More on soundboard crown

[ranjacob@umich.edu]

This discussion continues to be interesting!

This follows on a response of Ric's yesterday:

--On Tuesday, August 19, 2003 12:02 AM +0200 Richard Brekne 
<Richard.Brekne@grieg.uib.no> wrote:

((Snip))
((.....)) I meant that it is
> the ribs constraint upon the panel that cause the panel to either
> compress or become tensioned depending on what the MC was when the ribs
> were glued on and what it is at any other given time. If RH brings MC
> below that starting point the board becomes tensioned right ?? And when
> RH causes MC to rise above that starting point there will be some
> compression.

My current understanding is somewhat as follows (corrections
welcomed!):

If a rib has a convex curve ("crown") machined into the surface to
be glued, and gluing takes place at, say, 6% MC, the panel (section) 
immediately affected may, or may not, be held in
a condition of significant tension, depending on the radius of the
curve, and on the stiffness of the rib relative to that of the panel in the 
same direction, when the glued assembly gains its mechanical equilibrium at 
6%.  *Assuming* that we can leave
compression set out of the picture for the momentary purposes of
the present argument (and *only* momentarily), then if it is
possible to hold service conditions to 6% and above, it may not
matter whether or not the panel itself has significant tension at
6%.  The rib, as a beam, will, in any case, still be able to support the 
full downbearing load, at the relative rates of stiffening, or yielding, of 
the soundboard assembly and string as opposing springs that the design has 
aimed for.

The convex-surfaced rib, and the glue joint, also "support" the
"crown-shape" of the panel itself at 6%, with no compression,
and possibly also no tension, in the panel itself at 6%. That is, they 
*maintain* the crown-shape in question (and would continue to do so later, 
in the absence of the downbearing, e.g. when restringing).  However, I 
would be inclined to think of this
crown-shape of the panel itself at 6% as *somewhat like* an
arch, anchored at the ends (or a dome anchored at the perimeter).
That is, as the panel fibers take on, and so to speak, "capture",
or "entrap", moisture from 6% toward 12% or above, I visualize
the water molecules as being a little like the stones in an arch,
compressed against one another (though of course not by gravity),
outward, inward, *and upward and downward*.  The upward and  downward 
vectors of these compressive and compression-resisting forces of the 
complexes of water molecules and fiber are what
are crucial here, for the first function of the crown -- i.e.,
the *non-flatness* -- in the panel itself, in the absence of downbearing, 
is to control the responses of the total system to variations, in service, 
in humidity. That is, its first function, in the absence of downbearing, is 
to provide an essential condition for a sort of "baseline" of tuning 
stability.  The harpsichord, as I understand it, was not required to have 
this latter; it was expected to be tuned, to some extent, for each use.

This function has, so to speak, nothing to do with the "support"
of downbearing.  The rib -- as a beam, and not as an "arch", even
in the admittedly odd sort of visualization I used above --
is able to provide this support of downbearing.  The downbearing, that is, 
itself needs to be "supported" in a sort of "baseline" way by the rib, so 
that (to the extent that is possible in practice!) it can be adjusted, as 
necessary, during stringing in order to compensate for the manifold 
conditions of stiffness and rate of stiffening that the installed 
soundboard *assembly* will present to the tuned string set.

((snip))
((...)) ... I just was musing if there was some way of contiving
> a rib that gave crown support, but was a bit less constraining to the
> panels tendancy to expand and contract across the grain.... sort of
> sliding ribs if you get my meaning.
> --
> Richard Brekne
> RPT, N.P.T.F.
> UiB, Bergen, Norway
> mailto:rbrekne@broadpark.no
> http://home.broadpark.no/~rbrekne/ricmain.html
> http://www.hf.uib.no/grieg/personer/cv_RB.html
>

Ric, I sort of thought that was your question, and it's
a very interesting question!  I sincerely think
there's a place for this kind of speculation, and I hope
you don't entirely give it up.

Randy Jacob
University of Michigan Library