Killer Octave Question

[Ron Nossaman]

>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