Laminated Soundboard Ribs

[John Delacour]

At 9:53 PM +0000 12/2/02, Phillip L Ford wrote:

>In theory the bending stiffness of a beam (or in our case a rib) is 
>dependent on
>the length, moment of inertia of the cross section, and the modulus 
>of elasticity
>of the material.  Assuming two ribs of the same length we can eliminate that
>variable.  The moment of inertia is determined by the geometry of the cross
>section.  So, two sections with the same cross section (for example 
>a 1 x 1 inch
>square) will have the same moment of inertia, whether that cross 
>section is solid
>or built up of several layers.  The modulus of elasticity is a 
>physical property of
>the material.  So, pine will have one modulus, spruce another, maple 
>another, etc.
>Once again, the modulus of elasticity of the rib material shouldn't depend on
>whether the cross section is solid or built up in strips, as long as 
>all the strips
>are of the same material as the solid cross section.  That's the theory.  In
>practice your mileage may vary.

Spruce, or any wood, particularly softwoods will have very different 
values of Young's Modulus according to the direction of the grain. 
That's why ribs are needed in the first place!

>Here's a reference for some wood moduli:
>
>http://www.woodbin.com/ref/wood/strength_table.htm

You will find different figures at different sites.  Old soundboard 
wood and new that I have tested (and in rather humid conditions at 
that) give specific gravities of around 0.35 and nowhere near the 
0.40 given here for Sitka spruce.  I have no Sitka spruce to test but 
I've seen figures as low as 0.33 given in other places.

>You want something that's stiff but light.  Sitka spruce is very good in this
>regard, which is probably one of the reasons it has become a material of
>choice.  However, as the chart shows, there are some others which are better.
>Red spruce, for example.  Also, plain old doug fir (as long as you get a piece
>of coastal fir) is better still.

Wolfenden reported in 1919 that "A few American pianos are (except in 
the treble part) ribbed with pine; careful experiments show that this 
material gives better results than spruce, and it is now so scarce as 
to be (in this country [England]) only procurable at most extravagant 
prices"

As to balancing stiffness and lightness, it's not just a question of 
dividing the elasticity modulus by the density; the desired ratio can 
be achieved by making the rib deeper, since the stiffness is 
proportional to the width but proportional to the _square_ of the 
depth.  And all this presumes that the rib's sole purpose is to act 
as a girder, which is not so.  The stiffness of any part of the 
system will also affect the wave speed of the forced vibrations, not 
to speak of the resonant (modal) frequencies of the board as a whole.

JD

PS.  One of Wolfenden's pianos that I restored about 18 years ago has 
just reappeared in a rather dismal-looking state but behaving as well 
as I remember it.  It's the only Wolfenden piano (a Weber) I've ever 
seen and one of the best English uprights I've ever come across. 
I'll have a look and see if he ribbed it with pine before the prices 
went up!