Equation 4.5-7

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Re: Equation 4.5-7

Post by Craig Bumgarner » Wed Jun 26, 2013 1:30 am

Okay, thanks, that all seems reasonable.

I said I understood 4.5.2, but I do wonder how you arrive at the Predicted Panel Mass, last column in Table 4.5-3. If this simply the finished dimension on the rectangular panel that will make up the guitar, then I must be doing something wrong. Is there a calculation being made of the actual area of the guitar body shape?
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Re: Equation 4.5-7

Post by Craig Bumgarner » Wed Jun 26, 2013 1:41 am

Jeff,

Right, I figure I will have to come with my own parameter as a steel string flat top is quite different than a Selmac with the domed top, ladder bracing, floating bridge and tailpiece. To get thicknesses like I am used to using, I actually had to increase the parameter to around 85. Maybe I'm over building. Anyhow, it is all part of the fun.
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Re: Equation 4.5-7

Post by Trevor Gore » Wed Jun 26, 2013 1:06 pm

Craig Bumgarner wrote:I said I understood 4.5.2, but I do wonder how you arrive at the Predicted Panel Mass, last column in Table 4.5-3. If this simply the finished dimension on the rectangular panel that will make up the guitar, then I must be doing something wrong. Is there a calculation being made of the actual area of the guitar body shape?
The panel mass is computed from the actual area of the guitar top, which, of course you need to work out. I get the area from the design program I use to draw the body shapes. You can "reverse engineer" the area by various means. For example, if your top template is made of say perspex and you know the density (calculated from a rectangular off-cut, or straight from the manufacturer) and you know the thickness is pretty constant (usually is, but not exactly the spec. thickness) you can work out the area by weighing the template.

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Re: Equation 4.5-7

Post by Trevor Gore » Wed Jun 26, 2013 1:09 pm

Craig Bumgarner wrote:To get thicknesses like I am used to using, I actually had to increase the parameter to around 85. Maybe I'm over building. Anyhow, it is all part of the fun.
Hmmm. What thickness are you using, Craig? I thought that you'd have to be using thinner than normally used on a flat top to get the mobility figures you get, which would mean a reduction in the parameter f.

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Re: Equation 4.5-7

Post by Craig Bumgarner » Thu Jun 27, 2013 1:41 am

trevtheshed wrote: Hmmm. What thickness are you using, Craig? I thought that you'd have to be using thinner than normally used on a flat top to get the mobility figures you get, which would mean a reduction in the parameter f.
I've been using cedar for the last 18 months and the five guitars built in this period had tops in the 3.2 to 3.5mm range. I've checked three of these for mobility recently and had SM of 16.7 to 21.8.

When I input Equation 4.5-7 with size and frequency data on a piece from my cedar stock, I get a target thickness of 2.95mm, lower than I would normally use. A parameter of 85 puts me back where I'm used to, 3.34.

I ran 4.5-7 on an Englemann spruce top panel this morning and get 2.71 with a parameter of 75. That seems about right, so maybe I am over-doing the cedar a bit.

I've measured top thickness on dozens of good Selmer types. Spruce tops typically ranges from 2.5 to 3.5mm. Cedar tops typically run 3.0 to 3.5mm.

The following may be a conversation for the SM thread or a new one, but I did attend the Django in June festival last week and played a LOT of guitars. I tested ten Selmer types (including one real Henri Selmer guitar, #862), all of which I would consider very good examples, some are the best out of hundreds. Mobility of these ranged from 14.4 to 21.8. The mobility numbers track correspond well with perceived responsiveness and volume. The four best guitars there had mobility from 19 to 21.

I understand what you are saying above. Assuming my measuring techniques are okay*, the only thing I can figure is Selmer bracing must be fairly light relative to the top compared to other guitars. All are ladder braced and typically have only one - two light braces in the bridge area. The heavily domed top must contribute to the stiffness too, again relieving the braces of some of their responsibility and allowing them to be lighter still. I typically use one or two 7mm x 14mm cathedral shaped sitka spruce braces under the bridge.

* I'm using the method in the book. An Mitutoyo analog dial indicator measuring to 0.01mm, 1.0KG load, load applied directly to the indicator shaft, tapping strung guitar tops with pencil eraser just below the bridge (Selmer bridges are too small to hit accurately with a hand held tapper), using a Shure 57 mic with USB input to a laptop, Visual Analyzer set up as prescribed here and in the book. Plugging sound hole with styrofoam plug for uncoupled top.

