[pianotech] crown and radius

[Ron Nossaman]

Gene Nelson wrote:
> ****In regard to the half meter rib: Given a radius of 12 meters and  
> chord of .47 meter the calculator predicts 2.1mm of crown or segment 
> height.

I get 2.3, but that's close enough.


> If the center of load support (high point and thickest part) is 
> asymmetricly shifted off center of the chord, the calc cannot be 
> accurate and their will always be less crown than desired? Still a bit 
> confused.
> Gene


One more time. You will NOT, under any circumstances, WHATEVER 
you may do or think you're doing, move the high point to 
anywhere other than the center of the rib in a constant radius 
crown. Forget the high point, please. Moving the center of 
load will NOT effect the high point of the unloaded crown in 
ANY manner. It will slightly affect the bridge height, when 
the point of load isn't on the center, but you'll be quite a 
ways off center before that is a real problem. Look up the 
math for height of an arc segment at any position on the chord 
to find it. You'll find it's not very useful in practice. For 
instance, locating the bridge at 200mm, or 33mm off center, 
the height is 0.05mm lower. At 150mm, or 85mm off center, the 
height difference is 0.3mm. That's a closer tolerance than 
you'll likely be able to build to.

Also. There is a definite gap between what is theoretically 
absolute, and what in practice disappears in the background 
noise. Part of what you're doing with redesign is roughly 
defining that gap for yourself and your methods, against your 
expectation and results. Just like everything else you've ever 
done in, on, or to a piano.
Ron N