Touchweight was Cockeyed hammers / Don Gilmore

[Don A. Gilmore]

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Hi Richard:

I'm not sure what the qualifications of your "physics guy" are, but =
inertia is not even an engineering quantity.  There are no units of =
"inertia".  It is just a concept regarding the nature of matter.  All =
bodies with mass have inertia and tend to want to stay at a constant =
velocity and move in a straight line.

Though a piano action does a lot of fancy stuff, it still is a captive =
mechanism.  In other words, up till the point where the hammer is =
released there is a specific, repeatable relation between key movement =
and hammer movement.  So for any given position of the key downward, =
there is a specific angle of the hammer produced.  You could draw a =
graph showing key movement along the ordinate axis and hammer angle =
along the abcissa.  And an equation can be determined that describes =
this curve.  From this equation can be derived all the other equations =
of motion including those for velocity, acceleration and perhaps even =
jerk.  These would tell you exactly what that all-important "release =
velocity" is for any given finger motion.

Sounds simple, right?  But "finger motion" is another subject entirely!

Don A. Gilmore
Mechanical Engineer
Kansas City

----- Original Message -----=20
  From: Richard Brekne=20
  To: Pianotech=20
  Sent: Saturday, December 20, 2003 8:01 AM
  Subject: Touchweight was Cockeyed hammers / Don Gilmore


   =20
  "Don A. Gilmore" wrote:=20

    Hi guys: Before you all get too carried away, here is some food for =
thought. First of all, forget about momentum.  Momentum (and, once =
again, we need to think in terms of angular momentum) is moment of =
inertia x angular velocity and is in units of slug-ft^2/sec or kg-m^2/s. =
 It is really only useful in calculating elastic collisions between =
objects (like billiard balls, for example) that exhibit "conservation of =
momentum", or impulse calculations.  Impulse is only useful if we are =
worried about constant forces, etc.  You were all doing just fine with =
kinetic energy. Since the hammer is free from any outside influence =
between the time it is released by the action and the time it strikes =
the string, we are talking about two totally independent things: how the =
action gets it up to speed and what happens when it strikes the string.
  The origional concern of this was to compare the touchweight =
characteristics of  various methods of counterbalancing, primarilly lead =
vs springs. We were looking (compaitively) at two related issues =
really... the << heavyness >> (which we evidently still havent really =
defined in terms of physics) of the mass being moved at all possible =
(reasonable) speeds, and whether or not there exists some << ideal >> =
amount or range  of key inertia for top action inertia for any given =
overall action ratio (defined in terms of the Balance Weight Ratio =
commonly called the Strike Weight Ratio.) i.e... how the action gets up =
to speed and what the amount and character of the work the fingers need =
to do to accomplish that.=20

  I find all the rest of it very interesting... but personally I want to =
iron this (above) bit out once and for all... at least in my own head.=20

  My own confusions relating to some of this surround largely the term =
inertia. On the one hand I have been corrected just these past days by =
Sarah, Mark, and a few others and have been told that inertia =3D mass. =
But just today I get the following in the mail from a long time =
contributer who has a reputation about him for being a physics guy.=20

     "Inertia is directly proportional to mass, but proportional the the =
square of the velocity."
  Other places on the net seem pretty clearly to equate inertia with the =
equation  F =3D ma. Not strange at all that I was mixing momentum up =
with inertia. Obviously both these definitions cant be true. So which is =
it going to be folks ?=20
   =20
   =20
  --=20
  Richard Brekne=20
  RPT, N.P.T.F.=20
  UiB, Bergen, Norway=20
  mailto:rbrekne@broadpark.no=20
  http://home.broadpark.no/~rbrekne/ricmain.html=20
  http://www.hf.uib.no/grieg/personer/cv_RB.html=20
   =20

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