Never having done this before last month and having nothing much to compare with on these Selmers, I'm quite open to the possibility my methods are flawed, but results seem consistent with perceptions.

I haven't finished organizing all the data, but generally, air mode peaks are around 95-100 on most Selmer guitars tested. Main coupled top mode mostly run 225 to 250hz and uncoupled tops range from 205 to 235hz. When I get this better organized, I'll post more under the Good Examples thread.

Thanks for all your help,
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Re: Equation 4.5-7

Post by Trevor Gore » Thu Jun 27, 2013 9:42 am

Craig, your figures for cedar seem to correspond with mine. Typically, for a flat top using f=75 I get tops close to 3mm or just below in thickness.

So, with a top that is likely heavier (unless your cedar is a lot less dense than mine) the mobility figures are still a bit of a puzzle, because the top frequencies are also higher, therefore they must be stiffer (which is unsurprising because of the pliage and the thicker top). So (assuming the MM measurements are correct) that means that the effective mass of the top is a lot lower, because I don't think (but could be wrong) that the mass of the bracing is going to be the significant difference. Falcate bracing (for example) is a lot smaller than 7 x 14 mm. What's the mass of the bridge?

If the effective mass of the top is smaller, that would imply that the diameter of the monopole is relatively small, but it moves a lot, which is facilitated by the way it is braced. The small monopole is generally not too much of an issue as we know that small guitars can be loud if designed correctly, i.e. the mass that the strings have to move is also small, so that they have high mobility. So maybe that is the "magic" of the SM design - making a fairly large guitar behave as a small one.

All very interesting. I have a mate with a good Selmer copy (if he hasn't sold it!) so I'll see if I can get him to measure it, or let me measure it.

Craig, do you have a flat top that you can measure MM on as a "calibration check"?

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Re: Equation 4.5-7

Post by Craig Bumgarner » Thu Jun 27, 2013 11:29 am

Thanks for your thoughts on this. Sorry, but what is MM (Main Monopole resonance?) Otherwise, I think I'm following what you are saying. I suppose I would need Chilani patterns to determine the size of the monopole, something I have not done, but a logical next step any way as I have no idea what the peaks higher than the main monopole are. Most of the FRC of coupled tops I've looked at do not have many high peaks after the main monopole, so the lack of them may be more important than what they actually are but worth trying. Still have to set up for this.

I'll think about more about the bracing. While the centers are 14mm high, because of the cross grain arch, the ends are only about 6-7 mm high before the scallop. I'll look at you falcate bracing and try to compare mass.

My bridges are typically 9-11 grams, I hollow them out on the under side. The little mustache pieces either side of the bridge weight about a gram each.

I have an old dreadnaught, not a great guitar but has solid spruce top a solid mahogany b/s. I can check frequency responses, deflection and SM in the morning.

Thanks again
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Re: Equation 4.5-7

Post by Trevor Gore » Thu Jun 27, 2013 1:36 pm

MM = Monopole Mobility, arguably a more correct term than SM = Specific Mobility in these circumstances (and less confusable with Selmer-Maccaferri!)

Will be interesting to see what you get for the Dread.

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Re: Equation 4.5-7

Post by jeffhigh » Thu Jun 27, 2013 2:10 pm

Interesting the soundboard thicknesses you are measuring Craig.
I had just followed Michael Collins' figure 9.8 and used 2.1mm in spruce.
Still very stiff with a tapered pliage before jointing the plate halves.

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Re: Equation 4.5-7

Post by Trevor Gore » Thu Jun 27, 2013 8:34 pm

Jeff, do you have a monopole mobility measurement for one of your Maccaferris that you'd care to share?

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Re: Equation 4.5-7

Post by Craig Bumgarner » Thu Jun 27, 2013 11:05 pm

I ran the same deflection and Frequency Response Curves I've been using on the Selmacs on my Japanese made 1970 Cortley, a copy of the popular Gibson Hummingbird dreadnaught. Solid spruce top, solid mahogany b/s. Here is what I get:
  • Deflection under 1.0Kg: 0.13mm (a little less than most better Selmacs)
  • Spruce top thickness: 2.5mm +/- .1mm (average of ten spots with Hacklinger gauge).
  • Coupled top: air mode: 101Hz, main monopole: 175.3
  • Uncoupled top, main monopole: 157.8 (much lower than any Selmacs I've tested).
  • Calculated Monopole Mobility: 13.2
Looking at Fig. 1.7-8 in the book, I think a MM of 13.2 is high in relation to the guitars referenced. My Cortley is only an average guitar, probably less than average of the guitars in 1.7-8 and its response would probably be rated with those at the lower end of the chart.

