<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <html xmlns:v="urn:schemas-microsoft-com:vml" = xmlns:o="urn:schemas-microsoft-com:office:office" = xmlns:w="urn:schemas-microsoft-com:office:word" = xmlns="http://www.w3.org/TR/REC-html40"> <head> <meta http-equiv=Content-Type content="text/html; = charset=iso-8859-1"> <meta name=ProgId content=Word.Document> <meta name=Generator content="Microsoft Word 9"> <meta name=Originator content="Microsoft Word 9"> <link rel=File-List href="cid:filelist.xml@01C3C749.3C4FF940">  <style>  </style>  </head> <body bgcolor=white lang=FR link=blue vlink=blue = style='tab-interval:35.4pt'> <div class=Section1> Hi, Don, thanks for = your answer. That clear those concepts = enough.<o:p></o:p> <![if = !supportEmptyParas]> <![endif]><o:p></o:p> But still I = suppose that the whole energy transmission of the piano action is responding to this momentum concept very well , mostly I believe because a lot of = compression occur within the mechanism (and even on the key bed) and that as  this seem to work like a system = that stores energy and give it back when stopped (hence the importance of the hardness of the felts under the front of the key), the direction of = these moments are changing the way the hammer is = throw.<o:p></o:p> <![if = !supportEmptyParas]> <![endif]><o:p></o:p> I can’t imagine = the piano action during its move like if it was rigid, only on the paper it looks = like it, when playing from soft to forte the kinetic energy delivered is = certainly not changing linearly, and the momentum of the whole action stack is = certainly playing a role in for instance staccato playing. (it is just an = opportunity  to reintroduce momentum = !)<o:p></o:p> <![if = !supportEmptyParas]> <![endif]><o:p></o:p> To make a string = vibrate, is not a deformation necessary then an impact occur, I guess that with = voicing we look for a match between the rebound of the string and the rebound of = the hammer that allow for the best efficiency in bringing the string in its original vibrating mode in the most efficient way = .<o:p></o:p> <![if = !supportEmptyParas]> <![endif]><o:p></o:p> Coming back at that = less stiff support on the hammer pin side does it help the hammer to keep = more energy vs. the one that is lost in the pinning at hammer/string contact (decoupling) ?<o:p></o:p> <![if = !supportEmptyParas]> <![endif]><o:p></o:p> Sorry for my poor terminology, as often the things us technicians have a feel for because = we have meet them in the field, are not easily understood by ourselves with the = use of physics (particularly when like me I did not study those theories enough = !)<o:p></o:p> <![if = !supportEmptyParas]> <![endif]><o:p></o:p> BTW simples reminder = like the fact that drilling a lot of holes in a key can’t help in = stiffening it are of great value indeed. thanks Mr Ellis = ;>)<o:p></o:p> <![if = !supportEmptyParas]> <![endif]><o:p></o:p> Happy Christmas , and = 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> <![if = !supportEmptyParas]> <![endif]><o:p></o:p> -----Message d'origine----- De : Don A. Gilmore [mailto:eromlignod@kc.rr.com] Envoy� : samedi 20 = d�cembre 2003 17:09 � : = oleg-i@noos.fr; Pianotech Objet : Re: Cockeyed = hammers / Don Gilmore <![if = !supportEmptyParas]> <![endif]><o:p></o:p> Hi Isaac:<o:p></o:p></fon= t>  </sp= an><o:p></o:p> 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 = conservation</sp= an> of = energy.<o:p></o:p>  </sp= an><o:p></o:p> 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.<o:p></o:p>  </sp= an><o:p></o:p> Don A. Gilmore Mechanical Engineer Kansas City<o:p></o:p></fon= t> <div style='border:none;border-left:solid black 1.5pt;padding:0cm 0cm = 0cm 4.0pt'> ----- Original Message ----- = <o:p></o:p> <p class=MsoNormal = style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; margin-left:3.75pt;background:#E4E4E4;border:none;mso-border-left-alt:sol= id black 1.5pt; padding:0cm;mso-padding-alt:0cm 0cm 0cm 4.0pt'> <div style='font-color:black'>From: <a href="mailto:oleg-i@noos.fr" title="oleg-i@noos.fr">Isaac sur = Noos</a> </div> <o:p></o:p> To:</= b> = <a href="mailto:pianotech@ptg.org" = title="pianotech@ptg.org">Pianotech</a><font= size=2 color=black face=Arial> <o:p></o:p>= Sent:= Saturday, = December 20, 2003 5:41 AM<o:p></o:p> Subject:</fo= nt> RE: Cockeyed = hammers / Don Gilmore<o:p></o:p> <![if = !supportEmptyParas]> <![endif]><o:p></o:p> 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>  <o:p></o:p> Do you mean that momentum is only useful for = tone production ?<o:p></o:p>  <o:p></o:p> Best = Regards.<o:p></o:p>  <o:p></o:p> Isaac OLEG<o:p></o:p>  <o:p></o:p>  <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<o:p></o:p>  <o:p></o:p><= /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> <div style='border:none;border-left:solid black 1.5pt;padding:0cm 0cm = 0cm 4.0pt'> ----- Original Message ----- <o:p></o:p>= </div> <div style='border:none;border-left:solid black 1.5pt;padding:0cm 0cm = 0cm 4.0pt'> <div style='font-color:black'>From: <a href="mailto:ANRPiano@aol.com" title="ANRPiano@aol.com">ANRPiano@aol.com</a></fon= t> </div> <o:p></o:p> <![if = !supportEmptyParas]> <![endif]><o:p></o:p> </div> <div style='border:none;border-left:solid black 1.5pt;padding:0cm 0cm = 0cm 4.0pt'> To: <a href="mailto:pianotech@ptg.org" title="pianotech@ptg.org">pianotech@ptg.org</a></fo= nt> <o:p></o:p>= Sent: Friday, December 19, 2003 7:18 = AM<o:p></o:p> Subject: Re: Cockeyed hammers / Don = Gilmore<o:p></o:p>  <o:p></o:p> 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>  <o:p></o:p> 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>  <o:p></o:p>  <o:p></o:p>  <o:p></o:p> Andrew Remillard ANRPiano.com ANR Piano Service 2417 Maple Ave Downers Grove, IL 60515 630-852-5058<o:p></o:p> </div> </div> </body> </html>