More on soundboard crown

[Delwin D Fandrich]

----- Original Message -----
From: "Calin Tantareanu" <dnu@fx.ro>
To: "Pianotech" <pianotech@ptg.org>
Sent: August 13, 2003 1:54 PM
Subject: Re: More on soundboard crown


> > You can't leave the ribs out of the discussion. They are integral. And
> > we've been over the "arch" question numerous times, both on this list
and
> > in the Journal.
>
> What happens in the case of a compression crowned board?
> I think that there, the ribs tend to pull the boards down (because they
are
> straight to begin with, and then bent upwards by the board that forms the
> crown by gaining moisture and expanding).

That is correct.


>
> I would say that in this case the board works in a way resembling an
arch,
> because the it expands upwards due to a lateral force, not a vertical
one,
> or?

The structural arch works by virtue of being made of a non-compressible
material such as stone, concrete, etc. It is buttressed by an immovable
support on either end. When loaded, it supports the load because of the
non-compressible nature of the arch. The soundboard panel is made of wood
which is far from non-compressible. Even longitudinally. M&H makes much of
their little demo showing how their spider is supposed to support crown.
What they don't mention is that it takes only light finger pressure to
flatten the piece out. Nor do they mention that if they leave the piece in
place for any period of time, say a month or two, the crown disappears.
Wood, at least given the crown radii typical to the piano, is not rigid
enough to function as a structural arch.


>
> In a rib-crowned board, things get complicated and it seems obvious that
the
> ribs provide most of the stiffness.

It does not. For the same reasons given above.


>
> > > How significant is the stiffness added by the crown?
> >
> > Very.
>
> Sorry, I meant to ask how significant is the stiffness added by the board
> (not ribs) in a rib crowned soundboard..

Not vary.


>
> Del said he considers the panel neutral when calculating the stiffness.
Does
> that mean it provides (theoretically) zero stiffness?

It does provide some stiffness, but the amount is relatively insignificant
(compared to that of the rib set). The amount of stiffness contributed will
obviously vary with fluctuations in the moisture content of the wood. We
rib our boards at 6.5% MC. Once completed if the relative humidity of the
room in which the piano resides goes up and the soundboard panel takes on
more moisture even these boards will begin to contribute something to the
overall stiffness of the system. It still won't be much, however.



> Do you think that a panel, wether crowned or not, behaves in the same way
> regarding stiffness?

What do you mean when you say, "whether crowned or not...?" The soundboard
panel, by itself, is not crowned. It is only when it is affixed to ribs
that it becomes crowned. It is not like a violin in which the shape of the
soundboard is carved and shaped from a solid piece of wood. In good
violins, anyway.


>
> > > 3. Crown is a way for dealing with the expansion/contraction of the
wooden
> > > panel in a predictable way.
> >
> > Where did this idea come from? It does nothing of the kind.
>
> I understood that compression crowned boards don't always expand upwards
> only, they can also form some sort of S-shape, reverse crown, or
whatever.
> That's why I think that crowning the ribs would ensure that the
soundboard
> moves into one direction only.

That is a whole other issue. I wrote about this in one of my Journal
articles. You might want to dig them out and look at the included sketch.


>
> > > 2. What is the difference between making a board (for the same piano)
with:
> > >  a. Thick board with thin ribs,
> > >  b. Thin board with thicker ribs.
> > > For both cases, let's assume that the boards are designed to
withstand the
> > > same pressure from strings and to provide the same stiffness.
> >
> > This is a complex question that cannot be easily answered within the
scope
> > of something like this list. At least not by me. In general, the thick
> > soundboard assembly with thin ribs will have more mass, the thin
soundboard
> > assembly with thick ribs will have less mass. You can get a general
answer
> > by remembering that impedance is frequency dependent and is generally
> > mass-dependent above system resonance and generally spring-dependent
below
> > resonance. To tell where this resonance (resonances, actually) are
would
> > require building and measuring samples.
>
> Any idea on how this influences the piano's tone?
> Are any books on this subject available?

Not specifically. You might check the Five Lectures. Richard Brekne has
given the web site addresse several times on the list. A general (though
somewhat elementary) text is the "Fundamentals of Musical Acoustics by
Arthur H Benade, Oxford University Press, 1976. This is available from
Amazon.com. As is "The Physics of Musical Instruments" by Neville H
Fletcher & Thomas D Rossing, Springer-Verlog, 1991.

Del