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I have a question about judging the stiffness of soundboards. How does one determine cross grain stiffness in an absolute sense? Do any of you have some standardized method for determining this?

It is easy to make a comparison between sets, but if the stiffest thing one has is floppy to start with, then everything is floppy...

Thanks!

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Mmmm....wood.

Trevor Gore shows a technique to determine plate properties using tap testing in his wonderful book with Gerard Gilet.

All you need is a free download of a spectral analyser such as Visual Analyser and a decent mic on your computer.

Long grain, cross grain and twisting vibrational modes are determined simply by holding and tapping the plates and reading it into VA. Once you have these values they can be fed into equations which will give you the youngs modulus of each mode for a given length, width, thickness and mass of the plates. This adds more information than just stiffness because it also includes mass. A stiff but heavy top may not be as good as a less stiff but lighter top.

Then taking this a step further, the book then gives you equations that determine the desired top plate thickness to give you consistent results. That is, if you use these techniques to thickness your plates, all your tops will have the same frequency response and you have eliminated one variable from your building.

Nothing is that absolute but this technique is the only one I have seen that uses a scientific approach to get at these values. Get the books if you are keen on introducing a bit more technical rigor into your building.

Cheers
Dom

There are several methods of determining the elastic moduli of the wood you're using. All of them have advantages and drawbacks, and none of them is totally accurate. Still, any of them can be acceptible in the sense that they will be far better than a guess, and will usually get you 'close enough' so that a little fine tuning later on will take you where you want to go.

Some poeple simply develop a 'feel' for this. This is great if you're one of the folks who can do it. I've heard of tests done at a violin makers meeting that demonstrated pretty well that most people aren't anywhere near a good as they think they are.

'Deflection testing' is widely used and easy to impliment. Basically, you support the piece in some way, put on a load, and measure the deflection. The known measurments of the size of the piece, the distance between supports, the mass used to load it, and the deflection, are cranked into the appropriate equations and the Young's modulus is derived. There are some sources of innaccuracy that are hard to get around. Wood will often deflect differently on one side than the other, so you might need to take both measurements and average them. Also, wood 'cold creeps', so the longer you leave the weight on, the more the deflection. Often poeple will put on a small weight to 'pre-load' the piece, add another, zero the gauge, and then measure the deflection as the second weight is removed. This cuts down on the time between the load change and the measurement. If all you're worried about is information for your own data base, you don't even have to calculate the moduli: just find out what absolute deflection number you like, and go with that. David Hurd has some information on this in 'Left Brain Lutherie', and I'm pretty sure Gore/Gilet talks about it too.

One thing that deflection measurements won't tell you is the 'damping factor' which could be important. For that you need a dynamic measurement. Gore's tap test is an example of that. He goes into some of the issues with that in the book, but there are some other things to think about.

One major one is that you can't know, from a tap test, what the shape of the resonant mode is. This can be important in that it's an indicator of whether the mode you're listening for is 'coupled' with another. The evidence of that is that the node lines curve when there's coupling involved. This matters because coupled modes are mixtures: combinations of lengthwise and cross wise bending, or maybe bending and shear. This means that the properties are mixed as well. Also, as Gore points out, when you have modes that are close in pitch they 'push' each other farther apart in frequency. A near match in pitch is normally required to get coupling, so the pitch of the peak you see is not what it 'should' be in the case of a 'pure' mode, and the numbers you get out of the equations are not correct.

You can see the mode shapes using Chladni patterns. This requires some sort of signal generator, an amplifier, and some other equipment. There are software signal generators, and, for this application, not much power is required, although probably more than most computer sound cards can provide.

In any event, there are always limits as to how precise these measurments can be. These fall into a few categories: measurement limitations, data limitations and theoretical issues.

Basically, the accuracy of your result will be limited by your least accurate measuerment. If you're looking at the modes on a guitar top half, you probably can't get the thickness more accurately than to about .1mm, and if it's only 3mm thick that's about a 3% error. this implies an error in stiffness of about 10% that you just can't get around. Mass is another input: so how accurate is your scale?

Even if you can measure everything accurately, the data you've got is limited in it's nature. You can't for example, bend a piece of wood without giving rise to shearing stresses, and these will be mixed up in the data even if the node lines are ruler straight. There are , I'm told, mathematical ways of correcting for this issue: you have to collect data on a number of modes, some of which are nearly 'pure' shear, and others nearly 'pure' bending. Then it's possible to develop computer models that can sort every thing out. This is supposed to get you about 10% closer to 'reality', and I'm not sure it's worth the effort. After all, the density and stiffness of the wood sample vary from place to place by a fair amount, and it's likely enough that in itself introduced significant errors.

