Killer Octave Question

[Ron Nossaman]

>   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