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I'll take a shot at it.

Some terms.

So - your original stiffness
Sn - the new stiffness ( in your case that's 12.5% less than So)
Ho - the plates original height (thickness)
Hn - the plates new height (thickness) that's less stiff

I need to think about it in terms of the ratio of Sn/So

I'll take this slow, I"m still working on my second cup of coffee.

(so-sn)/so = .125

so -sn = .125 * so
sn = so -.125*so
sn = so * .875
sn/so = .875


Since the only thing we're changing is the height, we don't have to worry about Es and and all that, just ratios and cubes. (** means to the power, so 2**3, means 2 cubed, or 8, also, 2**(1/3) means the cube root of 2 or 1.259..)

For a brace or your plate:

sn/so = (hn**3)/(ho**3)
therefor
( (sn/so) * (ho**3) ) ** (1/3) = hn

an example might help. let's say your plate is .1"

then

( (.875) * (.1 **3)) **(1/3) = hn
( .875 * .001) ** (1/3) = hn
.000875 ** (1/3) = hn
.09564 = hn


That seems about right but hopefully others will check my math.

You'll get the same % reduction in stiffness in both directions.
There are more complicated ways of looking at this. See Hurd's book if you want that.

John

Aha! I will study this most carefully. I may hit you up with further questions....
Thanks

Sorry to 'jump in late' here...I'll just add a couple of thoughts. I'm also just starting to do more data collection on the wood I'm using, so not 'expert opinions' at all.... And, not addressing the issue of how to thin the top to your 'target'...

The usual grading schemes (AAA, Master, etc) tend to focus on cosmetic qualities, so an expensive top may not necessarily 'test' better in deflection or other numerical tests. I've tested some great-looking top wood which was just 'average' in stiffness and other measures.


Generally, I think most folks test cross-grain stiffness with the supports much closer together (~6"- to allow testing unjoined top wood), using a fairly heavy weight. You can, of course, use a different (lighter) test weight with the same 18" span and just plug the value into the calculation for Young's modulus (cross-grain), as Alan Carruth suggested.



I plugged your data into the spreadsheet I use, but it wasn't really necessary. Looking at the two tops, since they are the same thickness and deflect (almost) the same amount with the same test conditions, they are equally stiff. i.e. the Young's modulus (long grain) for the two tops is practically the same. Woody has pointed this out already.

I try to use weights that are 'long', BTW, so if using a weighted bottle I'd lie it down.

Looking at the density (specific gravity of the two tops, the Sitka is quite a bit denser than the Adi (.51 vs .39 by my calculation). So the sitka top will be heavier than the adi when they both meet the same target deflection/stiffness, which probably isn't a big problem in a steel string guitar. Looking at the ratio of stiffness/density can help to decide which woods to select if you want to get a stiff but light top.

Going through my stash of top woods and getting some data like this is on my 'to do' list. Hopefully it will help me decide which tops to use in a given project. I've heard that some builders actually like tops to be a bit on the 'floppy' side to work with their steel-string bracing patterns, so this is all more complicated that it might seem at first glance.

Cheers
John

That's how I'd do it as well- take the cube root of the new 'stiffness target' and you'll get the new thickness you need.

John

When we 'measure with the senses' (??- like Torres famous BS about the magic in his fingers), I think we're really saying that we just don't understand what we are doing, but we do something and it works (or not!) for us.
However it sounds a lot more impressive to tell folks to 'just build 50 (or 100, or...) guitars and you will 'know' - it can't be explained to you.

What exactly are the 'unmeasurable' qualities that we are talking about? 'Feel' and 'sound' are measurable.

Of course on the west coast folks are into reading auras and chakras and such, so perhaps that's what we are sensing??

Cheers
John

Hello,
The woods 'a cut above my usual' I referred to were the back and sides, first time cracking into the exotics instead of mahogany or EIR. I've been fortunate to have access to stellar tops from the get-go.
I was never good at math, so I sat down with my roommate and he was able to translate the equation into prose, which helped me a lot, and I was able to do the equation and come up with the answer I was after, and will be able to do so again, so to John Platko, thanks very much that was what I needed.
And then the confounding part...I was unable to get the same deflection readings that I originally had, and I also noted that the deflection changed if you left the weight on longer (which makes sense). The next trick will be to figure out a truly accurate testing system, but that's for a different thread.
So thanks everyone for all the help. In a few days after I take some more readings and do some averaging I will post a laymans version of the equation with my numbers as an example and see if it is correct and verifiable. And then the time consuming part of actually making the guitars and seeing if I like them or not!
Cheers

Great, I'm glad I could help.

