Vibrational stiffness for a back

[johnparchem]

I am sure I am missing something. Why in table 4.5-2 is the back vibration stiffness value lower on a classical than a SS? I understand the top; given that classical guitars have less string energy a light top is very important, so thinning the top for mass but really stiffing the falcate braces to move the T(1,1)2 up vs a SS makes sense to me.

I have been bracing the live back for a medium steel string and a classical the same but my target is 10 Hz or so lower on a steel string than a classical. From my experience of the 2 classical guitars and two SS falcate guitars I've built, the classical guitars usually hit close to the T(1,1)3 target but I have to drop the SS quite a bit.

Of course I have a motive for the question. I want to feel ok about a vibrational stiffness value of 50 for a SS I am making that would be a tad heavy using the thickness with a value of 55. If I use the lower number I will take almost nothing off the center of the lower bout brace until I have the guitar together. The back wood I would like to use is a gorgeous piece of zirciote with a Elong a bit more than 14 Gpa. It has a good tap tone and rings for quite awhile. But it its density 1000 kg/m^3.

Thanks for any insight or input.

[Trevor Gore]

The values in the table are driven largely by convention, to give panel thicknesses that correspond to the "normal range" for the guitar type. Using the plate thicknessing formula, tailored to the specific elasticity and density of the piece of wood you have, then gets you the same vibrational stiffness (i.e mode frequencies in the right zone) for the plate every time. But you usually want a higher panel stiffness on a classical, so that's done with the bracing. The live back bracing scheme has the adjustability (the central scallop) to cover that range to give you a live or non-live back on a SS or CL guitar provided the T(1,1)2 is in the usual range.

However, to get a live back means that the back has to have a minimum level of monopole mobility, or it is just too stiff and/or heavy to couple in effectively as a live back. This essentially puts an upper limit on the density of timber that can be used for live backs using the standard "f" numbers and the standard bracing scheme, and that number is ~850 kg/m3. If you want to use a denser timber you have to reduce its thickness significantly to get the mass down to a reasonable level (i.e to what a 750kg/m3 back would weigh) but that reduces the stiffness significantly, too (cube rule). So you then have to compensate with a much stiffer bracing scheme to get the panel stiffness (and modal frequency) back in the right zone, whilst still keeping the mass down. So you need to use taller braces or a brace shape with more material in the top or a different bracing scheme altogether. There's enough in the book to allow you to design such a bracing scheme to suit. Otherwise, just make it a non-live back, which takes very little design effort (and produces a fine, but different, result).

For example, there was Buckley's of getting a live back on this guitar. The density of the back timber was ~1300kg/m3 and with that figure in the wood, taking it down to ~half normal thickness was not really an option. I thinned the back more than usual just so you wouldn't need a fork lift to shift it and then added extra stiff bracing to make sure the B(1,1) was well out of the way.

[johnparchem]

Thanks Trevor,

I will give it some thought between taller braces and making a non-active back. The whole question might become a moot point after I try to bend the notoriously brittle zirciote for a Venetian cutaway.

John