Right, bridges serve to distribute load among the ribs, and don't support crown, and I was asking whether or not a counter-bridge or "sister bridge" had ever been intended, at least partly, to support crown. Or if, without adding way too much stiffness and mass, a set of counterbridges (or better, quasi-ribs parallel to the grain of the panel) *could* be designed to support crown, so that, *assuming* there was anything to be gained from it, ribs could be designed without having to have all of the crown support as one of their functions. I think that due to Del's reply and yours, I see better why this might not work, or, at least, might be wholly unnecessary. (Understand, by the way, that I am after grand piano tone, not, what might result if we tried to "simplify" matters by pretending that we are trying to reproduce string oscillations as found at the bridge cap, in the same way that an audio engineer tries to reproduce air oscillations arriving at a microphone.) First, I probably used the term "coupling" too generally. I did mean what Del calls the "mechanical coupling" that is gained from the combination of bridge pin angle and side bearing. (I think I've seen the term "string coupling" in the sense of the acoustical "coupling" interaction between the three strings of the same trichord (reinforcement, gradual increase of vertical phase cancellation from unavoidable lack of perfect unison, etc.), but I had thought that a string could be said to be acoustically coupled to a board assembly at the bridge, and that the term could then be used more generally to include mechanical coupling.) Second, what Del calls "a system of opposing springs" captures that part of the concept I've been missing the most. I knew that a board assembly is a downward-hardening spring, and therefore, in the absence of downbearing, would be an upward-softening spring. If one were to remove the downbearing entirely, it would rise to its equilibrium level as an a complex of unloaded beams, very much as a wooden girder, floor joist, and floor system, supported by a perimeter foundation, would do at the top of a basement, if a heavy live load were removed from the floor above. And at that equilibrium level, the board would be too flexible at zero amplitude, if the string were mechanically fastened to it (with help from the hitch pin...) at its own zero amplitude (condition of rest and silence). But, thinking so much of the string as having a great deal of tension, I tended to think that downbearing would be, so to speak, "borrowing just a little of the string's potential energy" that the string has gained from that tension, and "not enough to matter very much to its own -- the string's own -- function as a spring". I now see that as faulty thinking. One way of visualizing the problem lies in considering the consequences of the fact that the gaining of downbearing necessarily changes, from a right angle, the angle of the string to the downward vector of board assembly movement. (The assembly does have very high resistance to any change in the exact angle at which its own deflection, as a complex of end-supported beams, operates in response to the "live load" bearing down on it. ((Now, *there's* a simplification...)) :) .) Rather than being merely "just a very small change of angle", this lessening of the right angle fundamentally alters the right angle that is shown in a drawing, on acoustic theory of the string, of the string as having one vertically fixed termination (the capo or agraffe) and one termination that is fixed horizontally, but whose vertical "quasi"-fixing is to a mass that is free to move vertically -- e.g., a mass free to move vertically because, in fact, in that dimension, it is a spring. That is, the change from that right angle to a smaller angle in the grand piano will cause the string to have more tension than its resting tension at the top of its complete cycle of vertical oscillation, and less tension than its resting tension at the bottom of the complete cycle. These differences cancel each other out, yielding a tone that is steady in pitch, just as the process of the formation of the string's standing wave after the upward blow of the hammer is, in part, a process of cancelling out certain of the effects of the blow's having been upward rather than downward. It is, therefore, this lessening from the right angle to the assembly's vector as a spring that makes the string itself an *opposing* string, in the sense that, at the required times in the course of the fundamental's cycle (and, correspondingly, of the cycles of the harmonics), the string is a not "simply" a spring that hardens when moving upward from the rest position of zero amplitude, but a spring that has the required degrees of stiffness at that rest position and at all higher amplitudes. The provision and adjustment of the adjustment of downbearing, therefore, is a means to control the rate of vertical transmission "beyond", and, so to speak, horizontal reflection backward from, the coupling of the string to the bridge. If I haven't made a new mistake here, my next question is: are *lateral* transverse vibrations of the string (or, large lateral vectors of vibrations that are significantly "slanted" from the vertical) thought to be transmitted in any way that the theory of the board assembly, and of the interaction of its components, has been able to explain, or (usefully) speculate about? Thanks for your help! Randy Jacob University of Michigan Library --On Tuesday, July 29, 2003 2:40 PM -0500 Ron Nossaman <RNossaman@cox.net> wrote: > > >Ron Nossaman stated in a previous post that (if I understand > >correctly) he designs a rib set, for a rib-crowned board assembly, > >to give a certain set of ranges of deflection under different humidity > or >dryness conditions, for a certain range of > >expected downbearing forces from one end of the bridge(s) to the other, > >and that one of the criteria for the bottom of the ranges > >of deflection is, that the ribs should be the primary elements that make > >it certain that the