<!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 bgColor=#ffffff> <DIV><FONT face=Arial size=2>Hello Isaac (and = everyone):</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Let me give you a concise grounding in = how geometry and balancing affects the inertial properties of an object.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>As I mentioned before, moment of = inertia is due to a mass rotating at a distance from a pivot and is proportional to this = mass and to the square of the distance from the pivot point.  Simple; = right?  Well as long as the mass has no physical size you're doing just = fine.  </FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Now let's talk about a metal rod = spinning about one end.  metal at the middle of the rod is at one distance from = the pivot and metal at the end of the rod is at a larger distance, so the mass in = the rod affects the moment of inertia more and more as we go outward from the = pivot point, in fact it is affected as the <EM>square</EM> of the = distance.  If you think about it, it gets scary.  No matter how small a piece of = the rod we take into account, it still has some finite size and one end of the = piece is farther from the center than the other.  But we have to have some = size (volume) or we have no mass!  We would have to consider an infinite = number of pieces that are infinitely small and add their m.o.i.'s together to = get the total!  </FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Impossible?  Well, that's what = calculus is for.  By using integral calculus we can do this infinitesimal sum = (that's literally what calculus is for) and come up with a nice, neat little = formula for calculating the m.o.i. of our rod.  It turns out that it is a = simple little algebraic equation.  Now this equation is only good for a = cylindrical rod pivoted at its end.  For other shapes and pivot points we would = need to derive a different formula.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>"Now, Gilmore, how the hell is this = helping me?"  Well, now you have a general idea of what affects an object's = m.o.i.  So when you go playing around with an object's geometry, = you'll know what you're doing.  Just remember that more mass or a wider = radius both increase the m.o.i. and the radius is the more extreme of the = effects since it is squared.  If you are using small leads you can probably just = assume that it is approximately a point mass and figure its addition to the = overall m.o.i. by using m x r^2.  Remember also that a mass' angular = location has no effect on its moment of inertia...only radius.  So a lead weight = can be located anywhere on an object as long as it is the same distance from = the pivot.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Now, about balancing.  You can use = a counterweight to "counter" the effects of gravity by creating a = teeter-totter effect.  But this weight can only <EM>increase</EM> mass and = m.o.i.  It just depends on what your goal is.  If you are worried about the = weight of the hammer and its effect on key pressure you can counterweight and partially, or completely eliminate the weight.  But even with no = weight at the key, the m.o.i. will determine what happens when you try to = accelerate the object.</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><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=caut@ptg.org href="mailto:caut@ptg.org">College and University Technicians</A> = </DIV> <DIV style="FONT: 10pt arial"><B>Sent:</B> Sunday, December 21, 2003 = 5:21 AM</DIV> <DIV style="FONT: 10pt arial"><B>Subject:</B> RE: Touch Weight</DIV> <DIV><BR></DIV> <DIV><SPAN class=898455110-21122003><FONT face=Arial = color=#0000ff size=2>Vince, </FONT></SPAN></DIV> <DIV><SPAN class=898455110-21122003><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <DIV><SPAN class=898455110-21122003><FONT face=Arial = color=#0000ff size=2>I believe that you are also changing the moment of inertia with changes = in regulation parameters , attack angle of the keys, height of the = centers - while it does not make sense at first.</FONT></SPAN></DIV> <DIV><SPAN class=898455110-21122003><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <DIV><SPAN class=898455110-21122003><FONT face=Arial = color=#0000ff size=2>I concur to say that the leading of the keys is not the way the action = can be lightened, or make heavier, it is quite simple to experiment with = leads using double sided tape and normal cylindrical leads, you can experiment on = many kind of setups.