This, of course, suggests that my test regime and/or calculations are all on the high side compared to the chart. They still seem relatively correct as the Cortley is no where near as responsive as any of the Selmacs, but makes it problematic to compare with other builders/testers.

The most critical part of all this still seems to me to be the deflection measurement. .01mm is very small and .01mm seems to change MM by 1.0. I think loading the dial indicator shaft directly is a step in the right direction as separating the indicator and the load support locations introduces compression of other parts of the guitar other than the top. Even with the load on DI shaft, however, I still see swings of .01 to .02mm on every reading. I've tried three different dial indicators and they all seem to do this. I guess I'm still not supremely confident of my deflection measurements, but I'm also wondering about everyone else's. :)

The FRC data, on the other hand seems to be very consistent from test to test. It does not matter much exactly where I tap, how hard or with what. Peaks are consistent to 1-2Hz, which makes only a .1 to .2 difference in MM.

Jeff, you worked out MM on your Selmac already didn't you, and posted results in the Top Deflection Rig thread?

viewtopic.php?f=33&t=5464&p=62933&hilit=Selmac#p62933

Hope you don't mind me pasting your results here.

"Tried it on the Selmac...... I used 516.8 grams to get 0.04mm deflection... In conjunction with an uncoupled top frequency of 250 HZ this gave me a Monopole mobility of 12.2"

When I run your numbers through my spreadsheet, I get MM = 12.4. If I use grams (x 10^-2) instead of Newtons for the load, I get MM = 12.2. How would you rate the responsiveness of the guitar? You said earlier the top was 2.1mm ala Collins. Did you use Collins bracing dimensions as well (7mm x 19mm)? Standard Selmer bracing (5 main & 4 minor braces)? I've done that, but tend to go heavier on the top, lighter on the bracing these days.
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Re: Equation 4.5-7

Post by jeffhigh » Fri Jun 28, 2013 6:42 am

Hi Craig
I used the Collins bracing arrangement and size except that I left out the last transverse brace at the tail end, and after I had the top glued to the sides I thought it was too stiff and brought the two underbridge braces down to 17mm high.
I would probably go a fair bit lower next time.
The major difference from the Collins method was using a hard pliage formed on my bending iron, tapered to nothing at the edge then shooting and jointing the centre seam. it made no sense to me to have a uniform bend and then mash the edge down onto a flat rim.
I have no others to compare to. Comments from both listeners and players are how loud it is, but I think it is probably a bit stiff.

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Re: Equation 4.5-7

Post by Craig Bumgarner » Fri Jun 28, 2013 7:27 am

Jeff,

I knew nothing about specific mobility when I started building Selmac or even a good way to measure just stiffness on a completed top. Like most builders, I overbuilt. In order to get a handle on simple stiffness, I started deflection testing good examples. This showed right away that mine were way too stiff and over built. I also started measuring plate thicknesses on good examples and was surprised at how thick most of the tops were compared to what I thought they should be. These good examples sounded better than mine, so I emulated them, but in order to get the deflection numbers in the ball park with the thicker tops, I had to lighten up the braces a lot. In some cases the good examples and my copies had only three braces and tops that were thicker still, close to 4mm in some cases. That's probably going overboard in the other direction, but my approach has been to target a thickness for the top, brace it with narrow braces that are a little on the tall side and then deflection test and shave braces until the deflection measures about right. If the braces start getting too small, I might take a tenth of a mm or two off the top.

Trevor's book and methods seem like a far more scientific and multidimensional than my rudimentary approach. I've very pleased to be trying to include resonances, mass, stiffness in multiple dimensions, etc. in the calculus of my guitars. It is an exciting time to be a guitar builder.

