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! ;-)
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