Structure question for the pros...

Hey guys.. I have a question about the strength in a ukes (or guitar for that matter) design. Is the top, back and sides of an acoustic part of the structure integrety of the instrument. I am sure it does provide some, but is it mostly the job of the internal bracing and lining? I'm pretty sure I have an idea of the answer, but would still like to hear from you guys that have been building for years.

The reason I ask this in part it because I as many know I been building little mini ukes, in preparation to build full scale this next spring. I have read by many of you that thin is one of the many secrets of getting resonance from the top. The mini ukes I have been building have been 1.5mm thick top and bottom, with 1mm thick sides. I understand that is about what many build with even tenors. I am trying to squeeze as much sound out of these little minis as I can by playing with bracing etc. I am building one now with the top, bottom and sides all being barely 1mm thick. Man, it is almost like working with paper. It feels so fragil as I work with it, on such a small scale. I hope it doesn't end up folding up like a cheap lawn chair when I string it up, lol.. It will have lining, and bracing like the others I've built, I am just curious how much structure 1mm thick, at this size will provide.

Whole books have been written on the subject of structural integrity. Whole careers have been meeked out on the subject.

How well do you understand the cube rule of engineering and how it applies to beam length, width and height? There's not time to explain it all here but it is the golden rule of structural integrity. Then you need to get your head around what and where forces are acting in a uke strung to pitch. Once you've got your head around these things you'll have a better idea of where you can lighten things up and where things need to be beefed up.

P.S. I'm certainly no pro. I do try to gather information from as many sources as possible. I've got a bunch of books on instrument construction, I borrow from the library, I read alot on the internet (although you have to wade through a lot of crap to find the few gems), and I talk with luthiers when I can.

All of them play a huge role in the structural integrity of the instrument. As Liam said, you need to understand the cube rule. It applies not only to the bracing that you add to the structure, but also to those members that you are applying it to. The top, back and sides. And to make things even more interesting, the cube rule not only applies to the width and hight of a piece is, it also applies to it's length.

Quick lesson. If you have a piece of wood 1 unit tall by 1 unit wide it will have a stiffness of 1x1x1=1 a weight coefficient of 1

If you have a piece of wood 1 unit tall by 2 units wide you have a stiffness of 1x1x1x2=2 and a weight coefficient of 2

But if you have a piece that is 2 units tall by 1 unit wide you have a stiffness of 2x2x2x1=8 and a weight coefficient of just 2

So you can see that by increasing the hight of a brace, or top or back you get an exponentially stiffer piece but it's only a little heavier. In instruments, most times you are looking for light vs heavy.

You've got a hell of a lot of reading and study ahead of you. From there you take informed decisions to the workshop and start glueing up pieces of wood.

Your sidea are a bit thin mate!

I am not a structural engineer, nor know all the structural engineering formulas. But I do have a good better than average understanding of physics and engineering. I can see why more understanding of the forces can greatly improve design skills. I don't think most people realize the stresses string tensions put on an instrument. I think even I understanding that pretty good even under estimated it. My very 1st Aphid developed a crack near the heel, but almost immediatly I realized my mistake and made some adjustment to my design, and all the ones since has had no issues. But Pete, I hear ya brother. I think slightly thicker on the sides would greatly improve structure so I can get away with a thinner sound board.. I might take that a bit over 1mm up to 1.5.

liam_fnq said:

Whole books have been written on the subject of structural integrity. Whole careers have been meeked out on the subject.

Click to expand...

Can you recommend a good book to start??
Thanks!

Don't forget its not just string tension that stresses the body. It has to hold up to normal use and a bit of abuse....you might put your finger right through it on bad strum or punch a hole in it taking it out of the case.
There's a limit to how thin you can go. Thinning the top is good to a point to decrease weight. But at some point you start losing because the top isn't stiff enough to transmit vibrations and you lose sustain and volume.
There is a reason why the the range of top thickness you'll find is pretty tight....between 0.070" to 0.090". I guess the sweet spot is in that 0.020" range somewhere.

