Hello Sarah. I'm having a hard time following your paper clip experiment. Where and how is the paper clip supported/immobilized? Is the clip straightened out and supported at the two ends and depressed in the middle? Where is the leaf spring situated, etc. Please clarify. Thanks zillions. Terry Farrell ----- Original Message ----- From: "Sarah Fox" <sarah@gendernet.org> To: "Pianotech" <pianotech@ptg.org> Sent: Thursday, August 14, 2003 1:37 AM Subject: Re: More on soundboard crown > Hi Ron, > > > >>In a rib crowned and rib supported board, maybe 95%-100% of the > stiffness > > >>comes from the ribs. In a compression crowned board, probably somewhat > > >>over 120% of the stiffness comes from the panel, since the ribs supply > > >>negative stiffness and crown support. A rib crowned but panel supported > > >>board is somewhere above 0%, and under 100%. > > > > > >I'm sorry but I am not swallowing this one. This is very misleading. If > > >this were true a strip of cross grain soundboard panel say 5" wide and > 30" > > >long with a rib glued on using the panel crowning method would have the > > >same stiffness (or less) than the panel alone. This is just not true. > > > > Of course it's not true, and I said no such thing. A compression crowned > > assembly's panel is already supporting whatever load is required to bend > > the ribs from straight to crowned before a gram of string bearing load is > > ever applied. Therefore a panel in a panel crowned board under string > > bearing load is supplying over 100% of the spring resistance necessary to > > provide what we'd call stiffness in the assembly. That's not a theory, > > that's a fact. The bent rib is a built in pre-load, supplying negative > lift > > - it's trying to pull the panel flat - but the resulting stiffness comes > > entirely from the panel compression. The rib provides no positive spring > > resistance (to string load) of it's own until the board goes concave - > > often soon after stringing. > > I won't pretend that I know even a tiny fraction of what you do about > pianos, but this is a simple matter of physics, of which I am more certain > of my knowledge. You're confusing total force with the rate of change in > force per unit of displacement, the latter being synonymous with "spring > constant" or the more commonly used term here, "stiffness." > > Conceptual experiment: Push your finger against a paper clip, deflecting it > 1 mm. Easy. Let's call that amount of force (applied with your finger) F. > Now deflect it another mm. Still easy. That amount of force is actually > 2*F. Now repeat this experiment, only this time assist your finger with an > enormous leaf spring from a diesel truck, which you will use to deflect the > paperclip by exactly 1 mm. The force now required from your finger to > deflect the paperclip that 1 mm (i.e. no more than it's already deflected) > is zero. Cool. Does that mean the new assembly has no more stiffness? No. > Try deflecting the assembly (the two springs in combination) that second mm. > Good luck. > > The conclusion: Spring constant (stiffness) is additive. Total spring > constant in the above example is that of the paperclip plus that of the leaf > spring. Neither element can contribute more than 100% of the total > stiffness, although the leaf spring certainly provides 99.999999% of it. > > Applying this principle to the compression crowned soundboard, as you > describe it, the panel supports 120% of the total *downbearing* (i.e. > force), and the ribs support -20%. If the soundboard is depressed from its > equilibrium point, the total upwards force of the panel increases. However, > the total downward force of the (now somewhat relaxed) ribs also decreases. > In otherwords, the total upwards force of the ribs is *more positive*. > Thus, the total upward force of the panel/rib assembly increases by > contribution of both the ribs *and* the panel (a larger positive value, plus > a less negative number). In other words, the spring constants for the ribs > and the panel are additive, irrespective of the component forces contributed > by these elements. > > Soooooo.... > > Theoretically, the relative contributions to stiffness from the ribs vs. the > panel would not differ substantially between a rib-crowned and a > compression-crowned board, provided the ribs and panel are of similar > material, dimension, and layout, and provided the edges of both boards are > similarly immobilized by the rim. > > Hope that helps. > > Peace, > Sarah > > PS If it's any consolation, my performance in Freshling Physics was near > top in my class. Loved the stuff! ;-) > > _______________________________________________ > pianotech list info: https://www.moypiano.com/resources/#archives
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