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You can ask questions here about Trevor and Gerard's exciting new book on Luthiery.

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soundshooter
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Relationships

Post by soundshooter » Thu Mar 27, 2014 11:01 am

I’m curious about the relationship between top thickness and stiffness of an assembled top. Figure 4.4-9 shows that the flexural rigidity of the Fleta guitar is on a par with your falcate braced steal string, almost twice as stiff as a lattice braced guitar. How can that be and still hit the targets for T(1,1)1&2 and have good volume and responsiveness?

In section 11.2.3.1 you state, ”For good (not exceptional) quality cedar for Fleta style guitar should be around 2.2mm.”. Table 6-2 gives western red cedar a Target panel thickness range of 2.4-2.8mm for a fan braced classical. I had a piece that seemed better then good (on a par with your #13) and that when using an f of 60 and a size of 490x360 into equation 4.5.7 came out to 2.3mm. It seems that you are looking for a thinner panel on the Fleta. Did I miss something?

Correct me if my understanding is wrong, flexural rigidity is the combination of the top thickness and the bracing over a certain distance. So, for the same rigidity you could have stiffer braces with a thinner top or thicker top with weaker bracing. In the case of modal tuning we can thin the top and or thin the braces. In your book you generously offered an “f” for different styles of guitar based on years of experience. I realize that we are trying to reduce weight, because that is where the performance is. What are the sonic implications of moving around the ‘F” and adjusting the brace height? What are the sonic implications of lowering the “f” and increasing the brace hight with denser samples of top plate to help get back some of the responsiveness and volume?

Thanks
Frank

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Trevor Gore
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Re: Relationships

Post by Trevor Gore » Thu Mar 27, 2014 8:00 pm

soundshooter wrote:Figure 4.4-9 shows that the flexural rigidity of the Fleta guitar is on a par with your falcate braced steal string, almost twice as stiff as a lattice braced guitar. How can that be and still hit the targets for T(1,1)1&2 and have good volume and responsiveness?
The flexural rigidity of the Fleta guitar was calculated using the panel and brace dimensions published by Courtnal (as explained on p 4-40), with the caveat "if these guitars are representative of those makers' typical instruments". I make no claim about volume or responsiveness for Courtnal's Fleta. The resonant frequencies are dependent on the both the equivalent stiffness and the equivalent mass. I don't discuss the mass aspects at this point, as the focus of this section of the book is on the statics.

There has frequently been doubt about the the veracity of some of Cournal's dimensions, especially on his Fleta drawing, as soundboards built to his drawing are significantly over-built (hence the caveat noted above). Over the years, Gerard has had a number of amateur builders approach him asking him why their Fletas, built off the Courtnal dimensions, don't "work".
soundshooter wrote:In section 11.2.3.1 you state, ”For good (not exceptional) quality cedar for Fleta style guitar should be around 2.2mm.”. Table 6-2 gives western red cedar a Target panel thickness range of 2.4-2.8mm for a fan braced classical. I had a piece that seemed better then good (on a par with your #13) and that when using an f of 60 and a size of 490x360 into equation 4.5.7 came out to 2.3mm. It seems that you are looking for a thinner panel on the Fleta. Did I miss something?
Most fan braced classicals have 7 fan braces, one lower transverse brace, often without closing bars. Fletas are somewhat exceptional in that they have 9 fan braces, closing bars (sometimes let into the end block) and two lower transverse braces, set on the diagonal. So basically substantially more bracing, hence allowing a thinner top. The range in Elong that I have measured for WRC runs from 2.76GPa to 9.54GPa. Good, not exceptional, I'd call in the range 6-8GPa.
soundshooter wrote:Correct me if my understanding is wrong, flexural rigidity is the combination of the top thickness and the bracing over a certain distance.
Nearly. It's E * I, which is the combination of Young's modulus of the materials E, the top thickness and the bracing sections that I chose to measure at a certain distance from the bridge combined into I, the second moment of area.
soundshooter wrote: So, for the same [flexural] rigidity you could have stiffer braces with a thinner top or thicker top with weaker bracing.
Yes. Or woods with different Young's moduli.
soundshooter wrote:What are the sonic implications of moving around the ‘F” and adjusting the brace height?
The lower the F number, the thinner, lighter and less stiff the panel. F has the dimensions of frequency. Most of the mass of a completed top is in the panel, not the bracing. One logical limit of this way of thinking is the Smallman design, with its attendant acoustical consequences.
soundshooter wrote:What are the sonic implications of lowering the “f” and increasing the brace hight with denser samples of top plate to help get back some of the responsiveness and volume?
Can certainly be done. I mention that approach here, (4th para). Within the +/- 1 standard deviation ranges (68% of population) of the usual top woods (i.e. softwoods) it would be best to stick to a single F number if you want consistency. If you keep on moving the F number you have to keep on modifying the bracing design to hit your modal resonance targets, which defeats the objective of this approach. You'll hear differences in modal frequencies much more readily than minor changes in monopole mobility. But that's the trade-off in this approach: target your preferred modal frequencies and bridge rotation then live with the minor variations in monopole mobility. If, for example, you chose to fix the modal frequencies AND a high monopole mobility target, you'd be trading structural integrity, or would always be looking for "perfect" wood.

soundshooter
Kauri
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Re: Relationships

Post by soundshooter » Sat Mar 29, 2014 5:18 am

Thanks Trevor.
I just finished a Fleta from your book. It turned out that I had to remove a lot of bracing to get it to target. The asymmetric dipole did not fall close to the T(1,1)2 98.5, 190, 238. My top had a 8GPa but I thicknessed to f60. Somewhere in the back of my mind it seemed that it needed to be thinner. Next time I'll be more daring and maybe I'll get closer to "that" Fleta sound.
Thanks again
Frank

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