Question on stiffness and density

[weslewis]

I have two builds under my belt using the spread sheet to calculate thickness...my 15th and 16th builds...
I was measuring some tops I have for the next two builds ..here are some numbers,.... then a question???

#15 was Sitka density measured 404 top thickness , in inch's, .103
#16 was Euro spruce density 450 top thickness .116
both of these guitars were falcate braced and came out sounding great... I sold one and kept one for myself... both built the same, but with different back and side woods, and both sounded the same...

just measured a couple of tops I have ....1st is Adi spruce...I really like this wood.... measured 373 density with a target thickness of .112 < in inch's with a target mass of 150

then there is this Sitka set I have had for a couple of years ,it seems a little stiff when flexing by hand and here is how it measured density 514.6 calculated thickness .111, target mass 184 using 75 for the vibrational stiffness value for all samples....

So the first thing that slaps me upside the head is it is much denser wood...old school would tell me , tight grain taps like a "Bell" and should make a good top...looking at the numbers the target mass comes in at 184, which to me seems that it will be to heavy to sound as good as the other tops....

so here are the questions.....should I reduce the vibrational stiffness factor to say 60 which would bring the target mass to 147 but the target thickness, in inch's, is .889, old school says " that's too thin"..

or should I scrap this wood as a top?????

[Trevor Gore]

Well, the first thing I'd question is Adi at 373 Kg/m^3, which seems very low for Adi, but not implausible.

Otherwise, the book approach seems to be doing exactly what it's supposed to do. Generally, low density material will produce a lower mass top panel than high stiffness material, because to get the low density panel stiffness up, you increase the thickness. Stiffness moves with the cube of thickness whereas mass moves in simple proportion. So the material that will produce the lowest mass, highest mobility top is the low density stuff. Even after doing lots of this sort of analysis and comparing it to "intuitive" methods, I still cannot guess by "feel" which panels will produce the best tops and the evidence is such that no one else can either. That's why it's essential to measure.

If you use the book formulae and a standard bracing structure, all the tops will produce the same vibrational performance from the modal frequency point of view, so will have a consistent type of sound, but the lower mass ones will have higher monopole mobility, so have the potential to be louder/more responsive.

So essentially you are trading responsiveness in order to keep a consistent type of sound. There is always a trade with inconsistent materials, so you could decide to trade some other way. For example, you could target a constant panel mass and do the stiffness manipulation by brace carving and theoretically maintain both a constant modal frequency response and a constant monopole mobility. However, you would have to do the brace carving after closing the box, which effectively obviates the efficient use of CF in the bracing, because you would be carving/sanding it away and compromising your structure. My experience is that I'm better off trading a bit of monopole mobility, because with a good design I'm still miles ahead of the other stuff out there.

Steel string guitars are a lot more "tolerant" than classicals. The bar is pretty low for SS guitars despite what the Martin/Gibson/Taylor etc. pundits would like us to believe. Trading a bit of monopole mobility still leaves you miles ahead of these guys and well ahead of most builders not using these techniques. So it's possible to grade wood according to use. The material that will produce the very lowest mass tops is prefered for classicals, then the rest goes to SS and the stuff that will produce high mass tops goes to guitars for stage use with pickups, where the last thing you need is excess mobility turning a guitar into a huge microphone. So all "decent" wood can be put to good use. If you use the "very best" wood for SS guitars, you can actually run into a problem of raucousness, basically too many high harmonics. String harmonics higher than the 6th are dissonant in that they fail to produce a consonant chord against the fundamental, so you need to damp these out to get them below the psychoacoustic perception level. Classical strings generally don't produce sufficient high harmonics for this to be troublesome and one struggles to retain the higher partials that are there.

So, stick with what's in the book until you have enough confidence in your methods to deviate without producing an unpredictable result. However, research is always a learning experience, even if not financially beneficial!

[weslewis]

I questioned it too ...measurements are 567 by 250 by 5.05 thick weight 267 g
I haven't thinned the panel yet but the thichness is very consistent and a perfectly quartered piece...

[Trevor Gore]

Your arithmetic is correct, at least!

[Tom West]

Generally, low density material will produce a lower mass top panel than high stiffness material, because to get the low density panel stiffness up, you increase the thickness. Stiffness moves with the cube of thickness whereas mass moves in simple proportion. So the material that will produce the lowest mass, highest mobility top is the low density stuff.

Trevor: So well said, you woke up another of my sleeping neurons..............!!!
Tom