[pianotech] GH-1s

[David Love]

First, having a cut-off or no cut-off is really of no consequence in terms
of load bearing capacity.  A longer rib will have a larger cross section to
compensate for its length.  Simple enough.  A cut-off, especially a large
one, does have acoustic consequences but that is something different and I'm
willing to call that a matter of taste for the time being.  

Feathering the beam certainly reduces the strength of the beam.  But gluing
a panel on top, securing it around the rim and gluing a bridge on top of
that adds to the strength.  Before we can determine how far apart our
calculations are we need a bit more data.  First, what is the load per rib
that we are using from which we make our calculations.  Second, how much
deflection are we targeting per rib.  Third, how much crown do we start with
which might impact how much deflection we are targeting if we are using a
percentage of crown.  Fourth, what other criteria aside from spring rate are
we using in our analysis.  Once established we can more easily do a side by
side comparison.  As I mentioned, I'm not sure I want to delve into all the
details of that at this point--not quite ready to give it all up.  Of
course, anyone can figure out that sin radians(1.5)*35,000 (or whatever your
string tension is) = about 900 lbs. Distribute that over 12 - 14 ribs or
whatever you have and you have rough load per rib. After that it gets
trickier to describe without going into greater detail, but suffice it to
say that I think it's likely that my rib scales are lighter by virtue of
different beam formulas in use and by what I understand about what it is
that you advocate and from having built some assemblies myself that, in my
view, were too heavy.  

I can say that when the boards I'm building are fully loaded they react
pretty much as predicted losing about half the crown and half the preset
bearing.  Ultimately, however, the sound of the piano tells you a lot in
terms of how heavy the rib scale is.  You can hear it.  If possible,
modifications are then done to the bearing in order to tweak the impedance
by adjusting nose bolts or perimeter bolts.  These modifications, if they
occur, are generally very minor.  If they need to move a lot then I probably
would reexamine some things for the next project.  That might include rib
scale, panel thickness, feathering, bridge dimensions...  

I recognize that tonal goals may vary and that might well alter the design
concepts. Of course, the board has to support the load without going
negative and I have not had that problem in anything I've built so far where
I've followed my current guidelines.  While I do have an opinion about what
sound I like or don't like as it relates to design issues, I fully accept
that there are those whose tastes may differ.  That's why they make
chocolate and vanilla.  But the range of acceptable to me is relatively
narrow and is largely driven by scale differences and not the narrow window
of how the board should be set up given a particular scale.  It is narrower
than I might have thought when I first started all this.  There's no
question you can tweak these designs forever and even then you will always
have (hopefully) small surprises that require some minor tweaking.  I accept
that as the limitations of organic materials predictability.  But my general
design target is getting smaller and smaller and the focus on not too heavy
doesn't by any means take a back seat to not too light.      

David Love
www.davidlovepianos.com


This is where I was going. These calculations are done with full section
simple beams. After feathering, a fair bit of strength is given up. I did
some calculations and deflection tests years back that indicated around a
16% loss of strength. Calculated with simple ends, this loss is fairly
closely cancelled by gluing the final rib form into the rim, and what small
panel compression that exists also compensates. So my conclusion was and is
that the simple end full section calculation ends up being pretty close to
the reality after it's built. A fixed end calculation showing a beam of some
specific dimensions to be four times stiffer (however you care to describe
it) under a given load than a simple end formula produces a beam of 1/4 the
stiffness of a simple end calculation to produce a given deflection under a
given load. That means to me that, since I've verified to my satisfaction
the similarity to the real world of the simple end calculations after
feathering and assembly, that a fixed end calculation will produce a rib
that, after feathering, will be considerably weaker than the calculations
indicate. That is, unless there is some surprise secret windage compensation
(perhaps a factor of four?) that hasn't been mentioned just yet. Include a
low crown and a 1°+ bearing load on long ribs with no cutoff, and the
numbers say it doesn't work and won't support that kind of load at those
deflections without being stiffer than is claimed. So I'm wondering how this
works.


Ron N