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Today I tried a quasi scientific deflection test. I watched a Youtube video where a 5 1/4 pound weight was used to deflect a top 1/4" across an 18" span. Normally I sand my spruce tops down to .110 and go from there, maybe doing some perimeter sanding if I 'feel' it's needed. So I took five rosetted tops and put them through the sander till they all deflected to 1/4", and was quite surprised when the final thickness ranged from .92 to .95, all Sitka, and one adi top which came out at .100, which surprised me as I thought it would have come out thinner.
The tops are certainly a lot flimsier than I'm used to, but it could easily be that I've been leaving things a little heavy, with no real references to go by. Does anyone with a bit more experience with deflection testing have any comments as to whether these numbers are wacky or not? I know it was a highly uncontrolled test and that there are many more variables than this to consider, but, any thoughts?

The tough part about this sort this sort of thing is that the top is part of the system.... If the top is a little thicker, some of the bracing may end up a little thinner... and vice versa.

Or... a thinner top can be more responsive to a lighter touch... but conversely may be more easily overdriven by a heavy hand....

These are the sort of trade offs you end up making.

Thanks

John

I will not comment on whether this particular deflection test method and goal is valid.
But using tops that you have already installed a rosette in changes everything

I guess another way to phrase it would be...
Does anyone else find that your sitka tops end up in the .90-.100 range?
Thanks

I don't do a deflection test on the top I want to know the raw wood so I know how to brace a top. Still this may be able to tell you how well the top may be braced . After building over 100 guitars I think I have my bracing down very well. I have a good result with repeatability.
One thing that I don't like about this is that the top is not a load bearing surface like a floor . The stresses we are putting the top under are
1 compressive load from the bridge to the neck 2 torsional , we use this force at the neck block with the neck trying to pull the neck block over and at the bridge with the strings pulling on the plate , bridge and saddle , 3rd we have a tensional force from the bridge to the tail block.
How you can tel by placing a 5 lb weight on the top how these forces will be affected is what I don't understand. Also , not that there is no validity to but I do not see the value of this test. Martin used to use these weights for testing the neck deflection when setting up a new guitar to imitate the string load . When places at the shoulders of the body , the weight applied a similar force to the neck that full tension strings did and allowed to get the initial set up close.
Beware of Youtube ,if you don't know the contributor , there is much info out there , not all of it good.

_________________
John Hall
blues creek guitars
Authorized CF Martin Repair
Co President of ASIA
You Don't know what you don't know until you know it

Yes, that is very normal.

Did you also measure the density?

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Brock Poling
Columbus, Ohio
http://www.polingguitars.com

I will do tops to .095 depending on density and deflection tests. The key is to match the top and the bracing .

_________________
John Hall
blues creek guitars
Authorized CF Martin Repair
Co President of ASIA
You Don't know what you don't know until you know it

Brock,
No, I didn't measure the density. After I finish these guitars I'll be setting up to do deflection testing a bit more properly. A copy of left brain luthiery is in the near future. This was just a quick test that I could do with minimal set up. It's good to hear these numbers are in a normal range, and the tops certainly feel a lot livelier than what I've done in the past. Only gluing the rest of the guitar on them will tell me whether it helped or not.
John,
The test was from source I would consider trustworthy. I think the value of even a quick test like this could be to help achieve consistancy from top to top. Even if it doesn't load this way like it would on a guitar, using the same test on every top could help give you a control factor.
Thanks all...

I would need to see the video but the issue is if you test the top for a stress that isn't applied or applicable the test results are not that useful for a guitar.

_________________
John Hall
blues creek guitars
Authorized CF Martin Repair
Co President of ASIA
You Don't know what you don't know until you know it

My Esteban Retop got Sitka that started in the 0.095" range (And Cumpiano's book bracing... shaved a bit afterwards) .... Runs great with Medium strings...

So.. I have at least 1-data point within your range.

Thanks

John

How do you go about....to measure the density?