Yeah, I think 7mm x 19mm high braces, even with only four, is a too high and regardless of the top thickness, probably too stiff. By the way, I haven't heard many 5 brace Selmers that sound very good, not that it can't be done, but...... Django's 503 was a four bracer and by the recordings was an absolutely killer guitar. The early 500 series Selmer guitars, which are similar, are generally recognized as being the best sounding. The 5th brace was probably added to make them more durable, not to sound better. When I tested 5 braced Selmer #862 last week, its MM was 8th out of 11 guitars and in my subjective sound evaluation it was 9th. I agree with you, four, or even three is the way to go.
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Re: Equation 4.5-7

Post by Craig Bumgarner » Fri Jun 28, 2013 7:42 am

I hope I can get my testing rig calibrated so we can compare apples to apples. It seems we need a "standard" for our deflection rigs. Maybe a known material of specific size and thickness supported in an exact way would produce a constant result and we could all do this to set up our rigs. Maybe I could cut up a piece of plexiglass into equal size pieces, test them for consistency and them mail them to whoever wants one and we could compare. Maybe there is a much simpler way, I don't know.

The more I think about it, the more it seems likely this is where the difference might lie. The measurement is so small and the effect on MM is quite large. I almost think my dial indicator flutters when I breath on it.

Someone suggested a digital dial indicator, but I kinda like seeing the flutter. It tells me when there is play in the system. I'm told if you use a digital indicator, you want one that has a delay built into the zeroing function as touching the button is enough to flutter the gauge a little and you'll get a false zero.
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Re: Equation 4.5-7

Post by Trevor Gore » Fri Jun 28, 2013 10:05 am

Running the numbers for your Cortley Dread though my spreadsheet I get MM of 13.14, so close enough.

And yes, the trick is in getting the deflection measurement accurate. I do that by taking numerous measurements using different weights and averaging. Loading through the dial gauge shaft is the most accurate way with the error just being the friction in the shaft. I'm supporting on the back bindings, so I could be getting some side deflection, but that would increase my MM reading whereas they are generally smaller than yours. So that suggests I have a higher friction dial gauge shaft than you have. That's entirely possible and will give different levels of hysteresis in the measurement between loading and unloading. I try to eliminate that as part of the multiple readings by making sure that the load-on deflection is the same as the load-off recovery. If you just let the load sit you'll get a larger deflection reading for sure, at least on my rig, and that could be the explanation.

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Re: Equation 4.5-7

Post by Craig Bumgarner » Sat Jun 29, 2013 9:56 pm

Yes, that about how I do it too. I notice when I load the first couple times, recovery of the DI is .01 to .02mm short of zero. I reset zero and keep doing it in fairly quick succession, and take the average. Usually the end, I'm getting minimum differences and the measurements seem consistent.

I use a variety of spacers between the shaft and the bridge and find the harder ones (plex) give more solid readings than the softer ones (wood, PVC board). I don't let the load sit for long and yes, when unloaded, the DI will settle a couple hundredths.

I gather I'm using heavier weights than you and Jeff. I was using 5-20 lbs. but switched to 1.0 Kg a your suggestions, but this is still heavier. I'll try some lighter loads next chance I get. I think I like the heavier load as it spreads the measurement scale but the question is are the results linear with varying loads. My experience with the heavier loads says yes, but have not tried lighter than 1 kg. I'm wondering if DI internal friction becomes more of a problem with lighter loads. If so perhaps it leads to lower deflection measurements. I'll try lighter & varying loads next week.
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Re: Equation 4.5-7

Post by Craig Bumgarner » Sat Jun 29, 2013 11:35 pm

Maybe a better DI would help. I see they make them in .001 mm calibrations, albeit more expensive. I'm going to check next week to see if what I interpret as internal variance in DI is so or still a function of play in the mounting of all the parts.
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Re: Equation 4.5-7

Post by Jorge Bertholdo » Sat Aug 24, 2013 8:45 pm

I'm been trying to make the equ 4.5-7 work.

For the sample #1 on table 4.5-3 I'm getting 65.590. Also I did it by hand and I'm having the same result. So, obviously, OpenOffice is doing the math the wrong way (just like me).

So, what I did to solve this is:

-I divided the wrong answer for the thickness that should be and have 24.0xxx
-I did the same for samples 1 to 10 and 21 to 28, the average result is 24.0058549969 29.687765355 30.0073187461 for 60 55 and 75 hz
-In the spreadsheet, I divided the wrong result to one of these numbers (depend what f hz used)

I redo the calcs with the same samples as before, and now the results is correct.

I do all that because I couldn't find "where" and "what" openoffice was doing wrong.

cheers to all

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Re: Equation 4.5-7

Post by Jorge Bertholdo » Sat Aug 24, 2013 9:18 pm

One more thing.

