Shanks parallel to strings

[Phillip Ford]

Phil Ford wrote:
> >>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<<<<<<
>______________

Dean May wrote:

>I fear you are making the same mistake I was making earlier. You are
>calculating the Center of Gravity, not the Center of Percussion. Your
>formula for CP appears to be correct, but you fail to calculate the value
>for "I" which is not the inertia, but the Moment of Inertia.....

>Now for Center of Gravity:
>CG=(4*2.5+11*5)/15
>CG=4.33 in  (I'm not sure why I got a different number than you did)

Because I was calculating Center of Percussion.  This number is the Center 
of Gravity.

>Going back to your formula for Center of Percussion:
>
>CP=I / mr
>CP = 308 / (15*4.33)
>CP= 4.74 in

Which is exactly the number that I got.  See above.  Is this some sort of 
trick question?

Whatever.  The result is still that the Center of Percussion is not at the hammer.

Phil Ford

>...
>You are correct in that there is another "sweet spot", that is related to
>the natural frequency of the bat. I had never before heard of it having an
>effect on transferring energy to the ball. But it has been too long since I
>was a real engineer.
>
>
>Dean, P.E.