Shanks parallel to strings

[Phillip Ford]

>  What we want is for all of the momentum of the hammer, all of its kinetic
>energy, to be transferred to the string, or at least maximize it.

I agree that we want to maximize it.

>  Same is
>true with a bat hitting a baseball.

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.

>  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

>  On the other hand, if
>you hit the ball on the very end of the bat, or close to the handle, it can
>cause quite a stinging effect. When that happens, some of the energy of your
>swing is transferring to your hands, not to the ball.
>
>The sweet spot is called the center of percussion: it is that point on
>radius of the bat's swing where all of inertia of the bat's mass is
>effectively acting. Now in a hammer and shank assembly, the mass of the
>rotating shank is negligible compared to the hammer,

A typical grand shank might weigh in the neighborhood of 4 grams.  A 
typical hammer at the top end of the piano might weigh in the neighborhood 
of 5 grams.

>  so the center of mass
>of the hammer is effectively the sweet spot, or center of percussion.

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.

>  If we
>wanted to be really anal, we could extend the shank out a little ways
>further to compensate for the shank's mass. (That would involve a
>differential equation and I don't do those anymore.)

An interesting idea.  Might make checking difficult.

>  Since we take the mass
>of the shank to be negligible here, it really does not matter what angle it
>is on, or even where it is located when the hammer hits the string. What
>matters is that the hammer is oriented so that all of its inertial momentum
>is focused on the strike point, and we get there by making it perpendicular
>to the strings
>
>Dean

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