Hi Ed, If there is hair-splitting to be done, I am all for it. Your reasoning is correct in that the ratio peaks at the "magic line" and drops to either side. I think, the reason an action designer would be tempted to place the intercept with this line at half blow is to minimize the variation of the action ratio. The "magic line" at half blow will give the least variation of the ratio over the stroke. Your point about tailoring the ratio to the friction along the stroke is certainly more detailed than that. The place where the "magic line" appears (to me) really far off is between the wippen center and shank center. This line never comes even close to the contact point between the knuckle and the jack. There may be a very good reason for that, but short of building an action that corrects that, I cannot say what the practical effect of this misalignment is. I think Ron Overs dealt with both "magic lines", and those of you who had a chance to play his piano in Rochester could possibly tell the rest of us how the action felt in comparison to a standard geometry. Vladan ============================================== Ed Foote wrote: Greetings, 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. I think this is why: 1. There exists a variable "rate" when two arcs intersect, such as happens between the key and whippen. (I believe the technical reason for this is termed "angularity") In our case, for every unit of key movement, there is a corresponding distance the whippen moves. The farther the capstan/heel intersection is from the magic line, the less whippen movement per unit of key movement there is. The maximum rate is found when the two arcs intersect on a common axis, i.e., the "magic line". Assuming that the arcs' intersection point is below the magic line at the beginning of the stroke, the rate is at a minimum in the beginning. To a small degree, this allows more key movement per unit of movement of the whippen. In effect, the key is in a "lower gear" relative to the whippen. In overcoming the inertial resistance of the action, the lower rate helps reduce the effort to set the parts in motion. As the intersection point approaches the magic line, the rate increases, reaching a maximum when the intersection of both arcs is exactly between the centers. It is at this point that the key is moving the action at its maximum leverage, (a "higher gear"). This is advantageous in transferring power from the finger to the hammer with the least amount of effort. 2. 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. Even though the maximum misalignment is found at this point, the effect of friction is minor compared to the inertial effect of the parts at rest, which the lower "gearing" helps. As the contact point approaches the magic line, the friction lessens, finally disappearing as the magic line is reached. Since let-off represents the addition of friction from a variety of sources, (the movement of the jack against the knuckle, the friction of the tender on the let-off button, the contact between drop screw and pad), I think reducing the capstan/heel friction to zero at this point helps. With these two items in mind, consider what happens when the magic line is reached at half blow. From that point on the rate is decreasing and the friction is increasing. So, approaching let-off, the "gearing" is beginning to decrease as the hammer is supposedly reaching maximum velocity, and friction begins to once again increase as escapement approaches. These two conditions are opposed to what I want the action to do. In an attempt to facilitate the extremes, i.e., maximum power when needed, and the most delicate pianissimo playing possible, I want greatest mechanical efficiency and the least friction at the very point of escapement. I find that this is generated by placing the capstan/heel intersection on the magic line at the beginning of let-off. My experience says that all this is so, and my logic concurs, but that don't make it necessarily true! I would be interested in what others might have observed. Regards, Ed Foote RPT __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com
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