evaluating sdbd. crown & bridge downbearings in a new piano

[John Hartman]

Ron,

I am not surprised that Richard was a little confused by the two figures
you used, I was also. I did a little digging and may have solved the
mystery. BTW I checked your figures and they worked fine in relation to
my more rudimentary methods. That is, your methods are suitably accurate
but a little confusing to those less versed in engineering. 

Finding the angle as you did really stumped me, I would usually rely on
the more conventional formula. The sin of halve the angle = ½ the rib
length divided be the radius. Look this figure up in a table of
trigonometric functions. The inclusive angle is twice this angle. The
use of the number 57.29578 in your method is a sort of quick cheat for
finding the angles of long thin triangles. 57.29578 is the cotangent of
1 degree. It is a clever method and apparently yields accurate results
if the angles are small. If the rib was as long as the radius the angle
would be 57.29 degrees instead of the expected 60 degrees.

The other number, .01745 is two times pi divided by 360. This is not  a
cheat but simply a short hand method. The long version is two times pi
times the angle divided by 360.  The root of your equation was .01745
times the angle.

I don't have time right now but maybe you can find the force necessary
to bend a typical  uncrowned 2' rib  to a 60' radius. Simply apply the
force the center of the rib's length. To make it fare you should also
scallop the ribs as typically found. I would like to do a little
figuring to fine how much force the panel has to exert to form the
crown. I think this would be pretty simple and would give us some idea
how much of the plastic limit (580 psi) the panel crowned process uses
up.

I would prefer to call it panel crowned instead of compression crowned.

John Hartman