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RE: vertical string pull on the soundboard (torque)   You are logged in as Guest
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Tom Blackshear

 

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RE: vertical string pull on the soun... (in reply to RobF

The upper bout was 11-1/16th wide, the waist was 9-5/8ths, and the lower bout was 14-5/8th" wide. But I refit the length of the box to a 650 playing scale, from a little over 26" original scale, by removing a little off the box length at the 12th fret.

This was for the 1968 Conde but the 1950's was originally 14-1/2 " wide.

Go figure, the earlier model was more narrow with a thicker top, so this could mean Faustino was evolving toward making his model better for his 1968 pattern.

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  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 11 2020 18:45:40
 
JasonM

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From: Baltimore

RE: vertical string pull on the soun... (in reply to Tom Blackshear

I have to multiply all of those figures by 25.4 for them to make sense in my head

I wonder how many of those old style condes were thicker tops... or maybe that ‘68 was an Exception
  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 11 2020 23:20:41
 
Tom Blackshear

 

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RE: vertical string pull on the soun... (in reply to JasonM

quote:

I wonder how many of those old style condes were thicker tops... or maybe that ‘68 was an Exception



Come to think of it Nino Ricardo's '55 Conde was fairly thin in its top so it's obvious that there was experimenting going on.

I made a replica of a 1968 one year and thinned the top down to where it sounded like Ricardo's twin sister. But I went a little too far and had to replace the top; most of the thinning was toward the middle of the top area.

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  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 12 2020 13:56:04
 
Armando

Posts: 302
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From: Zürich, Switzerland

RE: vertical string pull on the soun... (in reply to Stu

You are right Tom

What i do is guesswork each and every time and i really hate it to be still at this point after 20years of building guitars although only as an amateur maker.

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  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 16 2020 17:48:58
 
Armando

Posts: 302
Joined: May 27 2005
From: Zürich, Switzerland

RE: vertical string pull on the soun... (in reply to RobF

I've done stiffness camparison tests with the method you are showing or a similar method. So that is ok. It allows to use material the best weight to stiffness ratio but this is still not exactly what i want to know for the soundboard deflection point.
I need to know at what point my soundboard will start to deflect under string tension and for that i need to know how much vertical pull will be produced by a certain scale lenght, bridge height and string gauge. If i would know that number or would be able to calculate it, i could then use a method to measure the deflection with specific weights,but unfortunately i'm still in the dark about that number. I mean it would work if you would know the weight of the block you need to put on the top but to just use any weight will not bring the results i'm looking for.

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  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 16 2020 17:58:00
 
Armando

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From: Zürich, Switzerland

RE: vertical string pull on the soun... (in reply to JasonM

"If the wave is expressed along the grain it looks like a bulge behind the bridge and a dish in front of the bridge. If expressed across the grain it usually looks like the bridge is in a hill with slight troughs on either side."

I've seen such guitars and they all sounded very well although i thought it was the result of a too weak soundboard/bracing.

I was told that this is not the case and the wave does not impact the sound in a negative way.

Personally i assume that the wave is a result of a top being built to that deflection point i'm talking about and the constant stress of the string tension deforms the top over time.

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  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 16 2020 18:37:11
 
RobF

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RE: vertical string pull on the soun... (in reply to Armando

quote:

I need to know at what point my soundboard will start to deflect under string tension and for that i need to know how much vertical pull will be produced by a certain scale lenght, bridge height and string gauge.

Why not build a test jig and arrive at the data empirically?
  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 16 2020 19:40:33
 
JasonM

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From: Baltimore

RE: vertical string pull on the soun... (in reply to Armando

Do you not like the results from sanding the braces down after the guitar is finished?
  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 16 2020 19:41:25
 
kitarist

Posts: 1304
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RE: vertical string pull on the soun... (in reply to Armando

quote:

I need to know at what point my soundboard will start to deflect under string tension and for that i need to know how much vertical pull will be produced by a certain scale length, bridge height and string gauge.


The string length, string gauge, and string material density give you string tension, which is what you wanted anyway, so you can just pick a string set and write down the total string tension T of it which is the sum of the listed individual string tensions.

