More on soundboard crown

[Farrell]

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!  ;-)
> 
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