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| Are deflection numbers linear? http://luthiersforum.com/forum/viewtopic.php?f=10101&t=49091 |
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| Author: | meddlingfool [ Sat Mar 04, 2017 7:50 pm ] |
| Post subject: | Are deflection numbers linear? |
For instance, if we used x load and the deflection was .100, then sanded the top or back to .200 under the same load, is it 2x as flexible, Otis that a numeric convenience and there's something entirely different going on? Any thoughts? |
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| Author: | johnparchem [ Sat Mar 04, 2017 8:59 pm ] |
| Post subject: | Re: Are deflection numbers linear? |
I think if you sanded the top to achieve twice the deflection, it is twice as flexible. |
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| Author: | DennisK [ Sat Mar 04, 2017 9:13 pm ] |
| Post subject: | Re: Are deflection numbers linear? |
...yes? It depends on your definition of the word stiffness. If you say Deflection = Force / Stiffness, then yes, it is linear. The full equation for a rectangular beam is: Deflection = Force x LengthCubed / (4 x YoungsModulus x Width x ThicknessCubed) So there you can see what variables are linear or cubic. The part that I would call Stiffness is (4 x YoungsModulus x Width x ThicknessCubed) / LengthCubed. So if you measure the deflection and it's twice what it was before, then the stiffness is half what it was before (linear). But how the stiffness ended up being half what it was may involve nonlinear effects. Note: That beam formula doesn't quite apply to a finished guitar top since it's loaded in the center so you have cross grain stiffness coming into play at the same time, and it's not rectangular, and it's not necessarily equal thickness all over, and it has braces drastically altering the stiffness... but the linear and cubic effects still apply. And it is accurate when thickness sanding a rectangular top and using a relatively wide weight so the cross grain stiffness isn't involved. |
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| Author: | Jim Watts [ Sat Mar 04, 2017 9:55 pm ] |
| Post subject: | Re: Are deflection numbers linear? |
If I'm understanding you question correctly, yes it is twice as flexible. However, just to be clear, you have not removed half of the material to achieve twice the deflection, only a little, see the formula Dennis posted. |
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| Author: | meddlingfool [ Sat Mar 04, 2017 10:48 pm ] |
| Post subject: | Re: Are deflection numbers linear? |
Yes. Basically, I'm trying to apply my usual settings to a 12 string top. Last time, I added 60% more weight and used the same deflection setting. However, doing it that way puts all the extra stiffness in the top itself and leaves the bracing like 6 string, so it's heavier than necessary. This time I want to make the top ~30% stiffer and the braces 30% stiffer. I have just enough math skills to translate into % and convert, but wanted to check if it was actually applicable, which it seems to be. Thanks! |
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| Author: | meddlingfool [ Sat Mar 04, 2017 11:18 pm ] |
| Post subject: | Re: Are deflection numbers linear? |
Well, it seems to have worked. I figured out what my deflections should be , 30% less deflection with the same weight, and 30% more deflection with 30% more weight, and when I added weight at the low number it seemed to match the high number. Close enough for rock and roll... |
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| Author: | DennisK [ Sun Mar 05, 2017 12:56 am ] |
| Post subject: | Re: Are deflection numbers linear? |
meddlingfool wrote: Last time, I added 60% more weight and used the same deflection setting. However, doing it that way puts all the extra stiffness in the top itself and leaves the bracing like 6 string, so it's heavier than necessary. I don't think that's right. If I'm doing my math correctly (and I'm not sure I am), then you need both top and bracing to be 60% stiffer in order for the total to be 60% stiffer. That's not to say you can't do 30% stiffer soundboard and 90% stiffer braces (or whatever it works out to be). But you might want to switch to a "thin top" bracing pattern (one with better behind-the-bridge support than the usual two diagonal tone bars). |
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| Author: | meddlingfool [ Sun Mar 05, 2017 2:25 am ] |
| Post subject: | Re: Are deflection numbers linear? |
Well, I hope I'm right... |
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| Author: | meddlingfool [ Sun Mar 05, 2017 2:27 am ] |
| Post subject: | Re: Are deflection numbers linear? |
What I remember from the last time I did it with the top at 60% stiffer was that I had expected it to have a better bass response than it did. We'll see... |
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| Author: | Alan Carruth [ Mon Mar 06, 2017 5:09 pm ] |
| Post subject: | Re: Are deflection numbers linear? |
I'd work for the 60% number anyway: you sure don't want the top folding up. If I'm doing my math correctly, making the top 60% stiffer only requires it to be 16% thicker, and the bracing to be 16% taller. That assumes you can think of the top as a congeries of rectangular beams side by side, with the stiffness of each varying as the cube of the depth. I've used that rule in making 12-strings before, and it seems to work. Since the power of the vibrating string goes as the tension and the square of the amplitude, with 60% more tension you've got 60% more power at a given amplitude. With the top only about 20% heavier (the bridge is bigger, and so on) and 60% more power you end up with a LOUD guitar. On the other hand, since the top is so much stiffer, but not all that much heavier, all the resonant frequencies will be higher. That tends to work against bass response. You could scale the guitar up, but then you have to leave the top thicker and the braces taller to retain the needed stiffness, and the mass goes up faster than the surface area. Since power output seems to relate to the ratio of area to mass, you start to lose power as you gain bass response. Making the sound hole smaller will drop the 'air' pitch, which is the lowest resonance on the guitar that can produce sound. THat might make it sound 'bassier'. On the other hand, making the hole smaller also reduces the power of that resonance, which might make it sound more 'treble'. Darn these things are complicated! |
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| Author: | meddlingfool [ Mon Mar 06, 2017 7:28 pm ] |
| Post subject: | Re: Are deflection numbers linear? |
Actually, in practice I have found that the extra weight of the bridge, and the dropping of freqs from the extra string tension, I'm able to target the same final numbers as a six string. We'll see how this one works! |
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