> 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
This PTG archive page provided courtesy of Moy Piano Service, LLC