More on soundboard crown

[Sarah Fox]

Hi Ron,

Put that way, I understand what you were arguing.  You were talking about
support of string bearing (spring force and/or "stiffness" of support), and
John was talking about resistance to deformation (spring constant and/or
overall "stiffness" of the spring system).  Unfortunately the terminology
was similar enough and the principles different enough as to result in a
misunderstanding.

Peace,
Sarah

PS  I do prefer the idea of a mosquito vs. a Concord, since I've always
thought the Concord somewhat resembles a monstrous mosquito.  ;-)


----- Original Message ----- 
From: "Ron Nossaman" <RNossaman@cox.net>
To: "Pianotech" <pianotech@ptg.org>
Sent: Thursday, August 14, 2003 11:15 AM
Subject: Re: More on soundboard crown


>
> >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.
>
> Hi Sarah,
> Yes, I do understand both the principal and the logic. Run your conceptual
> experiment with a more representative set of springs. The rib isn't a
truck
> spring. It's another paper clip. Clip#1 is the rib, pushing down, clip#2
is
> the panel compression levering the rib up. The spring rate of clip#2 is,
> indeed, slightly higher than #1, but not by tens of thousands. Now add a
> third clip. Clip#3 represents the string bearing. It is pushing in the
same
> direction as clip#1. To maintain relative position, clip#2 (the panel)
must
> balance the force of clips#1, and #3. That's compression crowned. In the
> rib crowned spring simulation (same cast of paper clip springs), both
> clip#1 (rib) and clip#2 (panel compression) are opposing clip#3 (bearing).
>
> I realize nothing can produce over 100% of what it can produce. The
> question I was answering about which (panel or rib) contributes more to
the
> stiffness in a rib crowned, vs a panel crowned board. In that context, the
> panel in a panel crowned board contributes more than 100% of the spring
> resistance necessary to support string bearing because it has to lift the
> spring resistance of the rib as well.
>
> Ron N
>
> _______________________________________________
> pianotech list info: https://www.moypiano.com/resources/#archives