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MARGIN: 0cm 0cm 0pt; FONT-FAMILY: "Times New Roman"; = mso-bidi-font-size: 12.0pt; mso-pagination: widow-orphan; = mso-fareast-font-family: "Times New Roman" } LI.MsoBodyText2 { FONT-SIZE: 11pt; MARGIN: 0cm 0cm 0pt; FONT-FAMILY: "Times New Roman"; = mso-bidi-font-size: 12.0pt; mso-pagination: widow-orphan; = mso-fareast-font-family: "Times New Roman" } DIV.MsoBodyText2 { FONT-SIZE: 11pt; MARGIN: 0cm 0cm 0pt; FONT-FAMILY: "Times New Roman"; = mso-bidi-font-size: 12.0pt; mso-pagination: widow-orphan; = mso-fareast-font-family: "Times New Roman" } A:link { COLOR: blue; TEXT-DECORATION: underline; text-underline: single } SPAN.MsoHyperlink { COLOR: blue; TEXT-DECORATION: underline; text-underline: single } A:visited { COLOR: blue; TEXT-DECORATION: underline; text-underline: single } SPAN.MsoHyperlinkFollowed { COLOR: blue; TEXT-DECORATION: underline; text-underline: single } P.MsoAutoSig { FONT-SIZE: 12pt; MARGIN: 0cm 0cm 0pt; FONT-FAMILY: "Times New Roman"; = mso-pagination: widow-orphan; mso-fareast-font-family: "Times New Roman" } LI.MsoAutoSig { FONT-SIZE: 12pt; MARGIN: 0cm 0cm 0pt; FONT-FAMILY: "Times New Roman"; = mso-pagination: widow-orphan; mso-fareast-font-family: "Times New Roman" } DIV.MsoAutoSig { FONT-SIZE: 12pt; MARGIN: 0cm 0cm 0pt; FONT-FAMILY: "Times New Roman"; = mso-pagination: widow-orphan; mso-fareast-font-family: "Times New Roman" } P.Adressedest { FONT-SIZE: 12pt; MARGIN: 0cm 0cm 0pt; FONT-FAMILY: "Times New Roman"; = mso-pagination: widow-orphan; mso-fareast-font-family: "Times New = Roman"; mso-style-name: "Adresse dest." } LI.Adressedest { FONT-SIZE: 12pt; MARGIN: 0cm 0cm 0pt; FONT-FAMILY: "Times New Roman"; = mso-pagination: widow-orphan; mso-fareast-font-family: "Times New = Roman"; mso-style-name: "Adresse dest." } DIV.Adressedest { FONT-SIZE: 12pt; MARGIN: 0cm 0cm 0pt; FONT-FAMILY: "Times New Roman"; = mso-pagination: widow-orphan; mso-fareast-font-family: "Times New = Roman"; mso-style-name: "Adresse dest." } SPAN.StyleCourrierlectronique23 { COLOR: navy; mso-style-type: personal-reply; mso-ansi-font-size: = 10.0pt; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial; = mso-bidi-font-family: Arial } DIV.Section1 { page: Section1 } </STYLE> </HEAD> <BODY lang=FR style="tab-interval: 35.4pt" vLink=blue link=blue = bgColor=white> <DIV>Hi Isaac:</DIV> <DIV> </DIV> <DIV>Well, momentum is sort of an imaginary = concept that is only useful in solving certain problems.  Energy is usually a = more useful quantity, whether mechanical, electrical, or chemical, since = everything obeys the laws of consevation of energy.</DIV> <DIV> </DIV> <DIV>The equations of energy are derived by = integrating (calculus) the famous F=ma equation with respect to distance.  If = we integrate it with respect to time we get the impulse-momentum = equations.  These formulas are no less accurate in the case of a piano hammer, = just not very useful.  There are three basic kinds of system where = momentum is useful as a tool in solving: impulse, collision and mass flow.  = Impulse is when a constant force acts on a mass for a finite amount of time, which = can be equated with a change in "momentum".  In a collision of two (or = more) objects, the momentum is conserved in one direction, or in the = case of angular movement, about one axis.  This is = sometimes useful.  If the piano hammer were colliding with another object we could calculate = how fast they would move or spin after the collision.  But since = we're talking about a vibrating string, momentum is not useful at all.