It's not about 'weight'. Tone and volume come from the 'stiffness' of the front relative to it's thickness. Go to youtube and the front end of the bill collings factory tour video he shows what looks like a mastergrade front as floppy as a sheet of rubber - absolutely no good for boutique guitars. His comment - $500 guitar maybe.... You also have to stress the front into a curve and brace it approriately with wood which 'likes' your front. There's a bit more to it than a few calculations....

resoman said:

Can you recommend a good book to start??
Thanks!

Click to expand...

A very good set of books that cover some of this are by Ervin Somogyi. They are called "The Responsive Guitar" and "Making the Responsive Guitar". They are pricey, but you will find that nothing in the luthier craft is cheap. He also has a DVD called "Voicing The Guitar" that is pretty good. Ervin doesn't give you a magic formula, but rather gets you thinking about what and why you do things.

A really good DVD on a similar vein is "Voicing a Steel String Guitar" by Kent Everett. Same deal here. While it has to do with guitars, the concepts are exactly the same. Different bracing patterns, but the physics still apply.

There are heaps of other books etc. out there that I'm sure will help out. These are just a few that I found particularly helpful that I have on the shelf.

And lets not forget David Hurd's contribution to the science, particularly because his specialty is ukuleles. "Left Brain Luthierie". It's pretty in depth and not for the faint of heart if you're not really the science geek type. You can find some of the information in the book on his website.

Also regarding the thickness of your components now. You say you are using a 1mm thick top as compared to what I think was a 2mm one an a previous build. Your 1mm top now is 8 times less stiff as compared to the 2mm one without taking any bracing into consideration.

This isn't necessarily a bad thing. You just need to keep in mind that it does need to be stiff enough to hold up. Design your bracing accordingly.

I build a line of ukes that have a top thickness in the lower bout of just 0.8 - 0.9mm thick, but they are lattice braced with balsa and Carbon Fibre. The tops are incredibly stiff. The hard part about building them is to not end up having them too stiff. They are based on an idea pioneered by Australian Luthier Greg Smallman who makes some incredible Spanish Style guitars.

I can offer you a maxim from aircraft building (a German glider designer):

"Simplificate and add lightness"

While aircraft builders were still using wood, the standard technique was to thin down structural members until something failed catastrophically. Then re-build it a bit stronger. Rather costly in test pilots though. With consistent materials like metal and GRP, computer modelling does most of this work.

As Pete and Allen have pointed out, for body woods you can't go by thickness (except to put yourself in the ball park). You hve to be able to tell by feel whether the wood is at the right thickness.

Hobby builders like me tend to start far too thick - it's inconceivable that we could safely go any thinner. Then we gradually gain confidence and creep up on the right answer. I suspect some go too far (haven't managed that yet), and learn the most from that.

My very limited experience is that if the top flexes across the grain, but is still springy, the uke will sound at least OK. If stiff, it will be quiet and dull. Allen tells us that you can compensate for floppy by cunning bracing (I've seen pictures of what he does, and it's not for the amateur!). On the other hand, flex along the grain seems less relevant (though the pros may tell you otherwise, and they know).

I can't be any more precise than "aim for springy", and that differs radically even for the same species of wood. Have just strung up a mahogany top around 1.5mm - sounds good (but an earlier mahogany build around the same thickness was not springy enough and sounds dull). I'm also working on a yew top, which felt right at just under 2mm.

I fear the answer may be that you have to develop a "feel" for this, and you only do it by building bad ukes.

resoman said:

Can you recommend a good book to start??
Thanks!

Click to expand...

Allen has pretty well nailed it. The only one to add is the new books by Gore & Gilet. Disclaimer: I haven't read it although it is impressing some people whose opinions I consider sound. The books follow a similar pattern to the Symogyi books, with one being about design while the other is about construction but while Symogyi is more qualitative, Gore & Gilet is more quantitative. Don't ever be afraid of buying books on guitar design. There is precious little of high quality out there on ukes, other than David Hurd's stuff.

Since you are building very small ukes, some of the building principles are going to vary. The smallest uke I have made has a 9 1/4" playing scale and I believe the ones you are building are even smaller. In my opinion you can keep the top and back thickness on the thin side, but the sides can be a bit thicker than the 1mm you mentioned. To keep the body integrity I would suggest using solid hard wood linings. You can even laminate the linings using 2 pieces of hard wood and gluing them together. For the hard wood I would use something like maple or rosewood. Using solid linings will help the body be very strong and stiff, and you are not adding weight to the top or back by making them too thick.

