TonyGonzales84 -> RE: vertical string pull on the soundboard (torque) (Jul. 19 2020 22:09:03)
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Everybody in the water! Note: I have edited and corrected my original response, to that shown here. I apologize if you have read my initial response and were confused by it; it would have been correct only in the case of an antique type of tie-block, prior to luthiers/guitarreros including a separate saddle. Armando, 1) Statically, the net vertical load due to the strings can be calculated, first, by calculating the string turning angle, A. A is the Arc Tangent of the quotient of the difference in height that the saddle sits above the tie-block holes, a (a is the numerator), and the distance forward of the front end of the tie-block that the string turns down from the top of the saddle, b (b is the denominator): Arc Tangent (a/b) = A. (I apologize for not showing a sketch - I am not near a printer/scanner, nor do I currently have good sketching software.) Next, take the sine of A and multiply it by the string tension F. F * sine A = Net Vertical Force. This force pushes down (against) the top. 2) The static torque applied to the top, by the strings via the saddle/bridge assembly, also causes vertical displacements of the top. 3) What type of simulation are you intending to perform? It's often a challenge to actually set up and perform a test that tests what you are attempting to test, and not a (possibly closely related) phenomenon. The above is the Reader's Digest version. Hopefully, this is not the place where Mr. T comes in with his, "get ready for the pain!" Addressing each of the three, numbered points, in slightly expanded form: 1) The vertical load (against the top) changes when the strings are set into vibration, due to these vibration induced dynamic vertical loads. Richard Jernigan has linked an interesting and enlightening article by Alan Carruth, here (excellent work in investigating the dynamic vertical loads, etc): http://alcarruthluthier.com/Downloads/stringTheory.pdf The vertical loads are dynamically present as reactions to the strings's transverse (vertical) vibrations. The static vertical loads, due to the torque caused by the strings, are a couple, reacted by the bridge, which then must be reacted by the top. The part away from the soundhole, which is trying to be pulled off, is exactly matched by the part towards the soundhole, which is being pressed into the top. The values of these static loads change during string vibration. I recommend caution in attempting to simulate such dynamic loads, overlaid on the static load caused by the saddle turning angle, as static loads: this can be self-defeating, especially in regards to the actual physics and design/construction problems and possible solutions. Please refer to Mr. Carruth's paper for more discussion on the vertical loads. 2) The vertical displacements caused by the applied torque also affect the top in buckling, between the bridge and soundhole (I believe that, statically, it is (somewhat?) relieving), actually inducing a top buckling load on the other side of the bridge. A guitar is a structure that is designed for (by) stiffness considerations, as apposed to a structure being designed by strength considerations. For example, the top probably doesn't want to be designed to buckle anywhere (although it might be interesting to some, to design and build a guitar (top?) lightly enough that it would be statically stable against buckling, but that might temporarily buckle in certain, well-understood dynamic modes); also, think of the pre-strung tone tuning performed by luthiers; in Mr. Carruth's paper, he discusses a 4 kHz mode of longitudinal string vibrations, that he recommends slightly lengthening the scale in order to avoid resonant effects caused by said modes. Designing for stiffness requires much finesse and attention to detail in, for example, local and minute structural deflections, and scares the hell out of many engineers! As to one of the kernels in your original post, the static torque applied by the strings, calculated at the bridge-to-top joint is just the height of the strings, h, multiplied by the total force of the strings (can be looked up on several manufacturer's sites), F (the same F as discussed above). Remember here, that, the bridge and top also have to react (withstand) the longitudinal load of the strings, F: The bridge-to-top glue joint has to not fail due to this shear load, and the top, between the bridge and soundhole has to not buckle. 3) Rereading your original post, it seems you wish to apply a (static) vertical load to simulate the torque. I don't fully understand what one might gain from this test: it does not fully simulate a guitar, as a guitar actually functions. Much or all of the foregoing might go into planning a test that would simulate the way a guitar actually functions. Best regards, and I look forward to hearing your thoughts! Tony
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