<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META http-equiv=Content-Type content="text/html; = charset=iso-8859-1"> <META content="MSHTML 6.00.2800.1276" name=GENERATOR> <STYLE></STYLE> </HEAD> <BODY bgColor=#ffffff background=""> <DIV><FONT face=Arial size=2> <DIV><FONT face=Arial size=2>Well, I didn't mean to imply that = the impulse at the pivot is all absorbed; but it is all lost as far as the string is = concerned.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>The center of percussion is one of = those counter-intuitive phenomena in dynamics.  For the multitude of = college students that only take a semester or two of physics, the concept of = forces on a free body acting at the center of gravity is a paradigm that is hard to dislodge.  For an object in free space or translating in a = straight line, which comprises most situations, the center of gravity is = always used.  But for an object pivoted at some location other than its = c.g., all bets are off.  The most publicized version of this is a baseball = bat's "sweet spot" as you described.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Think of a wooden board hung from a = pivot point at its top.  If you strike the board up near the hinge, the pin will experience a force coming from the direction of the strike.  But if = you strike the board at the bottom, the pin will experience a force in the = opposite direction as the board tries to spin about its center.  There is a = point in between these two where the pin force is neither positive nor negative = and the pin will actually see <EM>no</EM> force.  This is the center of = percussion and is <EM>not</EM> located at the centroid of the board.  It's not = usually even particularly close.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>It would seem to be a good idea to = design the hammer so that the string contact point of the head passes through = the center of percussion.  That way the maximum amount of = energy would be transmitted to the string...like dropping a ball on it.  But I'm = not sure if they actually design them that way.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV>Don A. Gilmore<BR>Mechanical Engineer<BR>Kansas City</DIV> <DIV> </DIV> <DIV></FONT>----- Original Message ----- </DIV></DIV> <BLOCKQUOTE dir=ltr style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; = BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"> <DIV style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: = black"><B>From:</B> <A title=sarah@gendernet.org = href="mailto:sarah@gendernet.org">Sarah Fox</A> </DIV> <DIV style="FONT: 10pt arial"><B>To:</B> <A = title=pianotech@ptg.org href="mailto:pianotech@ptg.org">Pianotech</A> </DIV> <DIV style="FONT: 10pt arial"><B>Sent:</B> Thursday, December 18, = 2003 2:38 AM</DIV> <DIV style="FONT: 10pt arial"><B>Subject:</B> Cockeyed hammers / Don = Gilmore</DIV> <DIV><BR></DIV> <DIV><FONT face="Courier New" size=2>Probably any baseball player = would know that it's not smart to hit the ball with the very tip of the = bat.  It makes for a nasty shock to the hands (and to the extent that the hands = are not rigid in space, it takes away from the power transferred to the = ball).  Why do they do this with piano hammers?  More to the point, is = this not considered an unneccessary demand to put on the hammer flanges and bushings?  Perhaps it's also a drain on efficiency?  = Wouldn't it make sense to have some sort of asymmetrical molding whose center of = mass is on the far side of the action center, so as to put the center of mass = of the hammer assembly closer to the line of strike?</FONT></DIV> <DIV><FONT face="Courier New" size=2></FONT> </DIV> <DIV><FONT face="Courier New" size=2>Also, wouldn't it at least = make sense to angle the head of the hammer inwards slightly, so that the radius to = the head's center of mass is perpendicular to the strike axis of the head?  It seems to me that this would help to control wobble in = the hammer</FONT></DIV> <DIV><FONT face="Courier New" size=2></FONT> </DIV> <DIV><FONT face="Courier New" size=2>I'm not sure I agree about = part of the impact being "absorbed" by the pivot.  Sure, there would be force = against the pivot, but for impact to be absorbed, the pivot would need to be = compliant and inelastic.  I realize that's true to an extent, as no system = is ideal.  However, do you think this would be a substantial drain = of energy?  It seems to me that the hammer felt and the strings are = far more compliant and are closer to the center of mass, such that almost all = of the energy would be dissipated there (rather than at the comparatively = rigid center).  Have you ever measured this?</FONT></DIV> <DIV><FONT face="Courier New" size=2></FONT> </DIV> <DIV><FONT face="Courier New" size=2>Just curious on your = take.  I can't do much more than scratch my head about this one.  If the hammer = were perfectly rigid and the center bullet proof and noncompliant, there'd = be nothing to worry about.  But considering that it does the hokey = pokey and shimmies all about...  Well, I don't know.</FONT></DIV> <DIV><FONT face="Courier New" size=2></FONT> </DIV> <DIV><FONT face="Courier New" size=2>Peace,</FONT></DIV> <DIV><FONT face="Courier New" size=2>Sarah</FONT></DIV></BLOCKQUOTE></BODY></HTML>