impedance (was negative crown_

[Frank Weston]

> So how would YOU measure the mechanical impedance of a structure?  Is it
> just the real and imaginary part of a transfer function?  I still don't
know
> how to measure mechanical impedance...
> 
> doug

Why Doug!  I think you've just hit the nail on the head (which by the way
can be a good example of mechanical impedance match/mismatch).  While
mechanical impedance is a convenient concept, it is very nearly impossible
to calculate in complex mechanical system like a piano given the resources
at the disposal of those who design pianos.  From what we read here, we
know it's a complex number and a function of inertia and "springiness", and
that the imaginary component drives the affect with respect to time.  What
we don't know is how to calculate it.  In fact, all the computers on this
list running in parallel until the end of the millennium would not have the
time or power to even dent the problem.  A more realistic approach, and the
one adopted by all who design pianos is the empirical one, which is to
build a piano, see what happens, make a change, see what happens, make more
changes, etc. 

Want a demo of just what mechanical impedance is?  Take a hammer and a four
foot 2x4 and a nail.  Lay the board flat on top of your workbench.  Pound
in the nail.  Easy, right?  Now take the board and extend it about two feet
off the edge of your bench, again, flat side down.  Clamp the other end to
the bench.  Now try to pound a nail into the board from the top near the
extended end.   Much more difficult.  Now drive the nail into the butt end
of the board at the extended end.  Much easier.  Now rotate the board 90
degrees and clamp as before.  Drive a nail from the new top.  Easier, but
not as easy as other approaches.  Try different sized nails, different
hammers, different angles and extensions.

What you will have experienced is a range of mechanical impedance matches
from good to poor.  In this simple case, it is even possible to calculate
impedance, but why waste the time?  It's much easier to just position the
board and drive the nail, no matter what impedance might be calculated, the
nail will be just as hard to drive.  Draw the piano analogy on your own.

Frank Weston -  Why yes, I am a rocket scientist.



 
----------
> From: Doug Richards <Doug.Richards@quantum.com>
> To: pianotech@ptg.org
> Subject: RE: impedance (was negative crown_
> Date: Wednesday, December 30, 1998 2:52 AM
> 
> 
: birketts@wright.aps.uoguelph.ca