Since I come from a different school of thought on all this, I have a few questions too.

For those measuring stiffness with and across the grain: Does the ratio of the two measurements seem to be some constant? That is, if you measure two tops and one has half the deflection with the grain do you expect it to have half the deflection as the other top across the grain? Or,can you have a very stiff top with the grain that is unusually floppy across the grain?

How do you factor density into all of this. I guess I'm trying to understand what the specific purpose for measuring the deflection is and how you use it. I mean, I understand how it's a better way to get a handle on how to tell a stiff from a floopy top than building 100 guitars, but is there a grand scheme for the use of this kind of measurement?

John

I forgot to mention that I was talking about 'percentage values' in this simplified re-statement of John's excellent derivation.

There are a few 'wrinkles' to the deflection testing setup - Brian Burns has done a lot of this work and I studied with him for a few days last month.
Some ideas which may help with consistency-
1: A 'pre-load' weight to make sure the wood sample is sitting on the supports securely. (Zero your dial gauge after pre-load).
2: Paying attention to the smoothness of the supports- Brian uses round steel rods which are quite slippery.
You can find some details at http://lessonsinlutherie.com/woodtestingandvoichirez.html
You can see the pre-load (hollow pipe) and the test weight (solid rod) in one of the pictures there. Also, the narrow-spaced supports for cross-grain deflection testing (on the same jig).

I tested a bunch of samples at Brian's and compared the results with data from my shop - some were pretty close, others varied up to 20% between the two setups. So some work to do before data like this is really 'portable'.

As you say, a different thread could look at some of those ideas more fully.

Cheers
John

John-
I'm just starting with this kind of work, so can't add a whole lot.
Parallel- and cross-grain stiffness seem to be quite independent, so I think you need to test both if you are interested in both. I don't think you can predict cross-grain stiffness accurately from the parallel data. (And the converse: Like many 'beginners' I was in the habit of 'testing' wood in my hands by only flexing cross-grain.)
As far as using the data in building decisions, you could imagine a scenario where a small brace (aka tone bar) was added cross-grain to increase the stiffness, or the angle of the fans (or lattice) in a classical was altered to deal with the parallel/cross grain ratio of a particular top.
If you are looking for the lightest top possible for a given stiffness, this sort of data (looking at the stiffness/density ratio) can be a big help in sorting top wood.
For actual thicknessing and voicing decisions, I'm tending toward using resonance testing nowadays.

Cheers
John

Tom-
I think that some archtop builders are measuring deflection on braced tops and even finished guitars. Dave Stewart may have more info on this.

I recall seeing some info on measuring deflection (at the bridge?) on finished flat-tops somewhere, sometime in the past.

John MacDougall, a local builder here in Victoria has a measuring fixture with several dial gauges for collecting deflection data on tops. I'm interested to see what he discovers as his work progresses.

To measure braced top deflection before attaching the top to the sides, you could build a fixture to hold the top at the edges - sort of a 'clamp-on set of sides' arrangement.

Resonance testing (& Chladni testing) comes at this idea from a different direction, but essentially is doing something similar- measuring stiffness/resonance of a braced top, or semi-(or fully-) assembled guitar.

Cheers
John

Young's modulus along the grain varies pretty reliably with density: about 2/3 of the tops I've measured fall within 10% plus or minus of a given line. If the specific gravity is about .3, E along the grain will be about 6500 MegaPascals, and if the SpG is .5, El will be about 16500 MPa. The relationship is linear, and almost _all_ softwoods I've tested (except Eastern Hemlock) fall on the same line. Woods with heavy latewood lines, or a lot of runnout, tend to have lower El values than the density suggests.

The only thing that seems to predict cross grain stiffness is the angle of the ring lines to the surface. I've got two Sitka samples that are about the same density and stiffness along the grain, but one has a stiffness ratio of about 8:1, and the other is 62:1. The floppy one (62:1) is dead skew cut, which gives the lowest cross grain E values and (interestingly) the highest values for shear modulus.

