<!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>Don/Sarah,</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>To design a hammer so that its = pivot coincides with the center of percussion is THE way to get a free sound and the = maximum of energy transfer to the string. it also allows the hammer to reject the = fastest way possible because oscillations in the pivot produce friction and slow down hammer movement at contact point. </FONT></DIV> <DIV><FONT face=Arial size=2>i did several simulations with software = called pro/mechanica and reshaped hammers after results found. one could say = that actual hammer with heavy felts have their center of percussion much far = away from the pivot than lighter hammers have. putting a small lead in the = tail of the hammer can make them come closer to that point. center of hammer = mass should ly on a line along the center of the hammer shank and the = center of percussion is at distance x from pivot that can be calulated by the = formula x=I/(m*y) with I= moment of inertia, m=mass, y=distance to = center of mass</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>regards,</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Bernhard</FONT></DIV> <BLOCKQUOTE dir=ltr style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; = BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"> <DIV style="FONT: 10pt arial">----- Original Message ----- </DIV> <DIV style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: = black"><B>From:</B> <A title=eromlignod@kc.rr.com = href="mailto:eromlignod@kc.rr.com">Don A. Gilmore</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> Friday, December 19, 2003 = 12:22 AM</DIV> <DIV style="FONT: 10pt arial"><B>Subject:</B> Re: Cockeyed hammers / = Don Gilmore</DIV> <DIV><BR></DIV> <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></BLOCKQUOTE></BODY></HTML>