I measure in g/in^3... I realize that is a bit odd since I am mixing metric and imperial, but that is how I do it.

measure the width, length and depth in inches and multiply them together. This gives you in^3

measure the top in grams. I have a triple beam balance I picked up on ebay for about $35. It is very nice. I am sure there are tons of these available all the time.

divide grams/in^3

Spruce should give you a number between 6 and 8 gm/in^3.. and some adi I have seen is in the 9's

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Brock Poling
Columbus, Ohio
http://www.polingguitars.com

Not for knowing what the actual stresses will do, but if those stresses relate in any consistent way to other more easliy measured ones (like span deflection under weight), then there's no reason measuring those won't yield information about what will happen under "actual guitar conditions." We're always talking about the stiffness of tops and braces, and deflection of a span under load is the canonical engineering stiffness determination. Kawika Hurd has used deflection testing of finished tops to good results and posted a tutorial here on his methodology.

Peace,
Sanaka

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...imagine there were no hypothetical situations...

Brock, do you find that's the conventional expression among luthiers?? I calculate g/cc typically (about .325 to .425 range), but then I hear weird numbers that are tough to relate.

Sanaka, Alan Carruth has said that Young's modulus along the grain ....... tracks the density pretty nicely and stiffness of the top will depend on the product of the Young's modulus and the cube of the thickness. So I use density as a guide to how thick I can carve the top. Now that I've built myself a deflection tester for my archtops, it'll be interesting to prove this out. (Not sure if this is what you were getting at.)

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Dave
Milton, ON

I use a standard deflection test with a standard size of 1/8" square 6 inch long and can measure the total deflection within a certain weight range . I can measure within .001 and this test allows me to know the bracing I need to gain the end result of the top.
I also use this method to plan the geometry of the top for the neck angle and final action height. In doing it this way I have 3 distinct areas on the top . This 3 sectioned top will incorporate added stiffness to the top in the shape . If you check this video you can see what is done and how it works . http://www.youtube.com/watch?v=QYHPCeVRUA4 If you look at my blog section in the website it was documented there and in the Guitarmaker Magazine.

_________________
John Hall
blues creek guitars
Authorized CF Martin Repair
Co President of ASIA
You Don't know what you don't know until you know it

Sorry John, I thought earlier you were saying that deflection testing in general wasn't that useful, but now I think I see what you're getting at: that you test the unbraced top and this helps guide your bracing decisions. I would think this, and measuring the braces simiarly, is indeed the most useful in the buidling process.

The tutorial I linked to earlier is Dr. Hurd's method of mapping the deflection or compliance of a finished top. The purpose being that if you like the sound of a certain instrument, you can attempt to reproduce that sound on a new instrument by recreating the distribution of stiffness/flexibility you measured on the original.

Dave, yes I've read that about stiffness tracking with density and it makes sense on the one hand, but on the other confuses me as to the meaning of strength to weight ratio. I have more reading to do For sure though the stiffness of any "beam" like structure, even if it's a wide flat "beam" like a top, varies in proportion to the cube of it's height. That's why a 2x8 floor joist in a house is twice as strong (i.e. will deflect half as much for a given load) as a 4x4 even though they have the same amount of wood, why tall skinny braces give you the most strength for the weight, and why a tiny difference in thickness can make a large difference in stiffness of a guitar top (hope this relates to what you were getting at... )

Peace,
Sanaka

_________________
...imagine there were no hypothetical situations...

sanaka wrote:
"Dave, yes I've read that about stiffness tracking with density and it makes sense on the one hand, but on the other confuses me as to the meaning of strength to weight ratio."

The trick is that the real controlling factor for us is not _strength_ but _stiffness_ to weight. It's easy to get confused, and that leads people off into experiments with things like carbon fiber that really won't do much good.

The thing that kills guitars is the deflection of the top under bridge torque. The area behind bellies up, and, even worse, the area between the bridge and soundhole dishes in. At some point, when the delfection gets too great, the guitar dies, if, indeed, the bridge doesn't fly off and kill the cat first. As a rule of thumb, the folks who make wooden airplanes say the the initial deflection under load should be no more than 1/3 the deflection you can tolerate over the long term; this accounts for the 'cold creep' of the wood over time.

