[pianotech] Measuring Crown Radius

[David Love]

BTW this is the second half of that useful equation for those interested.  Once you measure the crown along your 15" ruler and figure out the crown radius you can then plug that into this equation to figure out how much total crown you have over the entire length of the rib along which you've measured.  The entire rib length is equal to 2a, or a = 1/2 the total rib length.    

𝒅 =  𝒄 − √(𝒄^𝟐−𝒂^𝟐 )
c = radius, a equals ½ the rib length, d equals displacement (amount of measured crown).  
Not sure how this will come through but the c^2-a^2 should all be under the radical. 


 

Now on to the other issues below.  

RN
"I've never found rib scale analysis of a compression crowned board to be 
of any use whatsoever, since it's an entirely different system than a 
rib supported board. Rib crowned and panel supported, sure. You can 
learn what the panel will have to support."



I know it's been the argument recently that the ribs don't do anything in a compression crowned board to support the load but I'm not convinced of that.  I know the argument has been made that ribs are pulling the panel down and therefore the compression in the panel is supporting not only the load but resisting the pulling down of the ribs as well.  While the ribs would certainly be pulling the panel down outside of the piano, once you glue it in, I'm not so sure.  Once glued into the rim the rib becomes a clamped ends beam and even if it is not a buttressed arch, gluing it in affords it some additional resistance to bending.  If that's the case then an analysis of the rib structure even in a compression crowned system could be useful and even if it's not that useful it seems to be telling.  If one assumes on a rebuild using the original board that the ribs may have to do some additional work then knowing whether the rib scale is not up to the task or is imbalanced in terms of its load carrying capacity from rib to rib, then I would find that useful information.  As I do tend to run rib scale analysis on existing boards (even compression crowned boards), it's interesting not only the variation between the same models.  Also, I find, that weaknesses in certain sections in the array are fairly evident when you put numbers to them.  Often those weak areas correspond to problem areas in the piano.  Compression or not, it seems worth paying attention to.  


RN
"I don't know about you, but I've said probably a thousand times that 
either crown or bearing alone is useless. That's why both of these 
measurements are taken with the piano at pitch."


I was just meaning to reiterate that important point.



> Measuring the
> crown with tension and without tension and the bearing change with and
> without load tells you quite a bit about how the board is responding and
> whether it can withstand any significant load or not.

RN
"I disagree. It can confirm the initial diagnosis if the crown doesn't 
come up, but you learned what it would hold with the crown and bearing 
measurements under load."


We may disagree here then.  The assumption is that the original load was set up properly or that after the fact someone under read the desired load and increased it by pulling down the nosebolts or lowering the plate (if the piano had that system).  One could find (it doesn't happen that often but it does happen) that the piano had adequate crown but that the bearing was set too high.  Even if the loaded readings of crown and downbearing were not desirable, the crown coming up with the release of tension to adequate levels and a showing that the bearing was set too high might lead you in the direction of not replacing the board when you otherwise might have.


RN 
And the question you asked was about unloaded crown alone, which I answered.



Yes, you did answer the unloaded crown question and I should have worded it more clearly.  Given that you normally set up a board with a standard load of, say, 700 lbs then you're right the before and after measurements will tell you if the board will take that load--assuming everything goes back to where it was before you took it apart, which it doesn't always but that's another issue.  But it's not unusual to reset the bearing on older boards with less crown to something less in anticipation of the board's inability to withstand those original load settings without going negative.  So my question was more what would be a minimal load setting that would likely produce an acceptable, albeit not an ideal outcome.  Related to that, what would be the minimum crown required in order to do that.  I guess that's really the secondary question as it's easy enough to figure out the maximum bearing you can set on a given piano with a certain amount of crown  so that you avoid the risk of pushing the board negative.  

But how much load is required to produce an acceptable sound is my question, and that's assuming that the load can be set uniformly which it can't always in part due to poorly designed rib scales.  There are undoubtedly several factors to consider (original scale design being an important one) and I'm just thinking that if I had to come up with a rule of thumb what would that be.  Is it 350 lbs, 500 lbs?  



David Love
www.davidlovepianos.com