What's dimension a and b used on table 4.5-3?
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Re: Equation 4.5-7

Post by Trevor Gore » Sun Aug 25, 2013 5:58 pm

jbs wrote:...Also I did it by hand and I'm having the same result.
It sounds to me like Open Office is only doing what you tell it to do.

The most common error is getting the zero count wrong. For example gigapascals (GPa) is 10^9 pascals and all those zeros need to be carried through your calculations. Also, there are a few things that are raised to the power 0.5 (^0.5), which is the same as square root.

Finally, a and b are defined right under equation 4.5-6. They are the the overall length and overall width of the guitar box you're about to build. For the examples given, the box size was 490mm (0.49m) by 390mm (0.39m), page 4-62. Millimetres are 10^-3 metres, of course.

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Re: Equation 4.5-7

Post by Jorge Bertholdo » Mon Aug 26, 2013 12:18 am

Thanks Trevor for your answer,

I suspect the problem came cumulating from equ 4.5.2. By my calculation, EL is 11.90, (11.96 on table 4.5-3).

Any way, my "solution" is not the best one, but works. I already spend many hours on this problem, I'll stay with my "fix" for while, I will back to this problem later.

Thanks one more time

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Re: Equation 4.5-7

Post by johnparchem » Mon Sep 09, 2013 8:02 am

I finally was able to jump in on a new guitar, and start following the methods laid out in the design and build books. I took the 7 measurements before gluing up some nice sound WRC, and processed the numbers through an excel spreadsheet. When all was said and done I did end up with numbers that were in the range of the table 4.5-3. I also realize that the true value of this system comes with later guitars as I try to tune in the sound I want and derivations from that sound. All and all it was fun playing with the measurements and numbers.

Length of plate m 0.61
Width of plate m 0.189
Weight kg 0.181
thickness m 0.0043
Density = kg/m^3 361.7405597

Pacals Gpa
fl 58.58 El 4.5-2 8634589877 8.634589877
fc 118 Ec 4.5-3 322875335.9 0.322875336
flc 59.32 Glc 4.5-4 1092152563 1.092152563

Vibrational Stiffness 75
Guitar Length 0.49
Guitar width 0.355

Desired thickness 4.5-7 3.242620835mm

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Re: Equation 4.5-7

Post by Trevor Gore » Mon Sep 09, 2013 4:57 pm

Well done, John!

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Re: Equation 4.5-7

Post by mqbernardo » Wed Jul 27, 2016 12:56 am

Sorry for beating up this dead horse, but it seems that everyone going through the book must pass through this initiation rite...
So, Eq. 4.5-7 and i have been doing this little dance lately and i can´t figure my head around it... would appreciate some help. It should be said that i had never used a spreadsheet before trying to calculate eq. 4.5-7 and that i am using apache OpenOffice (latest build).

So, feeding Trevor´s values into my sheet i get spuriously high values for target plate thickness. At first i thought it would be easy to find such gross errors but it has since been escaping me where i get stuff wrong. For instance, with sample#1 of the top woods in table 4.5-3 (engelmann, 228 g, 605 mm length,...) i get reasonable elastic and sheer moduli (El = 11,84, Ec=0,82 and Glc=0,91) but i get a target thickness (h) of 87,49 mm (!!!).
Another example, Sample 11 (POCedar top, 270 g) i get El=12,69, Ec=0,57, Glc=0,72 and h=88,67 mm . And the story repeats with other samples.
On western red cedar sample# 13, h=13,697. Elong, E cross and Glc values seem to be close enough to Trevor´s so logic dictates the error should lie in my implementation of Eq. 4.5-7.

As i said, it was the 1st time using a spread sheet so i got to spend quite some time with this. I did the spread sheets over from scratch 4 times (!!!) so i could mitigate any distraction error (hard to do the same error 4 times, but not impossible), i then divided the complicated equation into simpler parts, one in each cell, and combined them at the end, i repeated all the calculations with a scientific calculation and a piece of paper and they all seem to agree on the high values for h. So, apart from me being stupid can you figure out any other possibility?
FWIW, quotient formula is =0,95977*D43*F45^2*F21^0,5 and divider is =F34+F47^4*F35+F47^2*(0,02857*F34+1,12*F36), then i do Q/D^2.


Any help is appreciated... i don´t want 1 cm thick tops :)

thanks,
Miguel.

- edited for clarity -

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Re: Equation 4.5-7

Post by mqbernardo » Wed Jul 27, 2016 1:05 am

Here´s an attached PDF. values are on page 3.
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