</FONT></SPAN></DIV> <DIV><SPAN class=898455110-21122003><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <DIV><SPAN class=898455110-21122003><FONT face=Arial = color=#0000ff size=2>I believe that the action mass may match the pianists hand weight so to = be comfortable, finding the way to express those parameters in numbers = should certainly be useful.</FONT></SPAN></DIV> <DIV><SPAN class=898455110-21122003><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <DIV><SPAN class=898455110-21122003><FONT face=Arial = color=#0000ff size=2>Best Regards.</FONT></SPAN></DIV> <DIV><SPAN class=898455110-21122003><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <DIV><SPAN class=898455110-21122003><FONT face=Arial = color=#0000ff size=2>Isaac OLEG</FONT></SPAN></DIV> <DIV><SPAN class=898455110-21122003><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <DIV><SPAN class=898455110-21122003><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <DIV><SPAN class=898455110-21122003><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <DIV><SPAN class=898455110-21122003><FONT face=Arial = color=#0000ff size=2></FONT></SPAN> </DIV> <DIV><FONT face=Arial color=#0000ff size=2></FONT> </DIV> <STYLE>A.psl { COLOR: #4e81c4; 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MARGIN-LEFT: 5px; BORDER-LEFT: #0000ff 2px = solid"> <DIV class=OutlookMessageHeader dir=ltr align=left><FONT = face=Tahoma size=2>-----Message d'origine-----<BR><B>De :</B> = caut-bounces@ptg.org [mailto:caut-bounces@ptg.org]<B>De la part de</B> madelyn mrykalo<BR><B>Envoy� :</B> dimanche 21 d�cembre 2003 03:10<BR><B>� :</B> College and University Technicians<BR><B>Objet :</B> Re: Touch = Weight<BR><BR></FONT></DIV> <DIV> <DIV><B><I>James Ellis <claviers@nxs.net></I></B> wrote: <BLOCKQUOTE class=replbq style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #1010ff = 2px solid"> <P><BR><BR>Touch weight and inertia are NOT the same thing at all. = "Tough weight" is<BR>merely a measure of static force. "Inertia" is a = dynamic quantity.<BR></P> <P><EM>Neither is front weight the same thing as moment of = inertia, which I have already said.</EM></P> <P><EM></EM><BR>That's why putting more leads closer to the center = of the keys<BR>will result in less "KEY" inertia. You will have to use = more lead, but the<BR>"key" inertia will be a little bit less. However, the = keys are NOT where<BR>most of the total action inertia comes from. It comes = from the hammer<BR>heads out on the ends of the shanks, because that's = where the (mass x<BR>velocity squared) is concentrated.<BR><BR>All I'm = saying is that moving the leads closer to the centers of the keys<BR>is not = going to buy you very much, because that's not where most of the<BR>total = action inertia is coming from in the first place.</P> <P><EM>But then that is the only place we <STRONG>can</STRONG> = change the moment of inertia, unless we lighten the hammer.</EM></P> <P>What it will do is<BR>weaken the keys, especially if you drill = more holes, plug holes, etc.</P> <P><EM>That's probably not going to be a = problem</EM>.<BR><BR><BR>Those two things are about all it will do for you, other than just = making<BR>the keys heavier in the middle. So, before you haul off and re-do a whole<BR>set of keys, drilling more holes, adding more leads, = plugging holes, and<BR>moving all the leads closer to the center, remember: = It won't buy you very<BR>much towarding lowering the overall action = inertia, because that's not<BR>where it's coming from, but it will = definitely weaken the keys.</P> <P><EM>If we are going to change the front weight anyway, because = we are also changing out hammers, the MOI might as well be dealt with = then too.<BR></EM><BR>Merry Christmas, Jim = Ellis<BR><BR><BR>_______________________________________________<BR>caut = list info: = https://www.moypiano.com/resources/#archives</P></BLOCKQUOTE></DIV></DIV><BR>= <BR>Vince Mrykalo<BR>University of Utah <P> <HR SIZE=1> Do you Yahoo!?<BR><A = href="http://pa.yahoo.com/*http://us.rd.yahoo.com/evt=21260/*http://p= hotos.yahoo.com">New Yahoo! Photos - easier uploading and sharing</A></BLOCKQUOTE></BLOCKQUOTE></BODY></HTML>