[pianotech] GH-1s

[Ron Nossaman]

On 12/20/2012 1:03 PM, David Love wrote:
> First, having a cut-off or no cut-off is really of no consequence in terms
> of load bearing capacity.  A longer rib will have a larger cross section to
> compensate for its length.  Simple enough.

The cutoff makes the rib effectively stiffer while it actually reduces 
the mass of the rib. A smaller cross section, shorter, lighter rib with 
a cutoff will support the weight of a bigger, heavier, longer rib 
without one. Similar strength with less material. Simple.


>A cut-off, especially a large
> one, does have acoustic consequences but that is something different and I'm
> willing to call that a matter of taste for the time being.

That's big of you, but we're talking about real physical structure here 
rather than your subjective evaluation of tonal consequences, which I've 
already read at great length.


> As I mentioned, I'm not sure I want to delve into all the
> details of that at this point--not quite ready to give it all up.

I think most of your secrets are safe.

So let's try a rib out of a S&S B, so we'll have something from some 
semblance of the real world though that won't affect the math much.

I've got a rib of 1090 mm length, which my addition of a cutoff reduced 
to 770mm. I added ribs to the original, so in this case the string load 
on this rib would come to about 25 lbs at the 1° bearing you like. The 
original, having fewer ribs, would have a bigger load on this rib, but 
this will serve for illustration.

Let's see what the deflections are.

With a 25 lb load, and a 770mm long rib:
  20mm wide, and 26mm tall deflects 3.34mm
  18mm wide, and 24mm tall deflects 4.71mm
  16mm wide, and 25mm tall deflects 6.88mm

Crown heights 770mm rib:

@12M= 6.18
@9M= 8.24
@7.5M= 9.89

What you have left in crown depends on what you started with.

With a 25 lb load, and the original 1090mm long rib:
  20mm wide, and 26mm tall deflects 9.46mm
  18mm wide, and 24mm tall deflects 13.37mm
  16mm wide, and 25mm tall deflects 19.52mm

Without the cutoff, the long rib deflects about three times what the 
shortened one does.

Crown heights 1090mm rib:

@16M= 9.28mm
@12M= 12.38mm


So with the cutoff, you can get about 50% deflection (if that's your 
goal) any number of ways by matching crown height from different radii 
with rib dimensions. But half of an arbitrary radius is a useless 
measure without some real indicator of stiffness, and these ribs are of 
considerably different stiffness. That's what spring rate is for. Once 
you make a map of what you'd like to see in rib stiffness in different 
parts of the scale, the crowns and deflections can be worked out to make 
it work. The stiffness is what makes it work, not the remaining 
percentage of an arbitrary crown.

I'd probably size the rib at 770mm x 20W x 26H, and a 9M radius.

Without another chorus of the dangers inherent in making ribs too stiff, 
what numbers would you put on the rib dimensions, showing the figures 
from your deflection formula. I expect you'd use the original length, 
right?

Ron N