Rib dimensions

[Sarah Fox]

Hi all,

Another method would be to clamp one end of the rib to a flat surface and
let the other end stick up.  While this may not sound much like the more
familiar crown depth, the free end would stick up much more than the
underside of an arch -- and would therefore be measurable with more
accuracy.  Using this technique,

Let:

h = height of free end of rib from flat surface
s = distance from clamped end to point on table just beneath free end
L = length of rib, measured in an arc
r = radius of curvature of rib

(Note that for a small angle of curvature, L and s are approximately the
same and can be substituted for each other.)

Then:

r = 180 L / ( 2 pi ArcSin (2 h s / (s^2 + h^2))),

where the ArcSin is in degrees (which y'all probably prefer).

The derivation is somewhat long-ish, so I'll forgo diagramming and typing
it!

For instance, if the end of a 4 ft rib pops up 1/2", which would be .0417 ft
<groan...  I hate imperial>, then

h = .0417 ft
s = L = 4 ft

r = 180 * 4 / ( 2 * 3.1416 * ArcSin (2 * .0417 * 4 / (4^2 + .0417^2)))
 = 180 * 4 / ( 2 * 3.1416 * ArcSin (2 * .0417 * 4 / (4^2 + .0417^2)))
 = 180 * 4 / ( 2 * 3.1416 * ArcSin (2 * .0417 * 4 / 16.002))
 = 180 * 4 / ( 2 * 3.1416 * ArcSin .0208)
 = 180 * 4 / ( 2 * 3.1416 * 1.195)
 = 180 * 4 / 7.506
 = 95.9 ft radius




----- Original Message ----- 
From: "Richard Brekne" <Richard.Brekne@grieg.uib.no>
To: "Pianotech" <pianotech@ptg.org>
Sent: Wednesday, December 10, 2003 7:31 PM
Subject: Re: Rib dimensions


>
>
> Ron Nossaman wrote:
>
> >
> >
> > radius=(4*crownheight^2+riblength^2)/(8*crownheight)
> >
> > I think that's got it.
> >
> > Ron N
> >
>
  ------------------------------------------------------------------------
> >
> > -
>
> Would you define crownheight for me in the above.... cant seem to get this
to
> add up.
>
> Thanks
> RicB
>
> --
> Richard Brekne
> RPT, N.P.T.F.
> UiB, Bergen, Norway
> mailto:rbrekne@broadpark.no
> http://home.broadpark.no/~rbrekne/ricmain.html
> http://www.hf.uib.no/grieg/personer/cv_RB.html
>
>
> _______________________________________________
> pianotech list info: https://www.moypiano.com/resources/#archives