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RE: vertical string pull on the soundboard (torque)
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kitarist
Posts: 1715
Joined: Dec. 4 2012
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 RE: vertical string pull on the soun... (in reply to Richard Jernigan)
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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
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Date Aug. 20 2020 3:32:48
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TonyGonzales84
Posts: 78
Joined: Apr. 23 2020
From: San Diego, CA
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RE: vertical string pull on the soun... (in reply to Tom Blackshear)
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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
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Date Aug. 22 2020 2:45:41
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RobF
Posts: 1611
Joined: Aug. 24 2017
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RE: vertical string pull on the soun... (in reply to TonyGonzales84)
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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.
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Date Aug. 22 2020 4:20:50
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RobF
Posts: 1611
Joined: Aug. 24 2017
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RE: vertical string pull on the soun... (in reply to Armando)
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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.
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Date Aug. 22 2020 20:50:11
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TonyGonzales84
Posts: 78
Joined: Apr. 23 2020
From: San Diego, CA
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RE: vertical string pull on the soun... (in reply to Tom Blackshear)
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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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Tony
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Date Aug. 22 2020 21:51:31
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