[pianotech] crown and radius and load

[William Truitt]

Hi Ron:

I'm trying to get a better handle on rib feathering and Japanese bows
(kyudo).  If anyone is interested, you can go to
http://kyudo.com/kyudo-t.html and see an animation of HASSETSU, the steps of
shooting the bow.  I think in part what Ron is referring to is the
asymmetrical construction of the bow, which is very long.  The arrow is held
and fired from a position at about 1/3 the length of the bow, and the shape
of the bow corresponds to that.

You are referencing the assymetrical feathering of the rib when you refer to
the kyudo, is there something more that you are referring to obliquely?
Master Po?

Today I made a point of looking at the relationships of the bridge and the
ribs on my Steinway A.  I positioned all the ribs into their notches in the
rim and belly rail.  There are 12 ribs which, though they have been
re-proportioned in height and width, will be relocated in the same
positions. I do not have a treble fish or bass cut-off.   I intend to third
my ribs (although not all thirds may be equal), with a straight taper at the
ends. I positioned the bridge in place on top of the ribs with my indexing
jigs, and traced with pencil the location of the bridge along the length of
each rib.  I also made a pencil mark on each side of the rib at both ends,
where the rib contacts the edge of the rim.  All measurements I took
reference the respective outer edge of the bridge to panel contacting
surface to the shortest side of the rim or belly rail.   

I took a look at the original ribs today.  Rib 12 has a bridge contacting
surface width of 27 mm., as does 11, with 10 having a contacting surface of
29 mm.  The distance from the belly rail edge to the outer edge of the
bridge on 12 is 54 mm, and the distance from the outer edge of the bridge to
the rim is 198 mm.  This means that the rim side of the 12 rib is 3.67 times
longer than the belly rail side.  Values for rib 11 are 89 and 251, so the
rim side is 2.82 times longer than the belly rail side.  Rib #10 is 148 and
271 mm., and the ratio is 1.83 to 1.  

How did Steinway address this in 1909?  They scooped the ribs on the belly
rail side and had a longer taper on the rim side.  Rib 12 is starts its
scoop at 48 mm. from the belly rail, which is just past the outer edge of
the bridge in relation.  The backside starts its taper at 120 mm.  The ratio
is 2.5 to 1.  Rib 11 is 70 mm. and 130 mm respectively, with a ratio of 1.85
to 1.  Rib 10 is 90 mm. and 123 mm., and the ratio is 1.37 to 1.

So Steinway addressed this by tapering the ribs asymmetrically to correspond
to the longer-shorter relationships of the bridge location front and back,
but it is not directly proportional - rib 12 is 3.67 ratio for lengths, and
2.5 ratio for tapering.  The ratio between the two is 1.47 to 1.  Rib 11 is
2.82 and 1.85, for a ratio of 1.52 to 1.  Rib 10 is 1.83 and 1.37, for a
ratio of 1.33 to 1.  

I do wonder if there was any kind of formula applied by Steinway to
determine where to begin the tapering on these ribs with such uneven end
lengths.  

My present thinking for these three ribs is to start my tapering on the
belly rail side at approximately the same location as Steinway began its
scooping.  The difference will be that I would be using a straight taper.

On the rim side I am less clear as to an appropriate place to begin the
taper.  I am thinking of taking the distance from the back side of the
contacting surface of the bridge to the rim edge, halving it, and starting
my taper there.  

For those of you who have a lot of experience doing this, I would be
interested in how you work these details out.  Thanks,

Will Truitt

   

-----Original Message-----
From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On Behalf
Of Ron Nossaman
Sent: Monday, June 15, 2009 6:18 PM
To: pianotech at ptg.org
Subject: Re: [pianotech] crown and radius and load

Gene Nelson wrote:
> 
> In reference to the attached illisturation:
> Assume the dimensions width and height at the center of the rib were 
> used to help calculate - lets say a 60 pound load from string 
> downbearing - throw in deflection as well.
> If the bridge placement is shifted three or four divisions to the right 
> of center - would these load supporting characteristics of the rib be 
> altered? 

Not a lot.


>If so is it worth altering the W & H dimensions at the offset 
> bridge location? Am I splitting hairs?
> Gene

I'd not worry about the W & H once you've calculated them to 
your load, and just make the feathering a little shorter on 
one side, and a little longer on the other. Ever see anyone 
shoot a Japanese bow?
Ron N