Shanks parallel to strings

[Phillip Ford]

> >>>Actually, I think this is the opposite situation.  You want the least
>amount of energy transferred from the ball to the bat.  You're trying to
>get it to rebound with as much energy as possible.  The batter is also
>adding additional energy.
>
>Read that through three times and tell me what it means. It looks like to me
>the last sentence is contradicting your opening statement. The only way for
>the batter to add energy is through force on the ball acting over distance
>and time. See on down.

Perhaps if we take the batter out of the picture my point will be more 
clear.  Rigidly attach the bat to a fixture.  Now throw the ball at it.  If 
the object is to get max transfer of energy from ball to bat, then you want 
the least amount of ball rebound (the greater the rebound, the more the 
ball's energy stayed in the ball).  What point on the bat will give the 
greatest ball rebound?  Will it be the center of percussion?  If so, then 
that doesn't seem like the spot that's giving greatest energy transfer from 
ball to bat.


> >  Now if you've played baseball you know
> >that there is a "sweet spot" on the bat. If the ball hits that sweet spot,
> >it maximizes the transfer of the bat's kinetic energy to the ball and you
> >feel very little of the impact force in your hands.
>
>I agree that this is the point that minimizes force on your hands.  I'm not
>sure about it maximizing energy transfer to the ball.  See:
>http://tennis.about.com/library/blsweetspot.htm
>There are different dynamics at work in a resilient tennis racket than a
>rigid system like a baseball bat.

I'm not that knowledgeable about this.  But when I went looking for 
information about it, the people who seemed to know seemed always to be 
referring to bats and tennis racquets in the same sentence.  Besides, a 
piano hammer and string are not a rigid system either.

>Energy is force acting over distance....
>
> >>Since more of the mass of the shank is concentrated back towards the
>flange
>end, what with the land for the knuckle and the knuckle itself, the CG of
>the shank is back towards the flange end.  At the top end of the piano,
>where the masses of the hammer and shank are in the same general ballpark,
>the CG (and probably also the center of percussion) would be well in from
> >>the hammer I think.
>The center of percussion is not the same as the CG.

I understand that.

>  A quick and dirty way to
>calculate it would be to divide the shank into uniform segements. Sum the
>inertial effects of the center of mass of each segment (mass of each segment
>X radial distance from pivot point) and divide by the total mass. That would
>give the center of percussion for the shank assembly only. If we added the
>inertial effect of the hammer into the summation, we could get the center of
>percussion for the whole assembly. The effect of the shank may be more
>significant than I thought. Somebody needs to do a finite element analysis
>here, very finite. I think one could section the shank assy into about 3 or
>4 segments to get a good estimate.

The formula for center of percussion is:

CP = I / Mr

Where I would be inertia of hammer and shank assembly about the axis of 
rotation
M is mass of the hammer and shank assembly
r is distance to center of mass of the assembly

Taking a couple of real examples:

Say the hammers are hung at 5 inches from the hammer center.
Assume the shank weighs 4 grams.  For the sake of simplicity assume it is a 
straight cylinder with its CG halfway out, at 2.5 inches.

To bracket this a bit:
For a bass hammer, assume hammer mass is 11 grams (a pretty heavy bass hammer).
For a treble hammer, assume hammer mass is 4 grams (a pretty light treble 
hammer).

Do the math and you get:

For the bass hammer CP = 4.74 inches from hammer center
For the treble hammer CP = 4.44 inches from hammer center

As the hammer gets heavier, the CP moves more towards the hammer, but even 
for a heavy bass hammer it isn't at the hammer.  If we had used a real 
shank, with its CG closer to the hammer center, the CPs would be slightly 
further away from the hammers.

>Alternately, one could simply do a measurement to see how far off we are.
>...
>If you want to make the CP focus on the strike point of the hammer, you must
>add mass further out from the pivot,

I agree.

>until the scale weight of the suspended
>hammer assy exactly equals the total mass of the assembly.
>Definitely on a vertical piano would the butt assy have more inertial effect
>on the center of percussion because of the effect of the rotating mass of
>the catcher. No doubt that is why you are more prone to see wobbly hammer
>centers on a vertical than a grand: those pivot centers take more "stinging"
>since the center of percussion is not as close to the hammer on a vertical
>as it is on a grand.

Yes.  Good point.  If nothing else, moving the CP to the hammer would seem 
to minimize hammer center wear.

Phil Ford


> >>I don't see why making the hammer perpendicular to the string orients it
>so
>that all of its inertial momentum is focused on the strike point.
>
>Phil Ford
>
>After thinking about it, I've come to the conclusion that it needs to be
>perpendicular to the vector from the pivot point to the strike point.
>Neglecting any gripping the string does on the hammer, there is one primary
>direction that the string can push on the hammer and shank assembly:
>perpendicular to the vector from the pivot point to the strike point. So it
>seems to me the hammer needs to be oriented diametrically opposed to that
>force vector.
>
>Dean May