</DIV> <DIV> </DIV> <DIV>Don A. Gilmore Mechanical = Engineer Kansas City</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">From: <A title=oleg-i@noos.fr href="mailto:oleg-i@noos.fr">Isaac sur = Noos</A> </DIV> <DIV style="FONT: 10pt arial">To: <A = title=pianotech@ptg.org href="mailto:pianotech@ptg.org">Pianotech</A> </DIV> <DIV style="FONT: 10pt arial">Sent: Saturday, December 20, = 2003 5:41 AM</DIV> <DIV style="FONT: 10pt arial">Subject: RE: Cockeyed hammers / = Don Gilmore</DIV> <DIV> </DIV> <DIV class=Section1> Excuse my question, but why is not momentum used, while the hammer felt have = some hysteresys (very slow indeed) and the string/mass hammer mass relation = is an important parameter � while we don�t know how to keep it = consistent in the treble where the hammers are too heavy vs/strings.<o:p></o:p> <![if = !supportEmptyParas]><![endif]> <o:p></o:p> Do you mean that momentum is only useful for tone production ?<o:p></o:p> <![if = !supportEmptyParas]><![endif]> <o:p></o:p> Best Regards.<o:p></o:p> <![if = !supportEmptyParas]><![endif]> <o:p></o:p> Isaac OLEG<o:p></o:p> <![if = !supportEmptyParas]><![endif]> <o:p></o:p> <![if = !supportEmptyParas]><![endif]> <o:p></o:p> -----Message d'origine----- De : pianotech-bounces@ptg.org [mailto:pianotech-bounces@ptg.org]De la part de Don A. = Gilmore Envoy� : samedi 20 = d�cembre 2003 00:36 � : Pianotech Objet : Re: Cockeyed hammers / Don Gilmore <![if = !supportEmptyParas]><![endif]> <o:p></o:p> Hi guys:<o:p></o:p>  <o:p></o:p> Before you all get too carried away, here is some food for thought.<o:p></o:p>  <o:p></o:p> First of all, forget about momentum.  Momentum (and, once again, we = need to think in terms of angular 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.<o:p></o:p>  <o:p></o:p> 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.<o:p></o:p>  <o:p></o:p> As I mentioned before, the kinetic energy of the hammer is dependent = upon its rotational speed only since its mass does not change.  No matter what kind of fancy things the action is doing = when it is accelerating the hammer, it all comes down to how fast it = is going at the time of release.  The "die is cast" at that point = and you get what you get.  Relating this to key force is complex, but as far as energy is concerned, it all boils down to the = angular velocity (rpm, basically) at release.  <o:p></o:p>  <o:p></o:p> Now, how much of this energy is transferred to the string is another = story.  This is all decided by the geometry of the hammer, or more = specifically, the relative positions of the center of gravity, the pivot point and the = contact face of the hammer.  There are only two places that can absorb = any energy at impact: at the string and at the pivot.  Obviously if you can reduce forces at the pivot to zero, any transfer of energy = will be to the string(s).  As I mentioned before this would be the case = if the strings contacted the hammer at its center of percussion.<o:p></o:p>  <o:p></o:p> Locating the center of percussion requires determining the center of gravity = and the radius of gyration.  Measuring the c.o.g. is a piece of = cake.  You can just balance the hammer on the edge of a ruler, then scoot it = around a bit and balance it again.  The two lines made by the edge of the = ruler will intersect at the center of gravity.<o:p></o:p>  <o:p></o:p> The radius of gyration is a little trickier.  The radius of gyration = (k) is an imaginary distance from the pivot point to where the entire = hammer can be considered to act if it were a point mass.  