Magic (splitting hair) lines

[ed440 at mindspring.com]

Mr. Foote-
Your analysis makes sense to me.
Consider as well that as cushion and knuckle settle, the capstan will get cranked up to compensate. If we start with perfect magic line orientation, we'll be above after settling and compensation. If we start with your arrangement, after settling and compensation we are closer to the official position.
Having said that, if these things had to be perfect to work very well, there wouldn't be pianos.
Ed Sutton
>
>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 
>http://www.uk-piano.org/edfoote/index.html
>www.uk-piano.org/edfoote/well_tempered_piano.html
>