There is another issue to be raised. How should one match the scale
tensions and anticipated downbearing angles to the rib scale. There are
choices to be made. I presume that you want a certain amount of deflection
of the soundboard assembly and that given a certain scale with a certain
downbearing load, you can calculate the panel assembly stiffness and preset
crown (in and RC&S board) to achieve that amount of deflection. But there
are yet various ways to achieve that amount of deflection. For a given
assembly you could increase the scale tension and lower the downbearing
angle or decrease the scale tension and increase the downbearing angle. You
can design an assembly with greater stiffness to go with a lower scale and
greater downbearing or a lower stiffness to go with a higher scale and less
downbearing, for example. Each combination, I presume, will produce its own
unique tonal characteristics and, probably, require a hammer of different
density and/or mass. Those of you who are designing boards, how would you
characterize your goals and why?. If we can produce a RC&S board that will
be able to accommodate any particular variation in load, what is so magical
about the .5 - 1.5 degrees of downbearing that seems like it came about
mostly due to the limitations of compression crowning. Further, in an RC&S
board, what combination is most likely to give the general tonal
characteristics of your successful CC board. And let's allow ourselves to
speculate even if we haven't actually built each variation.
David Love
davidlovepianos@comcast.net
-----Original Message-----
From: pianotech-bounces@ptg.org [mailto:pianotech-bounces@ptg.org] On Behalf
Of Overs Pianos
Sent: Sunday, February 19, 2006 3:15 PM
To: Pianotech List
Subject: Re: laminated ribs
Richard,
The downbearing (vector) force on the sound board
is equal to the SIN of the angle of deflection
times the string tension.
If there was absolutely no down bearing angle, it
follows that there would be no downbearing force.
The SIN of zero is zero so the string tension
vector component force would be zero.
If the down bearing angle was 90 degrees, with
the speaking length segment parallel to the board
and the back scale heading vertically downwards,
the down bearing force would be equal to the
string tension, ie. the speaking length segment
would be contributing nothing to the down bearing
force, while the back scale segment would be
contributing its full string tension. The SIN of
90 equals 1.0. String tension X 1.0 equals string
tension. You can see how it all works.
So if you have 160 lbs unison string tension with
a downbearing angle of 2 degrees, the downbearing
vector force for this unison string would be;
Downbearing = 160*Sin2.0
Downbearing =5.583 lbs
The downbearing force for the whole note would be
3 X 5.583 if the note was a trichord, at 16.75 lb.
If you are using an excel spreadsheet for your
calculations, remember that the downbearing angle
will need to be converted to radians.
Yes, there is a large variation in what people
believe is an appropriate level of downbearing.
If you measure a few pianos around the place
you'll find that there is a lot of variation in
the downbearing angle also.
The 2 degree figure you quoted I would consider
to be too high for a real world piano.
Bösendorfer have typically set their pianos with
angles approaching 2 degrees strung. This is a
little higher than I would feel comfortable with.
When Ron N was here a couple of years ago we
looked at our no. 5 with a Lowel gauge and it
measured almost right on 1.3 degrees over the
whole piano. This yields a total downbearing
force on our no. 5 of 427 Kg (941 lb). I wouldn't
recommend these figures for an older or weaker
panel but it works just fine for our I-rib
design. Setting the downbearing angle is a
balancing act between how much the board will
sink and how much force we wish to apply.
When looking at a given piano, I suggest that you
set up a spreadsheet to calculate the downbearing
force you are planning to set up per rib. Note
also that setting an unstrung angle of say 1.5
degrees won't result in a downbearing force of
tension X SIN(1.5). Its the resultant string
deflection angle when the piano is at pitch and
the board has stabilised (sunken to equilibrium)
under load which will determine the actual
downbearing force. So you need to make an
educated prediction on how much a board will sink
under tension to get an idea of the resultant
downbearing force.
A common scenario with new pianos is for techs to
measure a down bearing figure which on the face
of it looks OK, but very often the sound board
has sunken to a state where it is pushed almost
completely flat by the down bearing angle which
was set into the piano. In these instances the
board is too weak for downbearing loads which are
being applied or the unstrung angle wasn't set
properly. Either the downbearing unstrung angle
should be reduced or the board strengthened to
withstand the setting angles to which it is being
asked to resist. So often technicians will look
at a sound board and declare that it is fine
because the downbearing angle measures some
wonderful figure. But if the board has been
pushed inside out before the customer's ink is
dry on the cheque, things ain't too good,
regardless of what the downbearing gauge might
indicate.
Get an accurate downbearing gauge and a thread
length for looking at crown, and measure a few
pianos old and new. You'll develop a picture of
what's happening.
Ron O.
>Please correct if this is entirely wrong... but
>I thought that since the string was being
>measured in terms of its tension (pounds) one
>could simply the problem as a like sided
>triangle with half the pounds on each leg. Since
>the measurement is taken in the deflected
>condition... you have basically the hypotenus
>and all angels of a right angle triangle
>available to figure the amound of deflection..
>pounds in this case. So 160 pounds with a 2
>degree deflection at the bridge yields
>
>Sin 1 x 80 = 1.396192515 lbs downbearing,
>which is 1.745 % of the string tension.
>
>er... yes ??
>
>RicB
>
>
>-------------
>> So knowing all of the above, what is the equation that will calculate
>> an approximate string bearing load under the conditions I describe?
>
>Beats me. I use the SIN(RADIANS(degree measurement))*tension
>per unison, and add them up in my spreadsheet.
>_______________________________________________
>Pianotech list info: https://www.moypiano.com/resources/#archives
--
OVERS PIANOS - SYDNEY
Grand Piano Manufacturers
_______________________
Web http://overspianos.com.au
mailto:ron@overspianos.com.au
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