<!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></HEAD> <BODY style="FONT-SIZE: 14pt; FONT-FAMILY: Arial; BACKGROUND-COLOR: = #ffffff" bgColor=#ffffff> <DIV><FONT size=2>Hi Richard:</FONT></DIV> <DIV><FONT size=2></FONT> </DIV> <DIV><FONT size=2>I'm not sure what the qualifications of your = "physics guy" are, but inertia is not even an engineering quantity.  There are no = units of "inertia".  It is just a concept regarding the nature of = matter.  All bodies with mass have inertia and tend to want to stay at a constant = velocity and move in a straight line.</FONT></DIV> <DIV><FONT size=2></FONT> </DIV> <DIV><FONT size=2>Though a piano action does a lot of fancy stuff, it = still is a captive mechanism.  In other words, up till the point where the = hammer is released there is a specific, repeatable relation between key = movement and hammer movement.  So for any given position of the key downward, = there is a specific angle of the hammer produced.  You could draw a graph = showing key movement along the ordinate axis and hammer angle along = the abcissa.  And an equation can be determined that describes = this curve.  From this equation can be derived all the other equations = of motion including those for velocity, acceleration and perhaps even jerk.  = These would tell you exactly what that all-important "release velocity" is for = any given finger motion.</FONT></DIV> <DIV><FONT size=2></FONT> </DIV> <DIV><FONT size=2>Sounds simple, right?  But "finger motion" is = another subject entirely!</FONT></DIV> <DIV><FONT size=2></FONT> </DIV> <DIV><FONT size=2>Don A. Gilmore<BR>Mechanical Engineer<BR>Kansas City</FONT></DIV> <DIV> </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=Richard.Brekne@grieg.uib.no href="mailto:Richard.Brekne@grieg.uib.no">Richard Brekne</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> Saturday, December 20, = 2003 8:01 AM</DIV> <DIV style="FONT: 10pt arial"><B>Subject:</B> Touchweight was = Cockeyed hammers / Don Gilmore</DIV> <DIV><FONT size=2></FONT><FONT size=2></FONT><BR></DIV>  <P>"Don A. Gilmore" wrote: <BLOCKQUOTE TYPE="CITE"> <STYLE></STYLE> <FONT size=-1>Hi guys:</FONT> <FONT face=Arial><FONT = size=-1>Before you all get too carried away, here is some food for thought.</FONT></FONT> <FONT face=Arial><FONT size=-1>First = of all, forget about momentum.  Momentum (and, once again, we need to = think in terms of <I>angular</I> momentum) is moment of inertia x angular = velocity and is in units of slug-ft^2/sec or kg-m^2/s.  It is really = only useful in calculating elastic collisions between objects (like billiard = balls, for example) that exhibit "conservation of momentum", or impulse calculations.  Impulse is only useful if we are worried about = constant forces, etc.  You were all doing just fine with kinetic energy.</FONT></FONT> <FONT face=Arial><FONT size=-1>Since = the hammer is free from any outside influence between the time it is released = by the action and the time it strikes the string, we are talking about two = totally independent things: how the action gets it up to speed and what = happens when it strikes the string.</FONT></FONT></BLOCKQUOTE> <P>The origional concern of this was to compare the touchweight characteristics of  various methods of counterbalancing, = primarilly lead vs springs. We were looking <FONT = color=#00cc00>(compaitively)</FONT> at two related issues really... the << heavyness >> <FONT color=#00cc00>(which we evidently still havent really defined in = terms of physics</FONT>) of the mass being moved at all possible <FONT color=#00cc00>(reasonable)</FONT> speeds, and whether or not there = exists some << ideal >> amount or range  of key inertia for top = action inertia for any given overall action ratio (<FONT = color=#00cc00>defined in terms of the Balance Weight Ratio commonly called the Strike Weight Ratio.)</FONT><FONT color=#000000> i.e... how the action gets up to = speed and what the amount and character of the work the fingers need to do to = accomplish that.</FONT> <P>I find all the rest of it very interesting... but personally I want = to iron this <FONT color=#00cc00>(above)</FONT> bit out once and for all... = at least in my own head. <P>My own confusions relating to some of this surround largely the = term inertia. On the one hand I have been corrected just these past days by = Sarah, Mark, and a few others and have been told that inertia = mass. But = just today I get the following in the mail from a long time contributer who has a = reputation about him for being a physics guy. <BLOCKQUOTE> "Inertia is directly proportional to mass, but proportional the the square of the velocity."</BLOCKQUOTE>Other = places on the net seem pretty clearly to equate inertia with the equation  F = = ma. Not strange at all that I was mixing momentum up with inertia. Obviously = both these definitions cant be true. So which is it going to be folks ? = <BR>  <BR>  <P>-- <BR>Richard Brekne <BR>RPT, N.P.T.F. <BR>UiB, Bergen, Norway = <BR><A href="mailto:rbrekne@broadpark.no">mailto:rbrekne@broadpark.no</A> = <BR><A = href="http://home.broadpark.no/~rbrekne/ricmain.html">http://home.broad= park.no/~rbrekne/ricmain.html</A> <BR><A = href="http://www.hf.uib.no/grieg/personer/cv_RB.html">http://www.hf.uib= .no/grieg/personer/cv_RB.html</A> <BR>  </P></BLOCKQUOTE></BODY></HTML>