be quite valuable.

Indeed - it is a 3D problem with 3D elasticity properties, so not simple. And the constant (1/4 in this case) will be different depending on the shape of what is being loaded, and cannot be easily determined for (say) a shape like a top plate cut to a guitar outline, or a rectangular plate that is pinned (or clamped) around its perimeter.

I think you can get at this one step further by using an "effective modulus" which is the ratio of the Young's Modulus to the constant:

E/k = (PL³) / (ybd³)

and recognizing that for a rectangular beam, Area = Lb and Volume = Lbd. A little algebra gets you:



If you know the density of your (unbraced) top plate, you can weigh it to get the mass and then calculate the Volume from mass/density. And then get the Area from Volume/thickness (for any shape). The load and the deflection remain the same.

You could conceivably use this formula for any shape pinned or clamped around its perimeter, recognizing that "L" is an "effective length" and just using the actual pinned/clamped length for your top, any systematic errors in the difference between your actual length and the "effective length" end up in the constant k. So for this, you're not actually calculating a real modulus, it is an effective modulus which is the ratio of the 3D modulus to your constant k ; since you can't really calculate k, the best you can do is calculate E/k from deflection measurements of the top pinned/clamped around the perimeter.

If you wanted to get crazy, you could even do this for braced tops to see how the addition (and shaving) of braces changes E/k as your deflection measurements change.

Since E/k is directly related to the deflection (all else being the same), this is a long way of saying what has already been said above - that relative changes in the deflection are about the best you can easily do once the shape becomes more complicated than a beam.

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The member formerly known as erikbojerik....

'Truth' in this, as in much of life, is approachable, but not attainable. The best article I know of on measuring wood properties (by McIntyre and Woodhouse, 'Journal' of the Catgut Acoustical Society, in three parts in 1984, '85, and '86) showed that simple tests of single properties (such as E-long) only get us within about 10% of the 'real' values. It's almost impossible to avoid 'mixing' things: getting cross-grain bending when you're looking for long-grain, or a bit of one or other shear modulus or the Poisson's ratio(s). This is especially true whan you're testing things like top blanks, that you intend to turn into an instrument later. It would be much easier to find the 'real' values for the various constants if you could cut the thing up into 1" squares, or narrow strips, but then you couldn't make anything out of it. Given the limitations of testing you could either:
a) give up, or
b) do the best you can without wasting a lot of time, and use the results you get for 'ranking' your wood.

'B' is what I do, and it does seem to help. Remember that when relating stiffness and Young's modulus, the thickness of the plate comes in as a cubed term. It doesn't take many strokes with the sandpaper to change the thickness of a top enough (about 3%: reducing your 3mm top to 2.91) to make a 10% diference in stiffness, so is knowing the E value to any greater precision really going to do that much good? What you mostly need to know is whether this piece of wood is too heavy for a good classical, and should be put back on the shelf for a nice, flat-picked steel string. Getting into the ballpark gives you some basis for figuring out how thick this particuar top will need to be, and from there you can use whatever 'fine tuning' approach appeals to you.

If the fine tuning approach you like is 'free plate tuning', Mark Blanchard found out that the 'right' ratio of long grain to cross grain stiffness varies depending on the shape you're making. Basically, wide guitars need wood with higher cross grain stiffness. He looks at the 'free' plate modes of unbraced tops, and finds that if the un-braced top does not show a 'closed' ring+ mode, it will be difficult to get that mode to close on the braced top , no matter what you do with the bracing. In other words, the bracing only 'fine tunes' the sound, the real tone is in the top. Mark starts out testing tops using his widest outline, and, if that doesn't work well, keeps cutting the top down until he finds a shape that works for that wood. You can't fight Mother Nature... Mark gets an awfully consistent sound.

Hey Ti-Roux, while the final shape of the plates may be dred shaped or OM shaped etc, those are design considerations. As Jeff mentioned, what you want is the material properties of the tops in your collection. This is useful as you can record the properties of each top before you do things to them like cut them to shape and glue on braces which complicates your measures. Once you know these properties you calculate the ratio of long to cross grain stiffness and then it is easier to work out how thick your top should be for a given design.

Now, despite what others have said, there are techniques to measure these properties independently and accurately using simple free spectral analysis software and a half decent mic for your computer. Also needed are the Gore/Gilet books which go into great detail about how to use these and other techniques to improve your guitars. And the answer is not 'use HHG'.
Cheers
Dom

Dom Regan wrote:
"Now, despite what others have said, there are techniques to measure these properties independently and accurately using simple free spectral analysis software and a half decent mic for your computer."