board assembly will not go into flat crown > >or negative crown over the expected humidity and dryness range, > >and will make this certain for a reasonable expectation of > >lifetime for the assembly. > > Yes, almost. For crown formation and retention, I pretty much ignore the > panel when I design a rib set, so humidity isn't a factor in rib support > of bearing or longevity. Panel thickness and grain direction is important > for other reasons, but not to me in determining rib stiffness. I wouldn't > expect to see boards like this go flat in any humidity conditions, which > is one of the primary reasons for doing this in the first place. > > > >Factors that can bring about change > >over lifetime--and in some designs, begin to do so during, or > >even before, installation--include various possible compression forces > >within the elements of the assembly, as these interact with > >each other, and with the strings and case parts. > > Exactly, which is why I like rib supported systems. The stresses on the > ribs and panel are very light and dependably predictable as opposed to > the extremely high compression levels in the panel required to both bend > a straight rib (which resists being bent) and support string bearing as > well in a compression crowned system. > > > >The reason most commonly given for designing for the prevention of flat > or >negative crown is, that the coupling of the string to the board > assembly >is otherwise either likely, or certain, to become > >insecure. > > Regardless of reasons commonly given, coupling doesn't normally have much > to do with it until the board is flat enough to produce negative front > bearing on the bridge. If the soundboard assembly doesn't present enough > stiffness to the string plane, as in the typical old flat or concave > crowned compression crowned board, the impedance mismatch between board > and strings is too great and the tone suffers. Percussive attack and > short sustain in the killer octave is the classic example. A compression > crowned board depends on panel compression at destructive levels to the > material to provide that soundboard stiffness, thus impedance, to the > proper levels. A rib supported board depends on rib dimensions to provide > stiffness at much lower material stress levels for the same thing. > > > >But the prevention of excessive deflection in the board assembly-- > >under any humidity and dryness conditions--is also the prevention > >of a certain degree of stiffness of the assembly at the coupling, > >when the string and board are at rest (zero amplitude). This is, in a > >sense, independent of the question of the coupling's security. The > >assembly, as a hardening spring, must give that degree of > >resistance to the downward vertical transmissive force of the > >string when set into movement--"independently", so to speak, of its > >downbearing force at rest--to insure, at one and the same time, the > >(grand) piano's dynamic range, sustain, and desired tonal character. > > I'm not sure what you mean here, but there is certainly a difference > between static load support and dynamic response. This again, isn't > really coupling. It depends on the string bearing load and frequency, > spring rate of the soundboard assembly, initial crown height, deflection > under bearing load, mass of the assembly at that point, and back scale > length. For instance, compare two 500mm ribs, each with 1mm remaining > crown under identical loads of 25lb (11.34Kg) from identical string > scales and configurations. One was 20mm wide, 28mm tall, and had a 1.74mm > crown height before loading. The other was 17mm wide, 23mm tall, and had > a 2.6mm height before loading. They both support the same weight with the > same remaining crown, but I would certainly expect their dynamic response > to be different because their spring rates are different. > > > >This idea of a certain "independence of function" is, I take it, > >what has often led to proposals for a different sort of coupling. > > I don't understand your use of "coupling" here.. > > > >But it has also led me to wonder about such innovations as > >Grotrian's "counter-bridge", underneath the piano, under the bridge. Or: > >*whatever* Grotrian's own purpose may have been, why not consider having > >one or more counterbridge as a "garantor of crown", in the same sense > that >Ron's rib set is, and replacing a certain part of that latter > function? > > I don't see any connection here because bridges don't support crown. Some > combination of ribs and panel supports crown, and the bridges serve to > distribute load among the ribs. > > > >Ribs are still needed for the solid spruce planks, but - perhaps - the > >whole assembly could then be designed without as much of a problem of > the >effects of compression on the panel sub-assembly, i.e., especially > the >vector of compression that runs across (perpendicular to) the > plank's grain? > > Which is the first purpose of rib crowning - very little compression of > the panel across it's grain. > > > >My assumption in all this is, that, in many present designs, the > >planks benefit--as acoustical components--from having a longitudinal, > >end-to-end crown, and that the with the new approach, they could keep > >this, while otherwise suffering no damage. Of course, I'm far from sure. > > I doubt that there is any real benefit gotten from crown along the grain, > despite repeated assumptions to that effect, but it happens to be pretty > nearly unavoidable on a nominally flat rim with crowned ribs. > > > >Would this yield a sound that is too much like an early laminated > >board? > > ?? Too many undefined variables. Try it and see. > > > >And, what *did* Grotrian have in mind with a "counter-bridge"? > > > >Randy Jacob > > I don't know. They might have been trying to form a crown there, or > merely adding stiffness and mass to the bridge. > > Ron N > > _______________________________________________ > pianotech list info: https://www.moypiano.com/resources/#archives
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