Jim, Richard, Frank, and all the ships at sea, One more time. For the sake of illustration, I have two ribs, both 24" long and 1" high, one flat, one machine crowned to a 60' radius. I also have two "panels", both 0.375 thick, one dried to 4% EMC, and one dried to 6% EMC, and both exactly 24 inches wide. We will assume that the modulus of elasticity is such that we will end up with similar assembled crown heights with both ribs, though that's not necessarily the case in real life. Since this is an illustration of a basic principal, I'll try to keep it as simple, and with as few variables, as possible. I now glue the 4% EMC panel to the flat rib (compression crowned (CC)), and the 6% EMC panel to the crowned rib (rib crowned (RC)). At this point, the CC panel and rib are at rest, and neither is under any tension, compression, stress, or general discomfort. The rib of the RC assembly is of a similar condition, but the panel has been bent, and is under slight compression at the bottom, and slight tension at the top. The glue has dried, and we rehydrate both assemblies to 8% EMC, and both assemblies are now crowned at a 55' radius. The panel of the CC assembly has grown from 24" to 24.147" with the 4% EMC increase. The top surface of the rib is 24.018 long, which should make the top of the panel 24.019". That means that the panel has been compressed at the top by 0.128", and the bottom by 0.129". Note that the entire panel is under compression, top to bottom, before any string load is applied. The panel of the RC assembly has grown from 24" to 24.074" with the 2% EMC increase. The top surface of the rib, I admit, I haven't figured out exactly how long this would be, but it will be within a couple of thousandths of an inch of the CC rib. Assuming a top length of even 24.025, there is still 0.049" compression in the panel of the RC assembly. So both assemblies now have similar crown, and both panels are under compression, that's *compression*, before they are installed in the piano, and before any string load is applied. Under string load, the CC panel must, all by itself, support the string load, as well as the additional load of the rib trying to straighten itself out again. The rib is under negative load in the CC system, and doesn't assume a positive load to help support string bearing load until the crown is negative. In the RC system, under string load, the ribs are under positive load from the beginning, supporting the majority of the load, and the panel is under compression, though much less than in the CC system. The benefits of the RC system are predictability of crown height on assembly, predictability of deflection under load, predictability of impedance result, and the likelihood of a longer dependable service life because of the better distribution of load among the components. That's the basic outline. While I'm surprised that some CC boards have lasted as long as they have, that is not an endorsement. I am also disgusted that so many CC boards in brand new, or under five years old, pianos are shot. The rib crowned assembly is the only rational way to build a soundboard, in my opinion, and given the materials and methods we have to work with. When we switch to synthetic materials, there will be surely be different options and techniques. Hope this makes sense, I'm late... no time to proof. Ron N
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