This is a multi-part message in MIME format. ---------------------- multipart/alternative attachment 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. =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. 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=20 q =3D 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 -----=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 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=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/05/63/63/57/attachment.htm ---------------------- multipart/alternative attachment--
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