Cockeyed hammers / Don Gilmore

[Isaac sur Noos]

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Excuse my question, but why is not momentum used, while the hammer felt have
some hysteresys (very slow indeed) and the string/mass hammer mass relation
is an important parameter – while we don’t know how to keep it consistent in
the treble where the hammers are too heavy vs/strings.

Do you mean that momentum is only useful for tone production ?

Best Regards.

Isaac OLEG


-----Message d'origine-----
De : pianotech-bounces@ptg.org [mailto:pianotech-bounces@ptg.org]De la part
de Don A. Gilmore
Envoyé : samedi 20 décembre 2003 00:36
À : Pianotech
Objet : Re: Cockeyed hammers / Don Gilmore

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.

As I mentioned before, the kinetic energy of the hammer is dependent upon
its rotational speed only since its mass does not change.  No matter what
kind of fancy things the action is doing when it is accelerating the hammer,
it all comes down to how fast it is going at the time of release.  The "die
is cast" at that point and you get what you get.  Relating this to key force
is complex, but as far as energy is concerned, it all boils down to the
angular velocity (rpm, basically) at release.

Now, how much of this energy is transferred to the string is another story.
This is all decided by the geometry of the hammer, or more specifically, the
relative positions of the center of gravity, the pivot point and the contact
face of the hammer.  There are only two places that can absorb any energy at
impact: at the string and at the pivot.  Obviously if you can reduce forces
at the pivot to zero, any transfer of energy will be to the string(s).  As I
mentioned before this would be the case if the strings contacted the hammer
at its center of percussion.

Locating the center of percussion requires determining the center of gravity
and the radius of gyration.  Measuring the c.o.g. is a piece of cake.  You
can just balance the hammer on the edge of a ruler, then scoot it around a
bit and balance it again.  The two lines made by the edge of the ruler will
intersect at the center of gravity.

The radius of gyration is a little trickier.  The radius of gyration (k) is
an imaginary distance from the pivot point to where the entire hammer can be
considered to act if it were a point mass.  In other words, if all of the
mass of the hammer were concentrated at a single point, k inches from the
pivot, it would have the same rotational behavior.  It is calculated in a
composite manner similar to figuring the moment of inertia...in fact it can
be directly converted from the m.o.i. by dividing by the mass and taking the
square root.

>From these two things, the center of percussion can be calculated.  It's
just

q = k^2 / r

where q is the distance from the pivot to the c.o.p., k is the radius of
gyration and r is the distance from the pivot to the c.o.g.

Now that you know where the point is, you can play around with the hammer
geometry to move it to where you need it.  You can also change the location
of the c.o.g. (and thus c.o.p.) by strategically placing weights, but
remember that this will also increase the overall mass of the hammer.

Hope this helps!

Don A. Gilmore
Mechanical Engineer
Kansas City
----- Original Message -----
From: ANRPiano@aol.com <mailto:ANRPiano@aol.com>
To: pianotech@ptg.org <mailto:pianotech@ptg.org>
Sent: Friday, December 19, 2003 7:18 AM
Subject: Re: Cockeyed hammers / Don Gilmore

So my fine physics gents, put this in layman's terms.  Are you suggesting
moving the hammer up or down the shank, changing the bore distance, changing
the center of gravity of the hammer? Or all three?

Except for the last one, all would involve other significant changes to make
the hammer work, so please elaborate, I am very curious.



Andrew Remillard
ANRPiano.com
ANR Piano Service
2417 Maple Ave
Downers Grove, IL 60515
630-852-5058

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