of spline and catenary

[Farrell]

No answers for you Ron, but a confirmation. When I was trying to figure out
how to form the various arcs for my rib-to-panel clamps, I took a piece of
one-inch square aluminum tube and bent it as you describe below. I used
aluminum because I know no piece of wood will be perfectly (or even nearly
so) consistent in its composition, and thus bending properties, along a
length (aluminum will have more consistent properties throughout). I was
disappointed right at the get-go when I observed that indeed the curvature
was tighter in the center and tapered out to almost no bend at the ends.
What I ended up doing was every several inches along the curve I measured
and forced the aluminum section into the desired curve.

But your question remains unanswered: just what kind of curve results from
this bending technique, and what are the implications of ribs with such a
curvature?

Terry Farrell

----- Original Message ----- 
From: "Ron Nossaman" <RNossaman@cox.net>
To: "Pianotech" <pianotech@ptg.org>

> I did something similar here, only without the clamped end and distributed
> load examples. What I was wondering is what curve was described when you
> bent a piece of uniform cross section wood. There doesn't seem to be a
name
> for it. The rebuilders who are cutting rib crown in a jig which clamps the
> center of the rib, wedging the ends out to form the curve are obviously
not
> cutting a constant radius curve in their ribs. As far as I know, this is
> neither good, nor bad. It just is. But what is this curve?  It's close to
a
> catenary, but flatter at the ends. As this rib is cut by the table saw,
> these flatter curves at the end will tend to spring and bend more as wood
> is cut away, changing the saw cut line and producing a crown more nearly
> parabolic or catenary than was the case before the cut was taken. The
> bending response of the rib changing as the cut is made also means that
the
> crown profile will be asymmetric because half of the crown will be cut
from
> the outside to the center, and half from the center out - unless the cut
is
> done in two passes, with a bulk removal pass, and a light final pass.
>
> I'm just trying to figure out approximately what is actually being
produced
> here.
>
> Ron N