This is a multi-part message in MIME format. ---------------------- multipart/alternative attachment Hi, Don, thanks for your answer. That clear those concepts enough. 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. 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 !) 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 . 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) ? 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 !) 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 ;>) Happy Christmas , and best regards Isaac OLEG -----Message d'origine----- De : Don A. Gilmore [mailto:eromlignod@kc.rr.com] Envoyé : samedi 20 décembre 2003 17:09 À : oleg-i@noos.fr; Pianotech Objet : Re: Cockeyed hammers / Don Gilmore Hi Isaac: 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 of energy. 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. Don A. Gilmore Mechanical Engineer Kansas City ----- Original Message ----- From: Isaac sur Noos <mailto:oleg-i@noos.fr> To: Pianotech <mailto:pianotech@ptg.org> Sent: Saturday, December 20, 2003 5:41 AM Subject: RE: Cockeyed hammers / Don Gilmore 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. Do you mean that momentum is only useful for tone production ? Best Regards. Isaac OLEG -----Message d'origine----- De : pianotech-bounces@ptg.org [mailto:pianotech-bounces@ptg.org]De la part de Don A. Gilmore Envoyé : samedi 20 décembre 2003 00:36 À : Pianotech Objet : Re: Cockeyed hammers / Don Gilmore Hi guys: Before you all get too carried away, here is some food for thought. 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. 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. 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. 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. 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. 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. >From these two things, the center of percussion can be calculated. It's just q = k^2 / r 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. 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. Hope this helps! Don A. Gilmore Mechanical Engineer Kansas City ----- Original Message ----- From: ANRPiano@aol.com <mailto:ANRPiano@aol.com> To: pianotech@ptg.org <mailto:pianotech@ptg.org> Sent: Friday, December 19, 2003 7:18 AM Subject: Re: Cockeyed hammers / Don Gilmore 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? Except for the last one, all would involve other significant changes to make the hammer work, so please elaborate, I am very curious. Andrew Remillard ANRPiano.com ANR Piano Service 2417 Maple Ave Downers Grove, IL 60515 630-852-5058 ---------------------- multipart/alternative attachment An HTML attachment was scrubbed... URL: https://www.moypiano.com/ptg/pianotech.php/attachments/69/68/2d/3f/attachment.htm ---------------------- multipart/alternative attachment--
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