I would also use neck block large enough to make a very strong neck to body joint. You will lose a lot of string energy if this joint is sloppy or loose and you can't afford any energy loss with this small of the uke. One of the key components to Greg Smallmans work to keep the back and sides stiff, weight is not the main concern there. As the other luthiers have suggested, there is no substitute for hands on learning. Good luck.

The neck block is a decent chunk of solid mahogany, and the linings are also solid maple. It's been working. I have another body all together with the 1mm sides, top and back, and it did stiffen up pretty good and feels good now. I also added a brace on the upper bout just over the sound hole, when before I just had one under the sound hole. But all in all, the body feels pretty solid now, but of course, no neck on it yet, and no strings. So, we'll see how it turns out if it don't emplode on me..

Thanks for all the great feedback...

Allen said:

All of them play a huge role in the structural integrity of the instrument. As Liam said, you need to understand the cube rule. It applies not only to the bracing that you add to the structure, but also to those members that you are applying it to. The top, back and sides. And to make things even more interesting, the cube rule not only applies to the width and hight of a piece is, it also applies to it's length.

Quick lesson. If you have a piece of wood 1 unit tall by 1 unit wide it will have a stiffness of 1x1x1=1 a weight coefficient of 1

If you have a piece of wood 1 unit tall by 2 units wide you have a stiffness of 1x1x1x2=2 and a weight coefficient of 2

But if you have a piece that is 2 units tall by 1 unit wide you have a stiffness of 2x2x2x1=8 and a weight coefficient of just 2

So you can see that by increasing the hight of a brace, or top or back you get an exponentially stiffer piece but it's only a little heavier. In instruments, most times you are looking for light vs heavy.

You've got a hell of a lot of reading and study ahead of you. From there you take informed decisions to the workshop and start glueing up pieces of wood.

Click to expand...

There are three parts to the rules of beam strength. Funnily enough beams are three dimensional and each rule relates to one of those dimensions.
1. The stiffness of a beam changes as a linear function of it's width (double the width - double the stiffness).
2. The stiffness of a beam changes as a cube of its height (double the height - 8x as stiff)
3. the stiffness of a beam changes as the inverse cube of its span length (halve the span length - 8x as stiff)

These rules apply to top thickness as well as the bracing. Things get a bit muddy because the uke is a system. It's abit more complex than a simple beam.

I think the most critical rule for the bug sized uke is the third. With the same top thickness as a tenor and probably half the length the top is eight times as stiff. This is before taking into account the rest of the system.

left-brained lutherie

Tudorp said:

...I do have a good better than average understanding of physics and engineering.

Click to expand...

Then you should get a copy of David Hurd's book, which is available at Stew-Mac and probably directly from David:

http://www.ukuleles.com/LBLBook/TOC.html

Building stringed instruments is foremost an engineering problem, and David does a super job providing an engineering-based framework for building. Plus, he was foremost a uke builder, now retired, so that's his reference.

I agree with Pete, your sides need a little more left on.

Personally, reversed kerfed linings do more than for me than just being installed backwards.

Also, there's a reason why guitar builders put an arch in the tops, as well as the backs. Some `ukulele builders do that as well. . .

Aaron

At a Guild of American Luthiers convention several years ago, a very well respected and admired luthier Al Carruth presented a guitar he had made for the Classical guitar listening session. Al's work is science based mostly and the guitar he made was one he said incorporated most of the principles he had learned from his work in engineering the guitar. To make a long story short, the guitar was not what he had hoped it would be after we had all had a chance to listen to if being played by a professional. Al was very gracious in admitting that science alone sometimes comes up short and that for him it was back to the drawing board. While for some, engineering the guitar is a way to approach the problem, those who build with a more intuitive method can be just as successful in producing a very good if not great instrument. While I admire those like Al and David for their work, many of us do not study the guitar or uke through science, but from learned tried and true methods of observation and a simple hands on approach. I for one would have never made any string instrument if I had to first learn the science and engineering methods. I would encourage everyone who has any interest in building a uke, guitar, violin or whatever to give it a try. With a little common sense and some knowledge, this craft can be very rewarding.

And there you have it -the 'close' to the thread!

Do you have an issue with this discussion Pete?