More on soundboard crown

[Ron Nossaman]

>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