It terms of tension/compression loading, if the top stayed flat you could take all of the string load with no problem using almost any piece of wood and any 'normal' thickness. Again, iirc, the aircraft folks rate spruce at an ultimate load in compression or tension of about 3000 psi. With, say, 150# of tension, that's .05 square inches of cross section area: a stick about .22" x .22". We all know that would not work in the real world, because of the torque.

If you're planning on getting all of the stiffness you need from the bracing (like a lattice top) then you can make the top as thin as you like. I feel I get better results by 'balancing' the bracing and top stiffness in some sense: I don't like either of them to have to take the whole load. That's what 'plate tuning' is about IMO; the mode shapes tell you when you've got that balance. A thin top with heavy bracing won't 'tune' right. I like to start out with a top that has a certain stiffness, add the bracing, and then shave it down to get the 'correct' balance, at which point I figure I'm good to go.

Now, the stiffness of the top is going to depend on the Young's modulus of the wood, and the cube of the thickness. Although the crosswise Young's modulus gets into the act, I don't count that in, because I figure that, over time, top distortion is going to discount that as a useful factor. Besides, my math chops aren't up to figuring it in properly (although Dave Hurd talks about it in his book). So, when I'm deciding on how thick to make a new top, I'll use the lengthwise Young's modulus measurement to tell me what that thickness should be.

The process is simplicity itself, but you need to have a data base of some kind. I look at the 'best' previous guitar I've made that I know the Young's modulus (E) value on. Suppose that was a piece of Engelmann that had a lengthwise E value of 10,000 megaPascals (metric measure). I used that on, say, an OM, and it worked well at 3mm thick. I just take the cube of 3mm and multiply that by 10,000 to get an 'index number' of 270,000.

Now, the top I want to use on the next one is Red spruce, and it has a much higher E value, of 15,000mPa. I just divide the 270,000 index number by that, to get 18, which is the cube of the thickness I'll need to make a top with the same stiffness. That would be about 2.62mm, or, say, around .103", where the other top was closer to .120".

I'll note that the Red spruce top probably has a density of around 470 kg.m^3, where the Engelmann one was most likely closer to 370. If the Engelmann top weighed 120 grams without bracing, the Red would come in at around 133 grams. The higer E value of the Red doesn't make up for the extra density, basically because of the cubic factor in the thickness/stiffness relationship. The bottom line is that for softwood tops, you'll usually end up with a lighter plate if you use wood with low density.

If you're loking for volume, than a light top is probably what you want. What you do seem to lose with that is 'headroom'; dynamic range. I'm not just sure what's involvedin the 'breakup' of tone when a top is driven hard: there's a long series of experiments lurking behind that rock, I'm sure. But usually the woods that are cited as having the most 'headroom' are the denser ones, like Sitka and Red, while Cedar and Engelmann are usually though of as not having it.

Given the range of variation within any species, you really need to measure this stuff. Density is a decent surrogate for lengthwise E value, if you don't want to set up for the deflection measurement, but it's not as reliable as it ought to be for really high-class work.

As for the data base, I suppose you could start out with, say, the usual thickness of Martin tops, and a density/lenghtwise E value a little below 'average' to work up an initial index number. I figure that, in production setting, they have to plan on the least stiff top ending up with the weakest bracing once in a while, and plan accordingly. If you assume their 'average' top is somewhat over built, you are probalby going to be in safe territory to begin witrh, and can refine your numbers later as you gain experience.

Thanks again Alan, for another of your amazingly educational posts.

My confusion has been thus: "Isn't saying that 'wood stiffness pretty much tracks with density' the same as saying 'wood pretty much all has the same stiffness to density ratio'?"

Because then I'd be all over a Cocobolo guitar top! It would be gorgeous, and about .043" thick to yield the same mass as a Sitka top at .110". But somehow I don't think it would be stiff enough...

