Key Excursion

[A440A at aol.com]

Bill writes:

<< The inefficiency enters when the radius of the pivoting moves away  

from normal (perpendicular) to the direction you want the payload to go.

I agree.  Though I think there are various philosophies inre the "magic line" 
that are in contention with one another.  (see below)


>>Say (in a grand action) The back lever arm of the key  

 will move in an angular fashion,  At the moment when that lever arm is 
horizontal,the vertical vector  

will be 100% and the horizontal, 0%. Optimum efficiency, right? The  

further that lever arm swings upwards from perpendicular to the  

desired motion, the more the more the horizontal vector picks up at  

the expense of the vertical vector. << 

       I don't know that "horizontal" actually addresses the interaction with 
the whippen's arc.  If the whippen was also horizontal at the same time as 
the key, then yes, we get 100 % efficiency for that micro interval where it is 
all lined up. 
      I am a little foggy on the exact meaning of  "upwards from pe
rpendicular to the desired motion" because I am not sure if desired motion is indicated 
as straight up or not.  Maybe my problem is trying to link horizontal and 
"upwards from perpendicular"?? 

     As to the "magic line" approach to setting up actions; as both levers, 
(key and whippen) pass through the coincident point, (the point at which a line 
intersects both action centers as well as the contact patch),  there is the 
minimum amount of friction and the maximum amount of energy transferred.  Where 
do we optimally want this point to occur?  I agree with Bill, I like the 
actions that allow this to occur at let-off.  This is why. 
     My thinking is that friction is speed dependant.  At the beginning of 
the key-stroke, when the "wiping speed" (WS), is low, the friction is minimal, 
even though the geometry is at its most inefficient.  In an action that has its 
coincident point occuring at let-off,  WS will slow geometrically as the key 
is depressed, continually dropping through the keystroke, finally reaching 
zero at the point of maximum key velocity and control, (let-off).  Compare two 
examples:
     1.  The first situation describes a "rising-rate" geometry.  If the 
conicident point is at let-off, then there is an effective increase in the key 
ratio occurring during the key stroke, ie. for a given increment of key movement, 
the hammer moves more later in the stroke than at the beginning. This creates 
an effective "first gear" in getting the action started.  At the same time, 
the WS will be decreasing in step with increasing acceleration of the action 
parts.  The actions tend to feel like there is a lot of control and power. 
     2.  If the action has the coincident point at rest, then from there on, 
each incremental movement of the key produces less hammer movement, while at 
the same time suffering from constantly increasing friction.  The combination 
of increasing friction and constantly decreasing action ratio makes for poor 
response.   These actions often feel weak, unresponsive and often hard to 
control.  

     Setting the action up so that the coincident point occurs mid stroke 
might be a way of avoiding # 2. and is thus the factory standard approach. I 
don't know if they consider the advantage of rising rates in determining the 
action lay-out.  Production tolerances and balance sheets may make it a moot point, 
and avoiding #2 is more important that that last 2% of performance.   
        The Steinway accelerated action is, in theory, designed to create a 
rising rate during the down stroke.  However, whatever changes can be effected 
by the curvature underthe balance hole are not as big as what can be had by 
getting the whippen and key working together.   


>>What an extreme example of action inefficiency? How 'bout a vertical  

action with wood dowels on tall wires.<< 

      Agreed, however, I have a 1890 Steinway upright that plays like silk. 
Players rave over it, and there are them tall wires and all!  



>>Usually the matter of inclination is settled by how well the keyboard  

is going to fit within the case parts, and these ideal of efficiency  

of angular motion are left behind in the dust. >>

      I have seen the same thing.  Sadly, it is often the case that to make 
some simple changes requires that we also address the underlevers' 
installation, and suddenly it begins to look like a lot of work!  
Regards,



Ed Foote RPT 
http://www.uk-piano.org/edfoote/index.html
www.uk-piano.org/edfoote/well_tempered_piano.html