Finally, the equations that are used to calculate the moduli are, themselves' simplified. For one thing, they leave out the 'small' sources of perturbation such as the shear component in the Young's modulus. They are also assume linearity, which is probably not always the case.

There's a lot more to this, but I trust this has given you enough to start with. Daniel Haines has written about this, and documents his methods and reasoning well. I try to do things as accurately as possible with Chladni paterns, knowing that it's not all that accurate, and hope that I'm 'close enough'. It seems to work pretty well for me.

Thanks for the input, Alan.

Can anyone provide a range for cross-grain Young's Modulus for spruce species? If I knew the range of potential values I would know where an individual board falls on the scale once I've calculted the crosss-grain Youngs Modulus.

Seems that the long-grain Young's Modulus on spruce ranged from 9,000 - 15,000 MPa is what I remember reading on this site once........but I've no idea about the cross-grain Youngs Modulus.

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Formerly known as Adaboy.......

I think the difficulty with a question like that is that the range is huge - and is heavily dependent on how perfectly quartersawn or flat sawn the piece is.... and on how the wood is actually cut - whether it is sawed or sliced like veneer....

I think the range of crossgrain stiffness in tops that are reasonably well cut goes anywhere from 1/2 long grain to somewhere less than 1/100th of long grain.... The pieces I have fooled with seem to range somewhere between 1/10th to 1/20th long grain.... I do have a couple tops that are *WAY* off quarter - and you would swear you can roll them up into tubes....

Thanks

I have rolled some into tubes, particularly when the grain is about 45 degrees off vertical.
For a long time, I wondered why spruce (and most other softwoods) lose cross-grain stiffness so quickly when the grain is only a few degrees off vertical. It is not at all true with hardwoods. Then one day, when I was looking at magnified end grain photos of various species for identification, it finally dawned on me. In softwoods, the cells are basically rectangular in cross section. That means that the cell walls are very stiff when the load is in line, and it also means that the cells can distort into parallelograms when the load is at even a slight angle.
In hardwoods, the cells are basically oval or circular. That is why the grain orientation is much less of a factor in the cross-grain stiffness of hardwoods.
With this in mind, testing the cross-grain stiffness of softwoods requires a close study of the grain orientation to create a meaningful analysis.

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John

I'll admit up front that I haven't read everyones replies in any detail but I'll take a stab at posting an actual number off of some of the data I have from my deflection testing. I understand Al's comment about getting "Q" and it's need and I agree too, but if you couple the density with the moduls you kind of get a feel for "Q", also in the way it handles.
Anyway, here's some values off a nice European Spruce top i had a while back. My experience is this is a pretty stiff top across the grain and better than average along the grain. Made a nice guitar.
Along the grain modulus; 1,832,000 psi
Cross grain stiffness; 163,900 psi
long grain /cross grain = 11.2
Hope this helps.

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Jim Watts
http://jameswattsguitars.com

Here's some values for cross grain YM (SI units)

Engelmann: 41 samples, average 0.81 GPa, s.d. 0.20 GPa
Sitka: 8 samples, average 1.00 GPa, s.d. 0.08 GPa
Euro: 13 samples, average 1.29 GPa, s.d. 0.19 GPa

All this stuff was high AAA or master grade.

Typically, cross grain stiffness has very little influence on the low order mode frequencies, because the situation is dominated by the long grain YM which is 10-20 times greater.

If anyone has a preference for wood with a high cross grain YM, could they please let us know what it is they particularly like about it?

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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

As Alan has said, there's basically two methods: the static method and the dynamic method. The static tests involves a three point bend test and measuring deflections, the dynamic tests involves tapping and measuring frequencies. My testing has indicated that they correlate quite well. I use tap testing predominantly because it's faster for me to do it that way. I also like the idea of measuring a mode frequency in order to predict a modal frequency. Details on the process, hardware and software required for both methods can be found in the usual place.

If you use a spectral analyser as you tap test, you get the frequencies and the peak distribution. A strong indicator of Poison coupling is two peaks close together in frequency. This happens when Lx/Ly=(Ex/Ey)^0.25 (L=length, E=Young's modulus) and it will give curved nodal lines. If you can change the length or width of the board (and still get your template on it) you can move away from this situation and get a cleaner result.

The point of materials testing (for me, at least) is not to get an accurate modal performance result by "dead reckoning", there is too much scope for error for that, but to get close enough so that you can pretty well guarantee that you can trim it in to where you want from where you initially landed. With the range of variability in even "good" wood, it's nigh on impossible to do that if you start by (for example) building to standard dimensions.