Or if you want to be able to plug in string parameters or vary the scale length, here is the formula for a single string:






Next you measure the quantities a and b from Tony's post way up-thread. (He says a is "the difference in height that the saddle sits above the tie-block holes", and b is "the distance forward of the front end of the tie-block that the string turns down from the top of the saddle")




Finally you have your static vertical load F = T*sin(arctan(a/b)).

where T here is now the SUM of all individual string tensions each calculated via the formula above.

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Konstantin
  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 16 2020 19:44:02
 
Richard Jernigan

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From: Austin, Texas USA

RE: vertical string pull on the soun... (in reply to kitarist

Thanks Konstantin. As Estebanana observes, the effect is actually to deform the top into a wavy shape, not just to pull up on it. The strings press down on the saddle with the same force as they pull up on the tie block. The result is a torque about the lever arm dimensioned "b" in your diagram.

The deflection of the top, as a result of the torque about "b" depends upon the size, shape and flexibility of the bridge.

Holding "a" (=about half the saddle height above the soundboard) constant at 4mm and varying "b" for break angles between 26.5 and 45 degrees, the countervailing vertical forces vary considerably, but the torque varies only slightly, decreasing with increasing break angle.

The forces increase as the break angle gets steeper, but the lever arm "b" decreases more rapidly.

85.8 pounds is about the total tension for a set of D'Addario EJ-45s.

RNJ



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  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 18 2020 0:42:11
 
estebanana

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RE: vertical string pull on the soun... (in reply to Tom Blackshear

Math etiquette, how classy you broke it out into elegant steps.

This is literally the chart of the diminishing returns on break angle.

I still have to reference Gore’s book, the problem with Gore’s book is that it’s written at a mathematical level that I don’t understand. But he sort of dumbs it down with a paragraph or two after the equations.

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  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 18 2020 3:51:17
 
kitarist

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RE: vertical string pull on the soun... (in reply to Richard Jernigan

Thank you, Richard.

I am surprised how little torque is there - just 1 N.m or so. I put my smallest torque wrench on its lowest setting - 1.58 N.m - and can move the drive with my fingers almost with no effort.

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Konstantin
  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 19 2020 18:28:03
 
Richard Jernigan

Posts: 3134
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From: Austin, Texas USA

RE: vertical string pull on the soun... (in reply to kitarist

quote:

ORIGINAL: kitarist

Thank you, Richard.

I am surprised how little torque is there - just 1 N.m or so. I put my smallest torque wrench on its lowest setting - 1.58 N.m - and can move the drive with my fingers almost with no effort.


You're right, it's not much torque. I did the calculation on a spreadsheet, since Matlab won't work after I "updated" to the latest Mac operating system. The intermediate results using your formula for the force looked reasonable. The force is fairly strong, but the lever arm for the torque is tiny.

RNJ
  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 19 2020 21:49:38
 
estebanana

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RE: vertical string pull on the soun... (in reply to Richard Jernigan

The fulcrum is not high, say 8mm compared to the lever, which is 660 mm long

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  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 20 2020 1:22:08
 
Richard Jernigan

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From: Austin, Texas USA

RE: vertical string pull on the soun... (in reply to estebanana

The graph in my post just above accounts for only the vertical components of the forces exerted by the tension of the strings. The downward force on the saddle is balanced by the upward force on the tie block, but these vertical forces act at different points, resulting in the torque shown in the graph.

There is also a horizontal component of force acting at the top of the saddle, namely the full force of the total string tension. Since the bridge is motionless unless the string is vibrating, there must be an equal countervailing force. The deflection of the top and the flexibility of the bridge make a detailed calculation complex. An approximation to the resulting torque is just the product of the string tension by the height of the saddle.

85.8 pounds =381.7 newtons.

381.7 newtons * .008 meter = 3.05 n*m

Still not much, but considerably more than the torque induced by the break angle.

The two torques sum to about 3 1/8 foot-pounds, for those more accustomed to American units.

RNJ
  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 20 2020 2:40:38
 
kitarist

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RE: vertical string pull on the soun... (in reply to Richard Jernigan

quote:

An approximation to the resulting torque is just the product of the string tension by the height of the saddle.


I was thinking about this as well. I know Tony said the same thing, basically torque Tau = h*T where h is the height of the saddle above the soundboard.