Dave Hurd strongly suggests doing deflection tests from both sides of a plate. Things like grain curvature can make the deflection vary depending on which side is up.

Wood 'cold creeps', so the deflection will be greater the longer it sits with a weight on it. One recommendation I've seen is to load the plate, zero the gauge, then remove the weight and read the gauge immediately. If you like you could use two weights: a small one to 'seat' the peice on the supports, and a larger one for the delfection measurements. Put both on, and then remove the heavier one when the gauge has been zeroed.

The vibration tests I use get around the cold creep problem, but have other issues. There is no perfect test.

That's interesting. Do other folks see the same thing? Anyone care to share their data?



I could imagine it in principle but can't quite imagine how to go about it in practice to make everything balance out in any predictable way.



Ah, now that I understand.

John

Did any of you guys sit in on Bryan Galloups talk at the last ASIA convention?

If you want to know how to put it all together he offers a class on voicing that covers all of this.

While getting deflection is fine as a measure and predictor I think the biggest point/ factor that isn't mentioned above is quality. Are any of you guys measuring quality?

I took Bryans class with him and Sam, I was the 1st test student, and those two guys have it down better then any of the books (new and old) hold have ever shown. The biggest thing I pulled was the quality factor. Modulus (MOE) and Speed of Sound are great but the quality factor of the wood before build even starts, before it even starts being thicknessed, has made more of an impact then any of the other testing.

Weeding out the bad tops (low quality factor) and subbing in better Q factor tops has made a world of difference. Grain lines and silk are great indicators but I've learned that Q trumps them both.

http://www.galloupguitars.com/new-class-added-to-program.htm

_________________
Todd Lunneborg
http://www.tlguitars.com/
http://www.fretboardjournal.com/

What percentage of tops do you weed out? It sounds like it could get expensive. Do you just send the "bad" ones back?

Also, have you ever tried correlating measured quality factor with Luthiers selecting tops by tapping? I wonder if "quality factor" is what people tend to select for.

John

By 'quality', you are referring to the Q factor as used in electronics, etc?
http://en.wikipedia.org/wiki/Q_factor

I'm using the method I learned from Bran Burns to measure this - looking at the 'sharpness' (-3dB bandwidth of resonance peak) of the resonance peaks when wood testing. Interested folks can contact Brian for an article he wrote a few years ago, describing the method he was using at the time. (In the wood testing context, Q gives an idea of the 'damping' in a given wood sample', as I understand it.)

How are you measuring Q?

I've found that quite a few factors influence the Q result for the same piece of wood- smoothness of the wood sample, software setup, etc..
How are you controlling the variables in your system?

Cheers
John

I've heard of builders returning tops to the seller (after testing), if the seller had a 'no questions asked' policy on returns. I assume the returned tops just go back into the inventory for resale. Makes you wonder what we're buying!


Good question. Is that the 'ringing' or 'lively' quality that some folks listen for when tapping unfinished wood samples?
One more 'mini-experiment' to do.....

Cheers
John

Just so I'm clear on this, Alan. Assuming well quartered tops with no runout, is there a ratio, within say 20% between stiffness along the grain and stiffness across the grain or does it varry more than that?

John

I'd say no. Some of the stiffest tops I've had longitudinally have been the floppiest cross grain, though this is based on feel, and not statistics.

_________________
Waddy

Photobucket Build Album Library

Sound Clips of most of my guitars

Hey John, and all OLF’rs

No, my quality or Q is a calculated measurement combination of density, tap tone (FFT) and deflection. Not the link you posted. The quality of the top as according to my findings.

Tops and backs come in at .160 X 20" X 10 (ish). I'll do my deflection testing and density calculations and I'll also record the tap tone and check the resonance of whatever tone it's giving (FFT analysis on my computer). Calculate my MOE and Speed of sound (with and cross grain) and mash it all together and come out with a quality factor for that particular top. They range from 5-9, so my 6.00347 top isn't as "good" as my 6.7871 top or 7.5678 etc.

I am able to rate my material (thanks to Bryan Galloups and Sam G's work,... all of this is theirs) before I start working with it. That way I can weed out the tops that aren't given to "tone" as well as other tops.