I think you answered it for me where you say:

If I understand correctly, denser wood is generally stiffer, and this relationship kinda-sorta stays linear enough within the group of "similar" top woods to be useful? However, measuring deflection seems about as easy to set up for as density (no need even for a scale or an easily calculated top area...). So, if one were to choose one measurement or the other, doesn't it make more sense to just find stiffness directly rather than use density as an indirect stiffness indicator?

OK, I've avoided the "strength" versus "stiffness" thing. As far as structural wood function goes, I've been thinking of these interchangably, and defined as: "Deflection under given load for given span." I have a vague memory/notion that these terms have different strict engineering meanings - what is the difference? Why would it obviate consideration of carbon fiber?

I really appreciate your description of balancing the load between the top wood and the bracing. In fact, I appreciate how most everything of yours I read seems to be a synchronicity of intellect and intuiton. I'd love to play one of your guitars someday

Peace,
Sanaka

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...imagine there were no hypothetical situations...

The problem, and I'm as guilty as the next guy, is that we keep saying 'stiffness' when what we really mean is 'Young's modulus'. They're related, but not the same.

Young's modulus is a measurement of how much force it takes to stretch/compress a given sized piece of material by a certain amount. I use kilogram/meter measurments, and I think that the numbers I get from the equations I use tell me how much force it would take to stretch a cubic meter block to twice it's length. This is totally unrealistic, of course, but it's a standard that allows for comparison.

Stiffness is a measure of deflectino under load. If you're trying to bend something most of the force that resists that comes from the stretching and compression of the inside and outside faces of the piece. The material in the middle doesn't contribute much, which is why they tend to leave it out on I-beams and such; it's adding weight but not much stiffness. So long as the two faces are held apart, what counts is the Youngs' modulus and the distance between them: the thickness of the stock.

The actual stiffness of something like a brace or plate will be proportional to the Young's modulus times the width and the cube of the thickness. Two pieces of wood with the same Young's modulus will have the same deflection under a given load at the same thickness. If one of them is, say, spruce, with a density of 400 kg.m^3, and the other is a piece of Indian rosewood, with a density of 800 kg/m^3, the rosewood will weight twice as much at the given thickness, and deflect the same amount under load. This is not at all uncommon, BTW: the range of Young's modulus along the grain for Sitka spruce and Indian rosewod is much the same, from about 9,000-15,000 megaPascals according to my measurements. Sitka ranges in density from about 400-500 kg/m^3, while IRW runs between 750-900.

And that's why we use spruce for tops instead of hardwoods. All of the softwoods tend to fall on one line if you plot Young's modulus against density. The hardwoods are more variable, even within a single species, but tend to be denser for a given Young's modulus. You can make a guitar with a coco top, but it's likely not to be very loud. Sustain, OTOH... This is why they ted to use hardwood tops on electro-acoustics. You don't want much acoustic volume, for feedback resistance, and the heavy top can help make a UST work better.

Alan,

I have a question about using the frequency to calculate Youngs modulus. After your last post I started a spreadsheet to do the calculations.

After completing the spreadsheet, I'm playing with data to see if it's accurate. To test it, I'm calculating made up data. Using a density of 400 kg/m^3 and length=20", width=16", and thickness=0.120", the weight calculates to be 0.252 kg.

Now I started trying different frequencies to see what frequencies put me in the range of E values you listed above (9,000 - 15,000 megaPascals). 58Hz put me at 9,132 MP and 74Hz put me at 14,865 MP.

So do this frequency range of 58 - 74 Hz sound correct? (it's lower than I would have guessed) With a range of 16Hz, it's not a lot of resolution......16 Hz for a range of 6,000MP.......that's 375MP per Hz, sound correct?

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Formerly known as Adaboy.......

Yep, pretty much all of 'em! Though I don't use sitka too often anymore.

-Mark

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Pullman, WA

The more I know, the more I know I don't know.

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Darryl:
That's the right range alright. Now you know why I like the high frequency resolution on the Bradley signal generator. I usually find the resonant frequency to within a tenth of the Hz, or sometimes closer. You have to keep inmind that the frequency technique is, in itself, limited in precision. According to one article I read it gets you within about 10% of the 'true' value; far from perfect, but much better than guesswork.