But something doesn't seem right. This would be correct if the strings were attached to the top of the saddle. But they are just gliding there.

So surely the horizontal force at the top of the saddle (that multiplies h) must depend on the break angle alpha = arctan(a/b). Because if the break angle is zero, there is neither horizontal nor vertical force at the top of the saddle and thus no torque.

As far as the top of the saddle is concerned, there are two T forces as in the diagram, and their vector sum is shown in red.

The vertical component (in green) of that red force is as calculated before, T*sin(alpha).

But the horizontal component is tan(alpha/2)*T*sin(alpha) because that angle there is half the break angle.

This seems to have the desired features: as break angle alpha goes to zero, both the vertical and horizontal components go to zero.

And the moment (torque) Tau due to string tension T at the top of the saddle is now dependent on the break angle:

Tau = h*tan(alpha/2)*T*sin(alpha) where alpha = arctan(a/b).

Also if alpha = 90 degrees, i.e. the strings are affixed to the bottom of the saddle (b=0), the torque becomes Tau = h*T as it should be (functionally this is the same as the strings being affixed to the top of the saddle).

Does this seem right or did I screw up? Mechanics has never been very intuitive for me.

(NOTE: I shouldn't have drawn the vectors on the diagram as if T goes from the top of the saddle to the tie-holes so that the vertical force component is somehow numerically in magnitude the same as 'a', etc. Drawing them this way is just visually misleading, though it is the angles that are important so doing so does not affect the formulae).



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Konstantin
  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 20 2020 3:32:48
 
dartemo1

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RE: vertical string pull on the soun... (in reply to kitarist

For simple modeling there is a free on-line calculator: "mechanicalc.com/calculators/finite-element-analysis". In this free free version there are few predefined cross-sections and up to 50 elements. I've attached results for a crude model using 4"x2" cross-section (can use inches as mm :) and an arbitrary tension of 1077 lbf.





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  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 21 2020 3:26:26
 
estebanana

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RE: vertical string pull on the soun... (in reply to Tom Blackshear

Here’s a question for the math people-

If the saddle is rotated to stand forward at an angle, 5 degrees... does that enhance the ability of the saddle to operate better with the force bearing down from the string with a slanted saddle?

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  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 21 2020 6:41:11
 
JasonM

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From: Baltimore

RE: vertical string pull on the soun... (in reply to estebanana

Vicente Carillo says in this vid, talking about tension, that Paco's guitar was 670mm. Dang!

  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 21 2020 17:22:52
 
JasonM

Posts: 1701
Joined: Dec. 8 2005
From: Baltimore

RE: vertical string pull on the soun... (in reply to estebanana

quote:

If the saddle is rotated to stand forward at an angle, 5 degrees... does that enhance the ability of the saddle to operate better with the force bearing down from the string with a


Isn’t this what Gore talks about in his book?

quote:

I did the calculation on a spreadsheet, since Matlab won't work after I "updated" to the latest Mac operating system.


Ever use R? I’m taking a class on it at the moment for work
  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 21 2020 17:31:57
 
TonyGonzales84

 

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From: San Diego, CA

RE: vertical string pull on the soun... (in reply to Tom Blackshear

Lots of water under this bridge...

Reading the detailed discussions above, especially Konstantin's illustrated work (the figures grabbed my attention -- nice going!), and Richard's mention of the various forces on the bridge, I went back and actually drew up full free-body diagrams (FBDs) (thanks, Richard -- freshman physics stuff -- ha ha ha). The bottom line, as Richard points out, THERE IS NO VERTICAL LOAD ON THE TOP.

My quick Moment numbers are in good agreement with Richard's.
I hope the broken up FBD stiff is helpful.

Sometimes bulleted stuff is easier to skim and understand quickly, so I am including a quick discussion. I hope this helps. More to come...







