strike weight

[stanwood]

>Stephan wrote:

>Your measurement of `shank strike weight' will lead to inaccuracies
>if it's used for dynamic analysis. Consider just the shank
>temporarily. Assume this is a cylindrical rod (for simplicity). The
>shank strike weight measured as you describe will be 1/2 the weight
>of the shank, since it is resting horizontally on two pivots. For
>static analysis this is fine (first moment about the pivot). Using
>the same `weight' in dynamic analysis will give inaccuracies,
>because you need to use the moment of inertia (second moment about
>the pivot) in this case to find the `effective mass of the shank'.
>For a cylindrical rod the moment of inertia when pivotted at the end
>is 1/3ml^2, thus the rod striking another mass (e.g.the string) at
>its endpoint will behave as a mass of only 1/3 the total shank
>mass...rather than 1/2 as you get with the static shank weight. The
>same comments also apply to the hammerheads because their mass is
>distributed about the strike line. Unless all the mass of the
>hammerhead were located at the strike line there  is difference
>between static (first moment) and dynamic (second moment)
>`effective mass'. These differences may turn out to be not too
>significant, but they should be checked....bigger hammerheads and/or
>larger shank/hammerhead mass ratios would increase the significance
>of the effect.


Stephan,

Your arguments are well founded and I have given them due consideration in
the past.  Based on what you outline here, it would be improper to use
strike weight for calculations such as moment of inertia etc.

The strike weight measures make sense in that all modern pianos are
constructed in a like form, having the hammer mounted roughly 5 1/16" out on
the shank and the hammer bore distances are fairly consistant from make to
make.  Anyone know of a piano with a 3" bore?  Relative to eachother, strike
weight values may be used as an effective measure of how much weight is
being thrown into the string, and our experience bears this out.

The same could be said for the downweight and upweight measures.  Crude but
effective.  Pianos weren't invented by physicists.  Things like what you
speak of are very interesting but they don't have much to do with the day to
day chores of the piano maker or technician, nor do the Pfeiffer books have
much in the way of practical information.

I appreciate your comments.

David C. Stanwood