rib crowning

[Ron Nossaman]

>Greetings list members,
>    I am in the process of learning how to go about pre-crowning ribs
>for use in a new soundboard installation. I have seen at least one jig
>which seems to cut the rib with the crown directly in the center of the
>rib which will not necessarily be under the bridge. As I understand it
>it makes the most sense, at least to me, to have the thickest part of
>the rib directly under the bridge for the maximum support. Am I correct
>in assuming (Ooo there's that word again) that a different degree of
>taper exists from one side of the bridge to the rim than the other?  Am
>I correct in noting that the rib thickness at 3 inches from the bridge
>on either side would not necessarily be the same? If this is the case
>(on a middle rib for examples sake) then how does one go about laying
>out an even taper but with different degrees on either side? Does any of
>this make any sense at all? Am I even on the right track?
>
>--
>Greg Newell


Greg,
Good observation. Here are a few more for you. With a constant radius
crown, the high point will always be in the center of the rib because the
crown is an arc segment. A crown curve based on a parabola or catenary
curve will let you put the high part of the crown anywhere you want it, if
you want to go to the trouble. I'm not sure it's necessary. The old
compression crowned boards had a crown that was whatever the panel
expansion happened to bend the rib into, and was anything but constant
radius through the feathered ends of the ribs, or from rib to rib for that
matter. Some of them sound pretty good. In a rib crowned board, you can
build the crown and load handling characteristics you want. Looking at a
rib like a beam under concentrated load(s), you can move the load center
somewhere other than the center of the beam with the feathering, which
doesn't have to be symmetrical. The best way to see how different
feathering configurations and proportions work is to make up some small
scale model ribs out of scrap pine or something, try different feathering
approaches under different loading points on the rib, and observe the way
they bend under load at that point. Go with the approach that produces the
deflection action you think you want, and remember anything else
interesting you discover along the way for future prospecting potential.
The rib scale will be different on every model piano, so there will always
be a series of decisions to be made in the process.

Ron N