Killer Octave Question

[Farrell]

Del or you or someone also wrote a while back some examples of how much a rim might commonly move by every-day events - like someone leaning against it, or the size change caused by a humidity change. As I recall these movements easily were greater than the change in rib length between curved and straight. Any recollection of this?

I readily see that the case does not maintain the soundboard crown - the crown is from curved ribs and/or panel compression. But could a spreading rim tend to flatten the soundboard (like the Chris Robinson experiment)?

Terry Farrell
  
----- Original Message ----- 
From: "Ron Nossaman" <RNossaman@cox.net>
To: "Pianotech" <pianotech@ptg.org>
Sent: Thursday, April 10, 2003 11:50 PM
Subject: Re: Killer Octave Question


> 
> 
> >   I know that someone has done the math on this.  How much "spread" is
> >required of a rib that is 20 inches long, curved on a radius of say 40' to
> >allow the center to drop .020"???  It has been too long since I dragged my
> >kids through high school geometry to remember arc and such, but I know
> >somebody out there has the answer at hand.
> 
> >A 20" rib with a 40' crown radius has a crown height of 0.104". The 
> >measurement across the top of the rib, along the curve is about 20.0015", 
> >or just about 1.5 thousandths of an inch difference. Roughly half the 
> >diameter of a human hair.
> >
> >A 36" rib with a 40' radius crown has a crown height of 0.338, and a rib 
> >length to arc length difference of 0.008.
> 
> Sorry, I forgot something...
> A rib 20" long will typically be carrying string bearing loads of somewhat 
> over 40 pounds total. With a 40 foot radius crown, and a 40 pound load, the 
> thrust against the rim would be around 1,920 pounds. That's just for one 
> rib, not counting the other twelve or so. A 13" rib, for instance will be 
> carrying around 90 pounds, with an outward thrust of 6,640+ pounds. I know 
> I can't build a wooden piano rim that would hold anywhere near that kind of 
> force with under 0.0015" deflection (0.0004" for the 13" rib).
> 
> Ron N
> 
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