So yeah, when I buy tops I'll by 3 or 4 test em and send them back if needed. All they were was shipped to MN and had a weight put on them and a bunch of callipered thickness measurements taken, and tapped into a microphone and that’s it, so no need to roll your eyes. Or I'll put them aside for student guitars or sell them to someone else. I'm in a whole other rabbit hole now thanks to what I learned from Bryan and Sam this spring, but if the benefit of knowing I have a quantifiably better chance to come up with a "consistently better" sounding guitar, rather then a "decent" or "average" sounding guitar, then that is something I want for my work and as such I'll take the time to guitar nerd out on and calculate.

I’m trying to quantify the tone potiential of the cell structure of the material I’m working with. Crazy right? But think of it this way, just because its Adirondack Red Spruce wood doesn’t mean that it’s going to make a great sounding guitar, just like, just because Saran Wrap is plastic doesn’t mean it’s going to make a great drum head.

Honestly, what people are getting as AAAAA tops or mastergrade tops are just evaluated from the sellers side of things simply based on looks. Quarter, silk, runout... while these are all great indicators for good tone potential it's like Brazilian Rosewood, it can tap great but there are tons of ways a builder can make it sound average or if they are aware of what they can do to keep and use it's tone they can make it sound amazing. I can get a perfectly quartered and super silked piece of Phil. Mahogany but it's only going to be good for closet foam core doors. Could you imagine if you could actually buy a top that had been evaluated and graded based on sound, or sound potential?

C.F. Martin III said that he actually liked guitars built with tops that had less then "mastergrade" grain counts (AA and AAA by modern standards). Because I'm not looking for a pretty top, they’re nice to look at but do they sound better? I want the best sounding top I can find and if I can pre-evaluate my material based on something more tangible then how pretty it is to give me just that much more of a chance to build a “better to great-ish” sounding guitar then I’m all in.

Paying for return shipping is an easy price to pay. I'm still in the early stages of implementation here, but I've got my average, good, better, best piles started; and that's good enough for me. "But it's a whole other rabbit hole, " Brian Galloup.

_________________
Todd Lunneborg
http://www.tlguitars.com/
http://www.fretboardjournal.com/

Todd-
Thanks for that info.
When you record the tap tone and do the analysis (FFT), what data are you getting? Just the main resonance frequency (or frequencies) or other info about relative amplitudes, etc. ??
What software do you use?

Cheers
John

I'll try to contribute something as I've tested tops for many years now.
Here are some photos of my test fixture. This fixture isolates each axis as it spans the entire length/width of the top giving me a sperate number for each axis.
I test unjoined tops around .150-.160 and I use this primarily as a sorting guide. I look at youngs modulus in each axis and the ratio between the two. I also look at the desity of the wood and it's relationship to it stiffness. Stiffness tracks density rather nicely BTW, of course there are exceptions to that. I use standard engineering formulas to find the modulus of each axis. Here's a link to a good paper on wood testing by Charles Wood a violin maker that really got me thinking about this years ago. http://www.scavm.com/Woods.htm
He has all the formulas written out in the paper so you can get them there, it's easier than me retyping them and it's a good paper.
I've also attached a PDF of my spread sheet which shows the things I'm tracking if that helps anyone.
I also deflect my braced tops in multiple locations and track that also, the last 2 photos show that.
I don't know how coherent this is, but I hope it helps some.

_________________
Jim Watts
http://jameswattsguitars.com

Jim,
Excellent information. Thank you!

Jim-
Thanks!
Very slick (and compact) testing jig.

Q: You measure the deflection on raw wood samples from the top, just beside the 'beam' that applies the load? (rather than underneath, below the applied load...)

Q: Measuring deflection on tops and complete guitars- what is/where is the applied load?

Cheers
John

John, Yes I measure right next to the beam, same place every time.
Oh, I didn't mention it but I set a weight up on that platfrom also.
As ar as deflecting my braced tops normally I just push on it as I'm working the braces, you'd be amazed how repeatable a thumb push can be. I know it's hard to believe but it's true. I'm not making calculations from it mind, just more of a tactile thing. When I think I'm done I set a weight next to the indicator and take a reading using the weight. I actually like using the thumb push.
I also analyse the taps at various stages using Audacity.

_________________
Jim Watts
http://jameswattsguitars.com