In other words, if = all of the mass of the hammer were concentrated at a single point, k inches = from the pivot, it would have the same rotational behavior.  It is = calculated in a composite manner similar to figuring the moment of inertia...in fact = it can be directly converted from the m.o.i. by dividing by the mass and taking = the square root.<o:p></o:p>  <o:p></o:p> From these two things, the center of percussion can be calculated.  = It's just <o:p></o:p>  <o:p></o:p> q = k^2 / r<o:p></o:p>  <o:p></o:p> where q is the distance from the pivot to the c.o.p., k is the radius of = gyration and r is the distance from the pivot to the c.o.g.<o:p></o:p>  <o:p></o:p> Now that you know where the point is, you can play around with the = hammer geometry to move it to where you need it.  You can also change = the location of the c.o.g. (and thus c.o.p.) by strategically placing = weights, but remember that this will also increase the overall mass of the hammer.<o:p></o:p>  <o:p></o:p> Hope this helps!<o:p></o:p>  <o:p></o:p> Don A. Gilmore Mechanical Engineer Kansas City<o:p></o:p> <DIV style="BORDER-RIGHT: medium none; PADDING-RIGHT: 0cm; BORDER-TOP: = medium none; PADDING-LEFT: 4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: black = 1.5pt solid; PADDING-TOP: 0cm; BORDER-BOTTOM: medium none"> <P class=MsoNormal style="BORDER-RIGHT: medium none; PADDING-RIGHT: 0cm; BORDER-TOP: = medium none; PADDING-LEFT: 0cm; PADDING-BOTTOM: 0cm; MARGIN-LEFT: = 3.75pt; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: = medium none; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; = mso-border-left-alt: solid black 1.5pt; mso-padding-alt: 0cm 0cm 0cm = 4.0pt">----- Original Message ----- <o:p></o:p> <P class=MsoNormal style="BORDER-RIGHT: medium none; PADDING-RIGHT: 0cm; BORDER-TOP: = medium none; PADDING-LEFT: 0cm; BACKGROUND: #e4e4e4; PADDING-BOTTOM: = 0cm; MARGIN-LEFT: 3.75pt; BORDER-LEFT: medium none; PADDING-TOP: 0cm; = BORDER-BOTTOM: medium none; mso-margin-top-alt: auto; = mso-margin-bottom-alt: auto; mso-border-left-alt: solid black 1.5pt; = mso-padding-alt: 0cm 0cm 0cm 4.0pt"> <DIV style="font-color: black">From: <A title=ANRPiano@aol.com href="mailto:ANRPiano@aol.com">ANRPiano@aol.com</A> </DIV><o:p></o:p> <P class=MsoNormal style="BORDER-RIGHT: medium none; PADDING-RIGHT: 0cm; BORDER-TOP: = medium none; PADDING-LEFT: 0cm; PADDING-BOTTOM: 0cm; MARGIN-LEFT: = 3.75pt; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: = medium none; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; = mso-border-left-alt: solid black 1.5pt; mso-padding-alt: 0cm 0cm 0cm = 4.0pt">To: <A title=pianotech@ptg.org href="mailto:pianotech@ptg.org">pianotech@ptg.org</A> <o:p></o:p> <P class=MsoNormal style="BORDER-RIGHT: medium none; PADDING-RIGHT: 0cm; BORDER-TOP: = medium none; PADDING-LEFT: 0cm; PADDING-BOTTOM: 0cm; MARGIN-LEFT: = 3.75pt; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: = medium none; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; = mso-border-left-alt: solid black 1.5pt; mso-padding-alt: 0cm 0cm 0cm = 4.0pt">Sent: Friday, December 19, 2003 7:18 AM<o:p></o:p> <P class=MsoNormal style="BORDER-RIGHT: medium none; PADDING-RIGHT: 0cm; BORDER-TOP: = medium none; PADDING-LEFT: 0cm; PADDING-BOTTOM: 0cm; MARGIN-LEFT: = 3.75pt; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: = medium none; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; = mso-border-left-alt: solid black 1.5pt; mso-padding-alt: 0cm 0cm 0cm = 4.0pt">Subject: Re: Cockeyed hammers / Don