At 4:41 pm -0400 19/7/06, A440A at aol.com wrote: > I have a different approach to the "magic line at half blow" >concept. I find better response on actions that see the capstan/heel >contact point intersects the magic line at let-off..... Friction is >a function of speed. On the beginning of the stroke, where the >capstan speed is at its minimum, the effect of friction is >lessened... This thread has also had me working out a practical experiment to test this question, but I am certain that my conclusions would be very different from yours, Ed, and that the experiment would show a different picture. At the outset I would say that velocity plays but a minor role in friction, the two main quantities being the normal force and the coefficient of friction of the surfaces rubbed together. There must be a thousand books sites that deal with the question but wikipedia seems to sum things up quite well. <http://en.wikipedia.org/wiki/Coefficient_of_friction> The principle of having the two arcs touch at the contact point at half-blow is neat and tidy and has the one advantage that it can at worst be only half totally misconceived. As to its validity in practice in the dynamics of the system, it ignores everything except pure geometry. I intend to make nothing like a decision on the matter until I've had time to devise and execute the experiment that will demonstrate the matter, but I sense that the point where the lever-centre, the contacting profiles (lever heel meets pilot) and the fulcrum of the key should lie in a straight line is, by contrast with your hypothesis, when the system is at rest, in other words when the key is fully up. It is in this state that a) all the static friction needs to be overcome and b) the normal force is at its greatest. Once things are moving, at whatever velocity -- and even the maximum velocity in this case is low -- then we are dealing with kinetic friction. Besides this, we are not dealing with two perfectly hard and regular surfaces. When the key is struck there is compression of the cloth and a spreading of the load, which spreading of the load incidentally has no effect on the friction, and this compression is reduced as the blow progresses. In practice there is not a single point but rather an area of contact, especially as the blow is initiated. Which point in this area is to lie on the straight line and why should this part be preferred over another point? I'm not answering the question but merely suggesting that it's a valid question. The matter could be resolved mathematically but I suspect it would involve very difficult mathematics since we are dealing with a dynamic and not a static system, and a far more useful and convincing test would be a scientifically devised practical experiment, which is not quite as simple as it first appeared to me. Just as the religious measuring of static down-weights and return weights gives no accurate indication of the experience the player will have of the piano's heaviness, so the drawing-board "magic-line", as other posters call it, is quite unrelated to the actual forces at play and, as I've said, can be said with confidence only to be less wrong than other arbitrary positioning might be. JD
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