Killer Octave Question

[Greg Newell]

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That's certainly enough for me to chew on for a while! I reserve the chance 
to ask more questions later though. Thanks!!!

Greg



At 08:50 PM 4/19/2003, you wrote:


>>Now that's an area I could surely use some help in. How does one work 
>>this out?
>>
>>Greg
>
>I'm not sure how one does it, but here's what I do. I use a somewhat 
>modified version of a scaling spreadsheet. Starting with my revised string 
>scale, I assign expected bearing angles to each unison to get the string 
>downbearing load for each unison. Sin(angle)*tension*number of strings is 
>close enough at these low angles. I work out a new rib layout on a 
>cardboard pattern of the inside of the case and rim, with bridge and 
>unison location marked (punched in with a rubber hammer in the piano 
>before taking out the soundboard). I make whatever changes I want to the 
>bridge configuration and location, sketch in cutoff bar, and plan a rib 
>layout around that. This gives me rib lengths, and unison location for 
>each rib as it corresponds to the string scale. Then, I add up unison 
>downbearing for each rib (from half way back, to halfway to the adjacent 
>ribs), and apply a simple center loaded beam deflection formula to see how 
>much each rib will deflect under it's expected load - and size the cross 
>sections accordingly. I could dimension the ribs to have a low crown and 
>be stiff enough to deflect only a little, or have different dimensions and 
>a high crown to deflect a lot. Either approach will make a rib that will 
>carry the load just about where you want it, but will respond differently 
>acoustically. The load analysis is the easy part. Though it takes some 
>work, it's just simple mechanics. A good general purpose center loaded 
>beam deflection formula is D=(length^3*load)/(4*E*width*height^3). E is 
>the modulus of elasticity for your beam material. For Spruce, it's about 
>1,570,000. You can use inches or millimeters, and the deflection will be 
>in the same scale as the input. Note that deflection is affected much more 
>by rib height than by width. As far as the juggling act necessary to put 
>together a decent soundboard assembly design for a given string scale and 
>rim shape, calculating the rib deflections is well into the easy part.
>
>As an interesting exercise, you can do this load analysis on an existing 
>compression crowned soundboard and rib set, string scale, and bearing 
>schedule, and see what kind of "lift" panel expansion has to provide to 
>both bend the flat ribs to a nominally 60' (18M) radius, and support the 
>string bearing besides. It's scary. Makes you feel sorry for the poor panel.
>
>Ron N
>
>_______________________________________________
>pianotech list info: https://www.moypiano.com/resources/#archives
>

Greg Newell
mailto:gnewell@ameritech.net 

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