[pianotech] crown and radius

[Ron Nossaman]

Gene Nelson wrote:

>> Regarding the cutting of the radii in the ribs, forget about where the 
>> high point will be.  That is irelevent to the arc of the ribs.  The 
>> only concern in cutting the ribs is at what point will the rib be at 
>> its thickest, once the arc is cut.
> 
> *** I had been assuming that the high point and the thickest part of the 
> rib are one and the same.

Not necessarily. The center of load support of the rib is what 
you should be talking about, and it can be moved to where you 
want it by asymmetric feathering, and tapering. I was very 
careful to describe what I was saying based on what you called 
it. And what I described is still geometric fact.


> *** Maybe one difference is that a rib is glued to the board.
> I think that a good part of the spport of string downbearing on bridge 
> and rib comes from the glue joint of the rib as there is not much rib 
> leftover to anchor into the rim. The rib ends are tapered quite a bit.

I don't think there's much structural support there, and 
wouldn't count on it. The ribs can support a terrific load all 
by themselves if they're feathered to do it. Put one of those 
third/third/third straight taper feathered ribs on end blocks 
and center load it. It'll bend like a bow, with a nice even 
distribution of stress throughout. Do the same with a 
conventionally feathered rib and observe how ill suited it is 
as a structural beam. I've torn down plenty of lousy sounding 
pianos to find a soundboard that seemed to show a decent crown 
once the strings were off. But when I knock the board out, is 
goes flat, or concave. The rib ends, I presume, were levering 
up an illusion of crown, but it certainly wasn't enough to 
function under string bearing load.


> For the most part with exception of the treble, lo-bass the bridge is 
> centered on the ribs. Also, the high point or thickest part of the ribs 
> is also under the bridge to the extent possible. 

That would certainly follow, since you centered the ribs under 
the bridge.


>The bass and low tenor 
> bridges straddle the high point or thickest part of the lowest 4 ribs. 
> Rib #1 - lowest bass has the high point quite a bit offset from center 
> of rib. I do not understany why would I want to support a known string 
> bearing load with something less than the thickest part of the rib as 
> that was the dimension used to calclate load bearing?

No one has argued that in any way. You were talking about the 
high point, not the thickest. Had you said "thickest" we'd 
have been done some time ago.

Ron N