hammer momentum physics

[Stephen Birkett]

Looking at this hammer/string interaction for even a short while
indicates to me that no amount of elementary physics will
reveal very much about the process of energy transfer.
I believe arguments based on momentum, energy,
square pulses, fourier analysis etc. are all doomed to fail...sorry to
say it again...primarily because of inherent non-linearity, but also
because there are too many inter-related parameters.

For instance, the hammer is effectively stiffer at higher velocities
which will affect tonal spectra, efficiency of energy transfer, and
many other things. Therefore a fast light hammer is fundamentally
different from a slow heavier hammer.

Energy efficiency is less for a heavy hammer as the energy required
to push the hammer away from the string is greater. In at least one
of the references inharmonicity was seen to influence the harmonic
sprectrum. because of the response of the hammer head while in
contact with the string etc.

There are so many parameters involved here and they are quite
interdependent, so it's unlikely that a situation exists where
a pair of parameters may be changed so as to create no overall
change. I think we could all contribute to this research by
suggesting parameters that may influence tone, say those between the
shank pivot to the string (since it is the hammer/string
interaction that is in question)...I suggest the following list:
 shank geometry (length, cross-section, driving force and direction)
       mass
       pivot
       compliance
 hammer mass
        geometry
        compliance
 string length
        dia
        density (overspun?)
        compliance (inharmonicity)
 bridge coupling (for reflections)

Each of these parameters is measurable, although not all are easy.
Each of these is independently variable. The problem then becomes:
what are the sprectral energies imparted to the string when a hammer
shank is driven by a given force from the action. And how does this
harmonic structure change as a particular parameter is varied. Such a
problem is more meaningful than random `what-if' scenarios. But I
don't believe such a problem can be solved with
ordinary physics, or even at all analytically...which is true for
similar problems in robotics.

Any more suggestions for parameters that you think are important??


Stephen Birkett (Fortepianos)
Authentic Reproductions of 18th and 19th Century Pianos
Waterloo, Ontario, Canada
tel: 519-885-2228
fax: 519-763-4686