First, having a cut-off or no cut-off is really of no consequence in terms of load bearing capacity. A longer rib will have a larger cross section to compensate for its length. Simple enough. A cut-off, especially a large one, does have acoustic consequences but that is something different and I'm willing to call that a matter of taste for the time being. Feathering the beam certainly reduces the strength of the beam. But gluing a panel on top, securing it around the rim and gluing a bridge on top of that adds to the strength. Before we can determine how far apart our calculations are we need a bit more data. First, what is the load per rib that we are using from which we make our calculations. Second, how much deflection are we targeting per rib. Third, how much crown do we start with which might impact how much deflection we are targeting if we are using a percentage of crown. Fourth, what other criteria aside from spring rate are we using in our analysis. Once established we can more easily do a side by side comparison. As I mentioned, I'm not sure I want to delve into all the details of that at this point--not quite ready to give it all up. Of course, anyone can figure out that sin radians(1.5)*35,000 (or whatever your string tension is) = about 900 lbs. Distribute that over 12 - 14 ribs or whatever you have and you have rough load per rib. After that it gets trickier to describe without going into greater detail, but suffice it to say that I think it's likely that my rib scales are lighter by virtue of different beam formulas in use and by what I understand about what it is that you advocate and from having built some assemblies myself that, in my view, were too heavy. I can say that when the boards I'm building are fully loaded they react pretty much as predicted losing about half the crown and half the preset bearing. Ultimately, however, the sound of the piano tells you a lot in terms of how heavy the rib scale is. You can hear it. If possible, modifications are then done to the bearing in order to tweak the impedance by adjusting nose bolts or perimeter bolts. These modifications, if they occur, are generally very minor. If they need to move a lot then I probably would reexamine some things for the next project. That might include rib scale, panel thickness, feathering, bridge dimensions... I recognize that tonal goals may vary and that might well alter the design concepts. Of course, the board has to support the load without going negative and I have not had that problem in anything I've built so far where I've followed my current guidelines. While I do have an opinion about what sound I like or don't like as it relates to design issues, I fully accept that there are those whose tastes may differ. That's why they make chocolate and vanilla. But the range of acceptable to me is relatively narrow and is largely driven by scale differences and not the narrow window of how the board should be set up given a particular scale. It is narrower than I might have thought when I first started all this. There's no question you can tweak these designs forever and even then you will always have (hopefully) small surprises that require some minor tweaking. I accept that as the limitations of organic materials predictability. But my general design target is getting smaller and smaller and the focus on not too heavy doesn't by any means take a back seat to not too light. David Love www.davidlovepianos.com This is where I was going. These calculations are done with full section simple beams. After feathering, a fair bit of strength is given up. I did some calculations and deflection tests years back that indicated around a 16% loss of strength. Calculated with simple ends, this loss is fairly closely cancelled by gluing the final rib form into the rim, and what small panel compression that exists also compensates. So my conclusion was and is that the simple end full section calculation ends up being pretty close to the reality after it's built. A fixed end calculation showing a beam of some specific dimensions to be four times stiffer (however you care to describe it) under a given load than a simple end formula produces a beam of 1/4 the stiffness of a simple end calculation to produce a given deflection under a given load. That means to me that, since I've verified to my satisfaction the similarity to the real world of the simple end calculations after feathering and assembly, that a fixed end calculation will produce a rib that, after feathering, will be considerably weaker than the calculations indicate. That is, unless there is some surprise secret windage compensation (perhaps a factor of four?) that hasn't been mentioned just yet. Include a low crown and a 1°+ bearing load on long ribs with no cutoff, and the numbers say it doesn't work and won't support that kind of load at those deflections without being stiffer than is claimed. So I'm wondering how this works. Ron N
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