[pianotech] Measuring Crown Radius

[David Love]

I know that argument has been made but unless someone can actually show me
how a panel crowned by simply gluing it into the rim without any ribs
attached at a low EMC that causes it to crown up will be structurally more
capable of load bearing (let's put stability aside for a minute) than one in
which ribs are attached and caused to bend by panel compression prior to
gluing it into the piano then I don't buy it.  Because that's the
implication, that the unribbed panel when compression crowned will have
superior load bearing properties to the ribbed panel, or, more reasonably,
that a compression crowned panel with 5 mm tall ribs (let's assume the same
width) rather than 20 mm tall ribs will have more load bearing capacity
because the ribs will contribute less negatively.  

So you're saying that in a flat rib system that uses 4.5% EMC to create
compression to form crown that the ribs not only do nothing but contribute
negatively to load support.  OK so then at 5% and a 200 m radius on the
ribs, do the ribs do anything there?  What about 6% and a 15 m radius on the
ribs?  Even there, there is compression in the panel and some additional
crown formation (at certain times of year quite a bit).  Are you saying
there is some threshold that when crossed the ribs suddenly start doing the
load bearing work but up until that point the don't?  Doesn't make sense to
me.  What does make sense is that different designs rely more or less on the
contribution of rib support and compression and that it's a continuum.  At
one end of the continuum (the first example) the assembly relies more on
compression of the panel than rib support but that is not to say that the
ribs provide zero, or as you argue, negative support.  Just less support.
At the other end of the spectrum one can design a system in which the load
bearing properties of the ribs themselves will be adequate to support the
load even if the panel weren't there--more on that in a minute. 

The limitations of operating on either end of the continuum seem apparent.
If you need the panel to bend the ribs then you have to make the ribs light
enough to be able to be bent adequately by the panel.  That may limit the
amount of load bearing support that they can offer but it doesn't mean that
the support is negative--not once it's glued into the rim.  On the other end
you can produce massive enough ribs that the panel compression or
contribution is an irrelevant factor in your design.  But the danger there
is that you can easily over design the rib scale making the assembly so
massive that you inhibit it's responsiveness. I know, I've done it.  

You mentioned earlier that in part because of the thinning of the ribs at
the ends in a compression board that the ribs don't themselves offer enough
support.  But in the ribs I've measured on CC boards that thinning is
typically to a height of about 6 mm in the last 125 mm or so (proximity to
the rim). The recommendation on RC&S boards that I've read and have executed
has been that the ends of the ribs are thinned to about 3 mm.  If the RC&S
boards rely totally on rib support how does that square with the purported
weakness of CC boards with 6 mm depth in that area.  Further, the
recommendation on the tapering of RC&S ribs has been 1/3, 1/3, 1/3 meaning
(as you know) that only the middle third of the rib is full height and the
tapering starts from that point.  Thus, the RC&S rib actually has less depth
and at a point farther away from the rim where the proximity increases the
effective load bearing capacity.  For me the comparison of CC and RC&S
boards as if they are two completely separate entities leaves many
unanswered questions.    

With respect to the discussion of analyzing rib scales on compression
crowned boards I think it does have merit.  You find when comparing the same
model piano that the ribs scales vary.  Some are stronger than others.
While it's difficult to tease out all other variables when comparing tonal
output it's not unreasonable to assume that there will be differences that
can be attributed to the differences in rib scales.  Some rib scales on
compression crowned pianos seem more up to the task than others.  Some of
them have areas of strength as well as areas of weakness and you can see
that when you analyze their load bearing capacity individually.  It may be
interesting to note that I often find that the rib scale dimensions in the
killer octave section of CC pianos seem to be somewhat underbuilt.  Does
that mean that the ribs were made a bit less tall in that area in the belief
that the formation of crown was paramount and that the load bearing capacity
of the rib itself was secondary?  

When you come across compression crowned pianos that are still working and
yet show some of panel damage (and they do exist) to what do you attribute
that--simply less damage?  Or might the rib scales play a role.  I'm
inclined to think that the later point, though it may not tell the whole
story, is one worth considering.  

Look, I'm indebted to Del and Nick G. and others (you included) for the
notion of questioning assumptions.  But that also has to include new
assumptions derived from the questioning of those original assumptions.  In
my mind, there remain many unanswered questions (I'm willing to accept that
could just be my mind).  But it's all good.  My current view is that the
difference between pure CC boards (flat ribbed type) and RC&S boards is not
one of kind but of degree and the key component in making them similar in
kind is the point at which the ribs (and panel) are glued into the rim.  

Forgive any typos or omissions, this went out kind of fast.    


David Love
www.davidlovepianos.com


-----Original Message-----
From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On Behalf
Of Ron Nossaman
Sent: Tuesday, July 12, 2011 8:37 PM
To: pianotech at ptg.org
Subject: Re: [pianotech] Measuring Crown Radius

On 7/12/2011 10:02 PM, David Love wrote:
> Just one point for now, so you're saying that the rib in a compression
> system offers nothing as a functional supporting member?

Yes I am. It supplies something for the expanding panel to pry against 
to provide crown and stiffness. It resists crown, and is functionally 
negative in beam support. The expanding panel has to not only bend the 
flat ribs into a crown, but support string bearing as well.


>Why?  So let's
> assume a rib in that system is glued to a panel at 4.5% EMC.  At that
level
> you say it's not a functional supporting member.  So then when does it
> become a functional supporting member?

It doesn't, ever. That's why I said that.


>At 5%, 6%, 7%?  Are you saying it's
> only a supporting member if it's crowned and glued to panel at 6% or
higher?

No, it's only offering structural beam support if it's directly 
supporting load, as in a RC or RC&S assembly. CC ribs don't directly 
support load.


> That doesn't make sense.  A beam is a beam whether it's crowned or not.

Yes, it makes sense. Think about it. It's not the crown, it's the 
direction of load.


> It's relative strength may be influenced some be crowning (don't know
about
> that), by tapering at the ends (a feature that ribs in RC&S boards also
> have) but it still functions as a beam.

Yes, but not as a load support beam. The panel is doing the work, and 
the CC rib is adding to the panel's load as the panel forces the flat 
rib into a crown. The force on a CC board rib is reversed from that on 
RC and RC&S ribs. It's still a beam, It's just not doing a thing to 
support crown and bearing other than constraining the panel. It's 
actually trying to pull the crown flat. This is the fundamental 
difference between CC and RC(&S) boards, which is why I say I find rib 
analysis of a CC board to be of no use to me. The ribs aren't supporting 
the load, so their dimensions don't tell me anything useful.

RC&S ribs (at least mine) are built as structural beams to support crown 
under bearing load as if the panel wasn't even there.

Ron N