Shanks parallel to strings

[Dean May]

>>>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.

>  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.
Energy is force acting over distance. Power is energy acting over time. If
you are feeling stinging in your hands during the contact time with the
ball, that force is moving your hands some distance during the contact time.
Ergo, you are absorbing some of the power of the impact. If you don't feel
the force, then the only place for the force to be acting is on the ball.
And that is the only vehicle available for transferring any power to the
ball.

>>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. 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.
Alternately, one could simply do a measurement to see how far off we are.
Fix the flange, let hammer fall upside down and put a gram scale under the
hammer so the line from the pivot to the strike point is parallel to the
scale. (You'd have to pin it for very low friction beforehand) Say it weighs
12 grams and the distance from the pivot to the strike point is 150 mm (I am
making this up for ease of calculation). Now weigh the shank and hammer assy
by itself: no flange. Say it weighs 15 grams. If I'm not mistaken, the
equation looks like this:
CP x 15 = 150 x 12
CP =120 mm
If you want to make the CP focus on the strike point of the hammer, you must
add mass further out from the pivot, 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.

>>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

Dean May             cell 812.239.3359
PianoRebuilders.com   812.235.5272
Terre Haute IN  47802