Top thickness and bracing - Extremes

[Robin, Wales]

When thinking about how a guitar works, I got wondering about the tops on flat top guitars. The general consensus seems to be that the top should be thin enough to be "responsive" but braced enough not collapse under the tension of the strings.

But I was wondering about the extremes; simply because sometimes thinking something through to the extremes of engineering gives a better perspective for the ideal. And some questions come to mind:

1. How thick would a spruce top on a flat top guitar (standard bridge) need to be for it to require no bracing?

2. Would another wood (mahogany, plywood, double top) need to be thicker/thinner to work with no bracing?

3. How thick would a spruce guitar top with a floating bridge need to be for it to require no bracing - and is this different to a standard bridge?

4. How much bracing would you need for the top of a flat top guitar to be made from doped tissue paper (like a model aircraft)?

I have this picture in my mind of two guitars. One with a thick top and no bracing, and one with a tissue paper top stretched over a latticework of bracing. I wonder what both would sound like!

And then, of course, we have archtops - where all bets are off! My own archtop is made from 2.5mm cherry/maple/cherry plywood. The top has only two parallel braces (tone bars) running almost from the neck to the tail and no braces at all on the back. It seems pretty solid to me, and resonant, but then both the top and back have been steamed into an arch and that must be providing some strength. Plus the loading is that of a floating bridge guitar.

So, over to you luthiers. I'm sure that this is the sort of question that has kept you up at nights!

[Sage Runner]

Hey Robin. Good Question. On Flat tops Using spruce primarily-You have so many variables due to the Spruce variety—Sitka,German,Red,Engleman etc. But each individual top will have varying degrees of Stiffness regardless of the thickness. You will find flimsy top wood-all the way to extreme stiffness. That is why Tops are Graded and calculated in the rough by the Luthier before the Tops are Chosen. Typically Stiffer the better so the luthier can brace the guitar lightly. Less Stiff Spruce top wood typically will be left a tad thicker or maybe braced a tad heavier to get a desired result! Everything is considered though—what size of guitar—tiny parlor? Or huge Jumbo? A Luthier will take all things into consideration. Are they crafting a primarily Responsive Finger style guitar? Match up a Super stiff Adirondack top —with very light Sitka brace-Wood for a particular tone and response —they might be trying to Achieve. Matching a certain Spruce or maybe Cedar/Redwood type to a certain Back and sides to achieve a desired tone. The same concept applies to Solid Spruce Arch-top builders — but no doubt Boutique Arch -top makers are even more particular about the Top wood they will use.

[Alan Carruth]

Guitar tops are stiffness limited: any top that is thick enough to hold up for long enough under the string forces will almost certainly be strong enough, in the sense that it won't fold up immediately. IIRC, the FAA rates spruce as having a working limit of about 3000 PSI in direct tension. That would assume that the strings are on the center of moment of the top, which, of course, they're not.

The big issue in the long term is with cold creep. Again, iirc, the FAA says that wooden aircraft structures should not show more than 1/3 the deflection under short-term working loads that can be tolerated over the long term. As the top creeps the rotation increases, and you start running into issues with glue line failure due to the increases peeling load along the back edge of the bridge. With flat top guitars we can use the 'two degree rule': If the bridge rotates forward much more than 2 degrees under string load, the top is not stiff enough, and if it rotates much less than two degrees it stiffer than it needs to be. On that basis, given 'normal' string tension and string height above the top you could probably calculate a thickness given the Young's modulus along the grain.

One issue with this is that E-long can vary a lot, even with wood of the same species. I have two samples of European spruce, cut about 4" apart from the same plank, that are pretty extreme examples of that: the measured E-long of one is ~18,500 megaPascals, and the other is about 9200 mPa. Somewhere on the order of 13,000 mPa would be a decent 'average' to use for design purposes with spruce, but it varies depending on the density. The cross grain E value will be lower, and is far more variable, but it doesn't contribute as much to the working stiffness of the top. For design purposes you could assume the E-cross is somewhere around 1/8 of E-long and not be too far off.

It's surprising that the E-long values for hardwoods don't tend to be much higher than you see with softwoods. Hardwoods are structurally different (and more variable) than softwoods, so they end up denser, and (maybe) stronger, but not stiffer at a given thickness. That's why we use softwoods: to save weight given the limited horsepower in a plucked string.

One place where I'm not at all sure you could eliminate top bracing on a flat top is above the sound hole. There's a lot of leverage by the neck up there, and there are also shear loads to deal with. There has been a certain amount of work done on this over the years, of course.

It's interesting that the 'free' vibration modes (not glued to the rim) of a un-braced guitar top are quite similar to those you see on a braced one, with the major exception being the modes that are most affected by the upper transverse brace.

