This is a multi-part message in MIME format. ---------------------- multipart/alternative attachment 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 consevation of energy. The equations of energy are derived by integrating (calculus) the famous = F=3Dma 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 -----=20 From: Isaac sur Noos=20 To: Pianotech=20 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. =20 Do you mean that momentum is only useful for tone production ? =20 Best Regards. =20 Isaac OLEG =20 =20 -----Message d'origine----- De : pianotech-bounces@ptg.org [mailto:pianotech-bounces@ptg.org]De la = part de Don A. Gilmore Envoy=E9 : samedi 20 d=E9cembre 2003 00:36 =C0 : Pianotech Objet : Re: Cockeyed hammers / Don Gilmore =20 Hi guys: =20 Before you all get too carried away, here is some food for thought. =20 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. =20 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. =20 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. =20 =20 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. =20 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. =20 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. =20 From these two things, the center of percussion can be calculated. = It's just=20 =20 q =3D k^2 / r =20 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. =20 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. =20 Hope this helps! =20 Don A. Gilmore Mechanical Engineer Kansas City ----- Original Message -----=20 From: ANRPiano@aol.com=20 To: pianotech@ptg.org=20 Sent: Friday, December 19, 2003 7:18 AM Subject: Re: Cockeyed hammers / Don Gilmore =20 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? =20 Except for the last one, all would involve other significant changes = to make the hammer work, so please elaborate, I am very curious. =20 =20 =20 Andrew Remillard ANRPiano.com ANR Piano Service 2417 Maple Ave=20 Downers Grove, IL 60515 630-852-5058 ---------------------- multipart/alternative attachment An HTML attachment was scrubbed... URL: https://www.moypiano.com/ptg/pianotech.php/attachments/f0/b3/a8/f3/attachment.htm ---------------------- multipart/alternative attachment--
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