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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

WOW!!! Thanks everyone. This gives me a lot to chew on. Certainly a lot more sophisticated than "this one feels stiff". LOL

Thanks again.

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Mmmm....wood.

Trevor, how you pick up cross grain stiffness with a tap test? I'm asking because I would like to learn, I'm not challenging you. It seems to me I would get an average plate stiffness by doing a tap test.
Thanks,

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Jim Watts
http://jameswattsguitars.com

Trevor wrote:
"The point of materials testing (for me, at least) is not to get an accurate modal performance result by "dead reckoning", there is too much scope for error for that, but to get close enough so that you can pretty well guarantee that you can trim it in to where you want from where you initially landed."

Exactly. Almost any objective test will get you a lot closer than 'look and feel' can, and then you can use whatever fine tuning method you like to close the gap.

My own testing indicates that the lengthwise E values pretty well track the density in the same way for _all_ softwoods. If you know the density, about 2/3 of your samples are going to fall within 10% of the E value the density would predict. The line seems to run from SpG =.3 and E=6000mPa to SpG=.5 and E=17000 mPa. The main thing that seems to throw this off is the presence of 'compression grain': wide latewood lines that you tend to see near the bottom of large trees. The stiffness of such wood tends to be lower than the density would predict. Runnout decreases Elong, and Haines had some numbers on that, iirc.

Crosswise E values are all over the map: I'm not a statistics whiz, but it sure looks like a perfect scatter to me when you plot it against density. Ecross values I've seen run between 400-1400 mPa for the most part. I have one Sitka sample, almost perfectly skew (45 degree) cut, with Ecross at 205 mPa, for a ratio of 62.2:1. I've seen worse, but don't have the numbers on those. The only strong correlation I've found is with grain angle. So far, I've seen no correlation between grain spacing and Ecross values, although Burns said he saw a weak correlation, with the E peaking at about 24 lines/inch, iirc.

BTW, if you don´t mind me asking, if cross grain stiffness is higher when the wood is cut at 90º, when is it lower - at 45º or when approaching 0º? (i´m thinking 45º, but still would like be shure)

thanks,
miguel.

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member of the guild of professional dilettantes

Soft woods will be strongest when flat sawn and quarter sawn... They are weakest when the cut is 45* to the grain.

No problem with challenges Jim, I have good defences!

Tap testing the way I do it is a three part test, first described by Graham Caldersmith back in the 1980's with papers in both Acustica (for the really hard science) and the GAL rag (for the user friendly version). The first two tests are "marimba bar" tests which look at the frequency of the first mode along the grain then across the grain. This gives you E long and E cross. The third test is of the first twisting mode which gives you G, a shear modulus.

You put the frequencies, sample mass and its dimensions into the relevant equations and you get the elastic moduli which you can then use in another set of equations to tell you how thick to leave the plate. I have it all set up in a simple spreadsheet (which many others have now reproduced) so that you just dimension and weigh the samples, measure the frequencies, stick the numbers in the spreadsheet and out pops the target thickness. It takes all the guess work out of panel thicknessing. Works for top and backs. Detail in the usual place.

Schleske's paper is the one usually quoted here. 45 degrees.

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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

John, did you really roll the piece into a closed tube?
If you did,
I find that amazing!
How thick, wide, and log?

I was just sittin' out in my so called "shop",
and looking at some wood I've built with,
and started thingink.
What I was thingink was,
instead of thinning the edges of the top,
where they meet the sides,
to have more flexibilty there,
use a piece of 90 degree quartersawn spruce, at the middle joint,
and if the edges are less than 90 degrees,
might be more flexible...
I'm sure I'm over-thingink on this, but....
P.S. Don't tell me how to spell thingink,
Link.

As a few here have already mentioned - although it bears mentioning again....

The "Stiffness" you feel is proportional to thickness cubed and width x 1 and divided by Length... so if a piece is 25% thicker - it feels 2x as "Stiff".. The same piece - if you hold it farther apart, it feels less stiff... As you might imagine - very small differences in thickness can fool you into thinking that you have a piece with a higher or lower Modulus - and not just a different Thickness.... Like say a 10% difference in thickness = 20% difference in stiffness... so a sanded top at 3/16" vs 13/64" - 1/64" difference will be 20% stiffer just because of the thickness.... Very easy to get fooled.... because while you can easily feel 20% stiffer - you may not be able to feel 0.018" difference in thickness...

Thanks