Soundboard mass

[John Delacour]

At 07:10 -0600 24/11/07, Ron Nossaman wrote:

>>The stiffness of the bridge increases as the _square_ of the 
>>height, to that a bridge of 33mm is about 70% stiffer than one of 1 
>>inch and a bridge of 38mm is 33% stiffer than one of 33mm.
>
>Moment of inertia of the section for the flexure formula is 
>calculated on the cube of the height, but yes, a little added bridge 
>(or crowned rib) height makes for an assembly that's considerably 
>stiffer.

Indeed! I was not making the distinction between strength and 
resistance to flexure, ie. stiffness, presuming erroneously that they 
were the same, so it can be said that "the strength of a rectangular 
beam varies as the square of the depth, and the stiffness to resist 
deflection varies as the cube of the depth" as you say, which means 
that a 38mm bridge is more than 50% stiffer than one 33mm tall and if 
one were to increase the height to 40mm. there would be a 78% 
stiffness advantage.

>  A similar net effect can be gotten with a short bridge with the 
>addition of more crowned ribs.

That I am not qualified to calculate, but I am thinking of the whole 
length of the bridge and perhaps you are thinking more of remedial 
measures for weakness in a troublesome part of the scale as found 
commonly in old American Steinways (the "killer octave" ??).  To 
stiffen the whole stucture by this means would surely mean adding 
quite a lot of unwanted mass, many times more than by increasing the 
bridge height or adding a "mirror bridge" as used by Grotrian, 
Rittmüller et al.    To my mind a high ratio of stiffness to mass is 
of prime importance.

JD






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