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Tony
  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 22 2020 0:54:56
 
TonyGonzales84

 

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From: San Diego, CA

RE: vertical string pull on the soun... (in reply to Tom Blackshear

Some methodology notes.
1) This is hopefully not too much in the vein of, "measure with a micrometer, mark it with a chalk, cut it with an axe!"
2) I was trying to get a feel for orders-of-magnitude, and compare my results with Richard's values.
3) I measured (using a vernier caliper...ouch, my no-longer 20-year old eyes!) my 1970 Manuel Rodriguez (used for the illustrative photos -- note the pronounced doming - muy ahuevada, even with these marginal photos), and my 2012 Charles Sutton.
4) The dimension, a, is reasonably accurate, not really requiring calibrated eyeballing (i.e., it is repeatable). The dimension, b, does require eyeballing, so there's more slop in that measurement.

Some thoughts.
1) Romanillos, in his book on Torres, states that Torres was the first to standardize using a saddle, to give a significant degree of freedom in adjusting string height. This was because the double-domed top is difficult to build precision into (pg 138). Romanillos mentions nowhere the desire to vertically load the top. Interestingly, Huber, on pg 42 of his "The Development of the Modern Guitar," says the saddle "(allows)... a downward bearing of string tension..." Note, La Leona is from Torres's first epoch, and has no saddle (the picture included here).
2) Ricardo mentions, upthread, that he's played a guitar with break angle = 0, and it was sonically negligible in difference with when it had a small break angle. The classical players that play and concertize with La Leona, love that guitar's sound.
3) On the problem of extrapolating a guitar's response based on a (beam-based) simplified vertical stiffness measurement, I'm not sure what to make of this (I do understand that people need quick and ready guides). I know luthiers perform tap tests at various stages of assembly, but is this type of test frequently used? It would only take a few more minutes to set up a test where the majority of the top's edges are supported; would this "higher accuracy" measurement be worth performing, since it still does not simulate the string load's applied shear and moment? (This is possibly in the mode of thinking aloud...)
4) I can envision a rig that would load the stiffened top in shear and moment, but I can't see how the top would remain undamaged (crushed and compressed top).
5) I can also envision a test rig, using low friction installed pins (waxed, oiled, etc), perpendicular to the top, to convince oneself of the string loading. The pins on the front of the bridge would be compressed due to the moments, and those on the back of the bridge would want to be pulled out; all pins would see the shear force of the full string set, T.
6) I recall seeing somewhere, online, that someone has built a modern version(s) of Torres's papier mache guitar (or something like that). I could envision that challenge as a right-of-passage for some luthiers.
7) I'll shut up, now!



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Tony
  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 22 2020 2:45:41
 
kitarist

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RE: vertical string pull on the soun... (in reply to TonyGonzales84

quote:

I hope the broken up FBD stiff is helpful.


Thanks Tony. So just for the top of the saddle; not for the whole bridge assembly, you have the force in the x-direction T-T*cos(theta) = T*(1-cos(theta)).

And I derived it as T*tan(alpha/2)*sin(alpha) where my alpha is your theta.

So it looks like I accidentally proved the trig identity 1-cos(theta) = tan(theta/2)*sin(theta), meaning these two expressions are the same thing mathematically.

Haha. Though obviously it was easier to write it up the way you did.



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Konstantin
  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 22 2020 3:34:20
 
RobF

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RE: vertical string pull on the soun... (in reply to TonyGonzales84

quote:

3) On the problem of extrapolating a guitar's response based on a (beam-based) simplified vertical stiffness measurement, I'm not sure what to make of this

Hi Tony. If you are referring to the deflection rig I posted earlier in the thread, that was not the intended purpose of my suggestion.

Armando had mentioned at the beginning of the thread that he felt he has been overbuilding his guitars and, due to the timeframes involved with his projects, he didn’t trust his fingers to tell him how to dimension the wood. The purpose of the deflection rig, as presented, is simply a means to compare the longitudinal stiffness between tops. For example, if, using whatever arbitrary weight available, the typical deflection of previous tops was in the neighbourhood of ‘x’, and if it is suspected that the tops on the previous instruments were dimensioned too thick, then dimension the next top to allow it to deflect a little more. It was provided as a possible means to help him train his fingers, should he choose to use it. But, it appears it wasn’t what he is interested in, so I think Jason’s initial suggestion, coupled with elements of the discussion which has occurred later in the thread may be more suited to his desire.