It all depends on what you mean by 'accurate'. Any time you start pluging data into equations to derive something like a Young's modulus, you'ere limited by two things:
1) the accurcy of your data, and
2) how well the theory fits reality.

Gore and Gilet go into the data end pretty well. As they point out, it's fairly easy to get quite accurate frequency and bandwidth data from a sample using free or cheap software and a decent mic on your computer. The issue is with what that data means.

If the node lines of the long-grain 'bar' bending mode of vibration are curved that's a sign that there is some cross grain bending , or shear deformation, within the bandwidth of that long-grain mode. When this happens, the properties that determine the frequency of the mode are a mixture of long-, cross- and shear moduli. This is easy to undrstand, and easy to see if you look for it. Just holding a plate up and knocking on it won't tell you this: you have to look.

What's less easy to see, and just as important, is that _even when the node lines look straight_ there is still some admixture of moduli in there. You cannot, for example, bend a piece of wood along the grain without building up some shearing stress in it if it has any thickness at all (and I've never managed to build with a top that had no thickness). This is where the thoery is limited: the equations we use to calculate, say E-long, assume that there is no other modulus involved. It's a necessary simplification to preserve linearity, but it introduces errors into the final results. McIntyre and Woodhouse showed in their articles how to get around this with the use of a computer and information on a number of other modes. Sadly, they did not put this out as a 'recipe', and my math chops aren't up to setting up the spreadsheets, but I'm not sure that matters all that much anyway.

The reason for that is simply that wood is so far from uniform that 'the' Youngs' modulus along the grain of a particular piece of top wood is something of a fiction. If you cut the top into strips, which would give you more accurate readngs, you'd find that every one of them was probably a bit different. Since we're more interested in making guitars from the wood than finding ou some exact lab-grade value for the Young's modulus, we just leave them wide and live with the innacuracy. If you think you're doing something different you might be surprised some time.

Anyway, given the 'ills that flesh is heir to' (you've never dinged a top and had to sand it out?) and normal tolerances I think it's possibler to get 'close enough'. That, and some fine-tuning along the way, along with the sort of understanding that you can get here, and in the Gore/Gilet books, should enable you to make some pretty nice guitars.

Good points. There are always limits to accuracy. The acid test, I guess, is is it accurate enough to be useful/beneficial?

French did a bunch of tests on 30-odd Taylor guitars and got a spread of 20Hz in the T(1,1)2 ("main top") frequency. As these would have been tightly dimensionally toleranced, the variation is most likely to have been due to material properties. If you think hitting a particular top frequency is beneficial (I obviously do!) it helps if you can find a way of getting the effect of material properties into the building "equation" (if you'll pardon the pun). Some people claim to be able to do it by "feel", but trading off stiffness against density is very difficult to do by feel alone and measurements of these properties help you get very much closer, even though we all know that the measurements can never be truly accurate. But experience shows that they are sufficiently accurate to be beneficial, (and that theory sufficiently fits reality) especially when used with the "tweaking" techniques that get you from where your build landed to where you wanted it to be.

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

http://www.goreguitars.com.au

Of course, the variability of wood means you could not get a scientific level of accuracy but we are talking about achieving a level of accuracy that aids our guitar building, nothing more. We may not be able to measure the absolute value of a top plate with certainty. But if you ran the tests on a number of tops in your collection you could surely gather very useful relative data on your collection. And then when comparing guitars you have built this bit of information could again help determine some of the variability.

But what are the alternatives?

Other methods I have seen for determining plate thickness are flopping the joined top plate as it comes out of the sander to determine when it is starting to free up. But everyone I have seen doing this test flops the plates cross grain when we really need to determine the long grain stiffness. And flexing plates by hand might work for those who make a lot of guitars but for most of us it is going to take a long time to hold and flex 100 plates or so to properly calibrate the brain to accurately determine stiffness.

So any technique that can assist in removing variability has got to be worth pursuing.
Dom

I was told that some tests were done a few years ago at a violin makers meeting. Very few people were anywhere near as good as they thought they were at judging wood stiffness by hand. It's an aspect of what I call 'Feynmans' Dictum': "The easiest person for you to fool is yourself". My signal generator and triple beam balance are a lot harder to fool, although I've been known to fool myself when using them once in a while. Still, anything that adds to precision, even if it's not totally accurate, is probably helpful, so long as it's relevant. That's where theory helps, along with nice big samples.