Cockeyed hammers / Don Gilmore

[Don A. Gilmore]

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Hi Isaac:

The center of percussion should only come into play when the hammer =
strikes the string.  Ostensibly you would want the line of action where =
the string strikes the hammer to pass through the hammer's center of =
percussion.  This would result in no force at the pivot due to impact.  =
If you don't strike at the center of percussion some small amount of =
energy is lost to the pivot.  Only a small portion of the kinetic energy =
of the hammer is imparted to the string, the rest goes into deforming =
the felt, the leftover kinetic energy when the hammer bounces back and =
vibrational energy imparted to the wooden parts of the action, =
particularly the hammer shank.

The "touch" of the keys is really independent of this.  There are two =
independent parts.

There is a static balance: this is what you feel if you partially =
depress the key and stop...you will feel a force upward against your =
finger.  This is what the lead weights added to the key can adjust.  The =
more lead, the less static force against your finger.

Then there is dynamic inertia:  this is what you feel when you try to =
*accelerate* the key downward.  The quicker you accelerate the key, the =
more reaction force you will feel back from the key.  The dynamic force =
is added to the static one to equal the total force you feel with your =
finger.  The dynamic force depends on how fast you depress the key; the =
static force is there all the time and doesn't change.

Think of it as if you are holding a 20 lb. dumbell in your hand.  If you =
just stand there it will pull down on your arm with a force of 20 =
pounds.  If, however, you jerk it suddenly upwards you will feel more =
than 20 lbs. pulling downward, due to inertia.

The dynamic behaviour of the action is changed by modifying the moment =
of inertia of the rotating parts.  This can also be changed by =
moving/adding/removing leads, but the balance may be affected as a =
result.

Hope this helps!

Don A. Gilmore
Mechanical Engineer
Kansas City

----- Original Message -----=20
  From: Isaac sur Noos=20
  To: Pianotech=20
  Sent: Friday, January 16, 2004 6:23 PM
  Subject: RE: Cockeyed hammers / Don Gilmore


  HelloGetting back at that old post, I noticed that Yamaha hammers that =
have more wood on the tails side than many, seem to be better balanced =
and more stable in time, we also feel something while playing like if =
the hammer where thrower more naturally than on other kind with thinner =
keys.

  Is it the percussion point that is involved (I still did not get it =
really) or does it have to do with the actual center of gravity of the =
hammer/shank system ?

  Thanks in advance

  Isaac OLEG

    -----Message d'origine-----
    De : pianotech-bounces@ptg.org [mailto:pianotech-bounces@ptg.org]De =
la part de Bernhard Stopper
    Envoy=E9 : vendredi 19 d=E9cembre 2003 01:02
    =C0 : Pianotech
    Objet : Re: Cockeyed hammers / Don Gilmore


    Don/Sarah,

    To design a hammer so that its pivot coincides with the center of =
percussion is THE way to get a free sound and the maximum of energy =
transfer to the string. it also allows the hammer to reject the fastest =
way possible because oscillations in the pivot produce friction and slow =
down hammer movement at contact point.=20
    i did several simulations with software called pro/mechanica and =
reshaped hammers after results found. one could say that actual hammer =
with heavy felts have their center of percussion much far away from the =
pivot than lighter hammers have. putting a small lead in the tail of the =
hammer can make them come closer to that point. center of hammer mass =
should ly on a line along the center of the hammer shank and the center =
of percussion is at distance x from pivot that can be calulated by the =
formula x=3DI/(m*y) with I=3D moment of inertia, m=3Dmass, y=3Ddistance =
to center of mass

    regards,

    Bernhard
      ----- Original Message -----=20
      From: Don A. Gilmore=20
      To: Pianotech=20
      Sent: Friday, December 19, 2003 12:22 AM
      Subject: Re: Cockeyed hammers / Don Gilmore


      Well, I didn't mean to imply that the impulse at the pivot is all =
absorbed; but it is all lost as far as the string is concerned.

      The center of percussion is one of those counter-intuitive =
phenomena in dynamics.  For the multitude of college students that only =
take a semester or two of physics, the concept of forces on a free body =
acting at the center of gravity is a paradigm that is hard to dislodge.  =
For an object in free space or translating in a straight line, which =
comprises most situations, the center of gravity is always used.  But =
for an object pivoted at some location other than its c.g., all bets are =
off.  The most publicized version of this is a baseball bat's "sweet =
spot" as you described.

      Think of a wooden board hung from a pivot point at its top.  If =
you strike the board up near the hinge, the pin will experience a force =
coming from the direction of the strike.  But if you strike the board at =
the bottom, the pin will experience a force in the opposite direction as =
the board tries to spin about its center.  There is a point in between =
these two where the pin force is neither positive nor negative and the =
pin will actually see no force.  This is the center of percussion and is =
not located at the centroid of the board.  It's not usually even =
particularly close.

      It would seem to be a good idea to design the hammer so that the =
string contact point of the head passes through the center of =
percussion.  That way the maximum amount of energy would be transmitted =
to the string...like dropping a ball on it.  But I'm not sure if they =
actually design them that way.

      Don A. Gilmore
      Mechanical Engineer
      Kansas City

      ----- Original Message -----=20

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