Gilmore<o:p></o:p> <P class=MsoNormal style="BORDER-RIGHT: medium none; PADDING-RIGHT: 0cm; BORDER-TOP: = medium none; PADDING-LEFT: 0cm; PADDING-BOTTOM: 0cm; MARGIN-LEFT: = 3.75pt; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: = medium none; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; = mso-border-left-alt: solid black 1.5pt; mso-padding-alt: 0cm 0cm 0cm = 4.0pt"><![if = !supportEmptyParas]><![endif]> <o:p></o:p> <P class=MsoNormal style="BORDER-RIGHT: medium none; PADDING-RIGHT: 0cm; BORDER-TOP: = medium none; PADDING-LEFT: 0cm; PADDING-BOTTOM: 0cm; MARGIN-LEFT: = 3.75pt; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: = medium none; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; = mso-border-left-alt: solid black 1.5pt; mso-padding-alt: 0cm 0cm 0cm = 4.0pt">So my fine physics gents, put this in layman's terms.  Are you = suggesting moving the hammer up or down the shank, changing the bore distance, = changing the center of gravity of the hammer? Or all three?<o:p></o:p> <P class=MsoNormal style="BORDER-RIGHT: medium none; PADDING-RIGHT: 0cm; BORDER-TOP: = medium none; PADDING-LEFT: 0cm; PADDING-BOTTOM: 0cm; MARGIN-LEFT: = 3.75pt; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: = medium none; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; = mso-border-left-alt: solid black 1.5pt; mso-padding-alt: 0cm 0cm 0cm = 4.0pt"> <o:p></o:p> <P class=MsoNormal style="BORDER-RIGHT: medium none; PADDING-RIGHT: 0cm; BORDER-TOP: = medium none; PADDING-LEFT: 0cm; PADDING-BOTTOM: 0cm; MARGIN-LEFT: = 3.75pt; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: = medium none; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; = mso-border-left-alt: solid black 1.5pt; mso-padding-alt: 0cm 0cm 0cm = 4.0pt">Except for the last one, all would involve other significant changes to make = the hammer work, so please elaborate, I am very = curious.<o:p></o:p> <P class=MsoNormal style="BORDER-RIGHT: medium none; PADDING-RIGHT: 0cm; BORDER-TOP: = medium none; PADDING-LEFT: 0cm; PADDING-BOTTOM: 0cm; MARGIN-LEFT: = 3.75pt; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: = medium none; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; = mso-border-left-alt: solid black 1.5pt; mso-padding-alt: 0cm 0cm 0cm = 4.0pt"> <o:p></o:p> <P class=MsoNormal style="BORDER-RIGHT: medium none; PADDING-RIGHT: 0cm; BORDER-TOP: = medium none; PADDING-LEFT: 0cm; PADDING-BOTTOM: 0cm; MARGIN-LEFT: = 3.75pt; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: = medium none; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; = mso-border-left-alt: solid black 1.5pt; mso-padding-alt: 0cm 0cm 0cm = 4.0pt"> <o:p></o:p> <P class=MsoNormal style="BORDER-RIGHT: medium none; PADDING-RIGHT: 0cm; BORDER-TOP: = medium none; PADDING-LEFT: 0cm; PADDING-BOTTOM: 0cm; MARGIN-LEFT: = 3.75pt; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: = medium none; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; = mso-border-left-alt: solid black 1.5pt; mso-padding-alt: 0cm 0cm 0cm = 4.0pt"> <o:p></o:p> <P class=MsoNormal style="BORDER-RIGHT: medium none; PADDING-RIGHT: 0cm; BORDER-TOP: = medium none; PADDING-LEFT: 0cm; PADDING-BOTTOM: 0cm; MARGIN-LEFT: = 3.75pt; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: = medium none; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; = mso-border-left-alt: solid black 1.5pt; mso-padding-alt: 0cm 0cm 0cm = 4.0pt">Andrew Remillard ANRPiano.com ANR Piano Service 2417 Maple Ave = Downers Grove, IL 60515 630-852-5058<o:p></o:p></DIV></DIV></BLOCKQUOTE></BODY>= </HTML>