The problem on a flat top with a floating bridge is to provide the necessary impedance mis-match for the string, so that it will 'know' how long it us and make the right note. If you do this with a vertical break angle you end up with a down force on the top that is on the order of 5% or so of the tension on the strings. That's a considerable load on a flat top and usually requires some bracing and/or a bent 'cranked' top. There are bridge designs that convert the down load to a torque, but you need to brace for that too. One recent design uses sideways break angles and a notched saddle for this, but raises other issues. Besides, I think it's patented...

Archtops do with arch shape and thickness what flat tops do with bracing, for the most part. Arch tops don't have the torque of the bridge to deal with, and take up the down load of the string break over the saddle with the arch and thickness, primarily. They use a couple of braces on the top, mostly to replace the stiffness that's lost when you cut the sound holes. That is, the 'free' plate modes of an unbraced arched top with no holes are much the same as you see on the finished top once the holes are cut and the braces properly profiled. It's hard to avoid some 'lumpiness' of with added bracing.

Smallman's 'lattice' tops use a balsa/carbon fiber I-beam lattice to do all the work. He uses a veneer thickness 'top' of softwood (about .8 mm, iirc) as a membrane to move air. Tim White's 'Chrysalis' guitar used a CF lattice based on the wing veins of an insect, and an inflated balloon as the 'soundboard'. You might also want to check out the 'Sandwich' tops, using Nomex and softwood veneers, that were pioneered by Wagner and Damman on the order of thirty years ago. How thick the membrane needs to be is probably a function the spacing of the lattice that supports it; as long as it won't buckle in compression you're probably good to go.

[printer2]

Originally Posted by Robin, Wales

When thinking about how a guitar works, I got wondering about the tops on flat top guitars. The general consensus seems to be that the top should be thin enough to be "responsive" but braced enough not collapse under the tension of the strings.

But I was wondering about the extremes; simply because sometimes thinking something through to the extremes of engineering gives a better perspective for the ideal. And some questions come to mind:

I have thought about it in the same way and have tried a few odd things along the way but some of them are temporarily on hold.

1. How thick would a spruce top on a flat top guitar (standard bridge) need to be for it to require no bracing?

I have a nylon stringed guitar that I modified to try some ideas. I was surprised that it only had three braces on the top (four with the bridge). One brace on either side of the sound hole (quite normal) and only the bridge patch below it. I strung it up with steel strings and it is holding up fine. It has a plywood top, way too heavy for nylon and holding up fine. It is a 3/4 size so in less need of bracing. It does not answer your question of a spruce top with no bracing but the best example I have.

2. Would another wood (mahogany, plywood, double top) need to be thicker/thinner to work with no bracing?

3. How thick would a spruce guitar top with a floating bridge need to be for it to require no bracing - and is this different to a standard bridge?

I made a guitar with a pine top with minimal bracing, it was my first attempt at building a guitar, I did not know much about acoustics at the time. More in line as a hollowed out electric with a floating bridge. The top thickness was about the same as a regular braced guitar but the size of the body was the same as a Telecaster. So rather small. The downward tension did not seem to bow the top down.

4. How much bracing would you need for the top of a flat top guitar to be made from doped tissue paper (like a model aircraft)?

This would be an interesting one, how small the distance between the braces? The tissue would flap back and forth at some frequency. The smaller the distance the higher the frequency. Even with a honeycomb Nomex section acting as the braces I doubt you can use tissue as it is not stiff enough to take the load.

I have this picture in my mind of two guitars. One with a thick top and no bracing, and one with a tissue paper top stretched over a latticework of bracing. I wonder what both would sound like!

I would put my money on the solid top with no bracing before the tissue one. It can be made to sound guitar-like but with lower volume. I do not think the tissue would hold up. Going up a notch, a balsa skinned lattice has been done many times, at least for nylon strings.

And then, of course, we have archtops - where all bets are off! My own archtop is made from 2.5mm cherry/maple/cherry plywood. The top has only two parallel braces (tone bars) running almost from the neck to the tail and no braces at all on the back. It seems pretty solid to me, and resonant, but then both the top and back have been steamed into an arch and that must be providing some strength. Plus the loading is that of a floating bridge guitar.

So, over to you luthiers. I'm sure that this is the sort of question that has kept you up at nights!

I have made a few guitars out with softwood back and sides and they still sound like guitars, so that is one extreme investigated. I have a balsa bodied nylon guitar also almost finished to show how light a wood can be used. The balsa is thicker than I wanted, I think 1/8" thick. Might be light on trebles but the body seems like it will have no problem reproducing bass. Thinking about it now, I might have to use a heavy bridge to tell the strings how long they should be (thank's Alan).

[PineMarten]

I had a laminated electric archtop with no top bracing, a Vintage EY80. The bridge was glued in place but with a tailpiece, and it had a set-in neck pickup. The top on that was relatively thick - probably around 5mm, it was stable over the decade I had it and it had a likeable but not especially loud unplugged tone.