<!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>Hi Isaac:</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>The center of percussion should only = come into play when the hammer strikes the string.  Ostensibly you would want the = line of action where the string strikes the hammer to pass through the hammer's = center of percussion.  This would result in no force at the pivot due = to impact.  If you don't strike at the center of percussion some small = amount of energy is lost to the pivot.  Only a small portion of the kinetic energy of the hammer is imparted to the string, = the rest goes into deforming the felt, the leftover kinetic energy when the = hammer bounces back and vibrational energy imparted to the wooden parts of the = action, particularly the hammer shank.</FONT></DIV> <DIV> </DIV> <DIV><FONT face=Arial size=2>The "touch" of the keys is really = independent of this.  There are two independent parts.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>There is a static balance: this is what = you feel if you partially depress the key and stop...you will feel a force upward = against your finger.  This is what the lead weights added to the key can adjust.  The more lead, the less static force against your finger.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Then there is dynamic inertia:  = this is what you feel when you try to *accelerate* the key downward.  The quicker you accelerate the key, the more reaction force = you will feel back from the key.  The dynamic force is added to the = static one to equal the total force you feel with your finger.  The dynamic = force depends on how fast you depress the key; the static force is there all = the time and doesn't change.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Think of it as if you are holding a 20 = lb. dumbell in your hand.  If you just stand there it will pull down on your = arm with a force of 20 pounds.  If, however, you jerk it suddenly upwards you = will feel more than 20 lbs. pulling downward, due to inertia.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>The dynamic behaviour of the action is = changed by modifying the moment of inertia of the rotating parts.  This can = also be changed by moving/adding/removing leads, but the = balance may be affected as a result.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Hope this helps!</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Don A. Gilmore<BR>Mechanical = Engineer<BR>Kansas City</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV>----- Original Message ----- </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=oleg-i@noos.fr href="mailto:oleg-i@noos.fr">Isaac sur = Noos</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, January 16, 2004 = 6:23 PM</DIV> <DIV style="FONT: 10pt arial"><B>Subject:</B> RE: Cockeyed hammers / = Don Gilmore</DIV> <DIV><FONT face=Arial size=2></FONT><BR> </DIV> <DIV><SPAN class=749381900-17012004></SPAN><FONT face=Arial><FONT color=#0000ff><FONT size=2>H<SPAN = class=749381900-17012004>ello</SPAN><SPAN class=749381900-17012004>Getting back at that old post, I noticed = that Yamaha hammers that have more wood on the tails side than many, seem to be = better balanced and more stable in time, we also feel something while playing = like if the hammer where thrower more naturally than on other kind with = thinner keys.</SPAN></FONT></FONT></FONT></DIV> <DIV><SPAN class=749381900-17012004><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <DIV><SPAN class=749381900-17012004><FONT face=Arial = color=#0000ff size=2>Is it the percussion point that is involved (I still did not get it = really) or does it have to do with the actual center of gravity of the = hammer/shank system ?</FONT></SPAN></DIV> <DIV><SPAN class=749381900-17012004><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <DIV><SPAN class=749381900-17012004><FONT face=Arial = color=#0000ff size=2>Thanks in advance</FONT></SPAN></DIV> <DIV><SPAN class=749381900-17012004><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <DIV><SPAN class=749381900-17012004><FONT face=Arial = color=#0000ff size=2>Isaac OLEG</FONT></SPAN></DIV> <DIV><SPAN class=749381900-17012004><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <BLOCKQUOTE dir=ltr style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #0000ff 2px = solid; MARGIN-RIGHT: 0px"> <DIV class=OutlookMessageHeader dir=ltr align=left><FONT = face=Tahoma size=2>-----Message d'origine-----<BR><B>De :</B> pianotech-bounces@ptg.org [mailto:pianotech-bounces@ptg.org]<B>De la = part de</B> Bernhard Stopper<BR><B>Envoyé :</B> vendredi 19 = décembre 2003 01:02<BR><B>À :</B> Pianotech<BR><B>Objet :</B> Re: = Cockeyed hammers / Don Gilmore<BR><BR></FONT></DIV> <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"> </BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE></BODY></H= TML>