Magic (splitting hair) lines

[V T]

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 

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