Of course, if that’s not what you were referring to then please ignore my explanation.
  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 22 2020 4:20:50
 
Tom Blackshear

 

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RE: vertical string pull on the soun... (in reply to RobF

quote:


Armando had mentioned at the beginning of the thread that he felt he has been overbuilding his guitars and, due to the time frames involved with his projects, he didn’t trust his fingers to tell him how to dimension the wood.


Rob,

What I've been tying to communicate with most of my posts is to basically take a Spanish style guitar top and build it as close to its original pattern, then fine tune the tension as soft or hard toward it desired level of articulation and tone variation as possible. The more I do this the closer I get to perfection.

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  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 22 2020 12:39:22
 
Armando

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From: Zürich, Switzerland

RE: vertical string pull on the soun... (in reply to RobF

To do that empirically would be very hard. I mean you could make a frame, clamp a similar soundboard on it, glue a bridge on it and string it up and then go thinning the braces until the soundboard starts to dome but for that you need to know the basic thickness of the soundboard. Ok a standard thickness could be used but still you had variables in the material used as not every piece of wood has the same stiffness.

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  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 22 2020 20:36:10
 
Armando

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From: Zürich, Switzerland

RE: vertical string pull on the soun... (in reply to JasonM

That is maybe the right way to do it but very hard in my opinion, unless you are Tom Blackshear.

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  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 22 2020 20:37:55
 
RobF

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RE: vertical string pull on the soun... (in reply to Armando

quote:

...but for that you need to know the basic thickness of the soundboard. Ok a standard thickness could be used but still you had variables in the material used as not every piece of wood has the same stiffness.

That’s going to bite you, no matter what. Even if the calculations performed by Konstantin, Tony, and Richard end up supplying you with something meaningful, you’re still going to have to characterize the wood, and determine what to do with it. There’s no escaping that.

A deflection test can provide an enormous amount of useful information. But, ignoring the contents of this entire thread, if you feel you have been leaving your tops a little too stiff, then why not use that information when dimensioning your next top? Go a little thinner on the plate and lighter on the braces than what sits within your normal comfort zone and see what happens. Not a dramatic amount, but just enough that your intuition feels challenged.

The book Jason recommended might be a good fit for you, there are also other fairly theoretical/technical works out there. Searching out some of the discussions Alan Carruth has been involved in online is also a great idea. He was a colleague of Carleen Hutchins of the Catgut Society from way back and has dedicated a lifetime to studying and characterizing the behaviour of instruments. Many of his tests are empirical, but it would still be well worth getting acquainted with his work.
  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 22 2020 20:50:11
 
TonyGonzales84

 

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Joined: Apr. 23 2020
From: San Diego, CA

RE: vertical string pull on the soun... (in reply to Tom Blackshear

Armando,

I do not mean this to be in any way disrespectful, but you need to "let go of the poolside rail and get in the water" -- you won't drown, and you can see that there are many helpful Luthiers here to lend a hand when you call out. You've been given many great ideas, Tom Blackshear's possibly being the best, in seeking out someone who will take you under their wing and mentor and coach/teach you many of the fine points that will give you greater self-confidence.

The analytical stuff that has been discussed in your thread (at great length) is all nice and good for getting an understanding of the basic static loading of the guitar's top, but, importantly, Luthierie is a rich and experience-based art , and you need to gain the experience by doing.

Scratching my head, last night, and discussing this with my wife, it occurred to me that you may be asking for a formula that will give you a guitar top's static deflection, given a certain load applied at a certain location. Is this possibly what you're looking for? -- If so, you're looking for a tabulated relationship/equation that does not exist: stiffened plates, with stiffening unique to each individual instance, and whose planform shapes resemble a young lady's figure are impossible to solve analytically. Period. Modern computational methods, such as finite element analysis, are the best way of attacking such problems, and you might be able to find something online that leads you to such work.

Still scratching my head,

Tony

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  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 22 2020 21:51:31
 
TonyGonzales84

 

Posts: 78
Joined: Apr. 23 2020
From: San Diego, CA

RE: vertical string pull on the soun... (in reply to Tom Blackshear

Rob,

Thanks for your response on the deflection test setup. It does answer nicely.

Tony

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Tony
  REPORT THIS POST AS INAPPROPRIATE |  Date Aug. 22 2020 21:52:57
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