More on soundboard crown

[Ron Nossaman]

>Its a
>question of degrees... and as somebody (I wont get into who... grin)  pointed
>out a couple years back in another soundboard discussion, with something about
>a mosquito colliding with a Concord....  relative to what deflects what....
>every little bit counts...

An aircraft carrier, not the Concord, and if you want relativity, pay 
attention this time and I'll try again. These figures are approximate, and 
I'm not interested in all the details of what might happen on the molecular 
level. Just in case.

A rib of 800mm (35.5"), crowned at 18M (59') radius, is 0.069mm (0.0027") 
longer over the "arch" than the straight shot of the rib length. The crown 
height is 4.44mm (0.175"). The outward "thrust" of an arch of these 
proportions should be roughly proportional to the leverage arms of half the 
span divided by the arch height, or 90.09:1, so every pound or Kilo of 
bearing put on the bridge in the middle of the arch would put 90 pounds on 
the edge of the soundboard. Ten pounds of load would put 900 pounds on the 
soundboard edge. A rib half that long will produce over twice that thrust 
ratio. A piano with an overall bearing load of 700lbs will be putting 
considerably more (since most of the ribs are shorter than 800mm) than 
63000 pounds of outward thrust on the rim. A considerable portion of this 
thrust will be on the less substantial belly rail. The panel that was dried 
down to 4%MC for assembly and re-hydrated to 8%MC has already been 
compressed 5.5mm (0.2") or so, and is already under considerable PSI load. 
It will take a lot less than the additional string bearing load to compress 
the panel another 0.066mm (less than half that on a rib half that long). So 
the physical compliance of the material is considerably higher under the 
loads imposed than would make it possible for a soundboard to work as a 
buttressed arch. Even if the rim was infinitely stiff, the soundboard 
material would not make it possible. The centripetal tension resonator does 
not, and can not in any way support and maintain crown for any length of 
time and to any degree. The compressibility of the panel material just 
won't allow it.

Arguably, and I know that if it is, you will, the "resonator" might just 
actually help to support the soundboard crown until enough strings are 
installed for the bearing  to overpower the compressibility of the wood, 
but it's all over long before it's chipped up to pitch.

Ron N