measuring ratios/ popsicle puzzle

[A440A at aol.com]

I wrote: 
 >> a 6 mm block attached to a weighted length of 2X2 on the 
top of the key, and a dial caliper to measure how much the hammer rises. << 
and 
>>progressively using two 3 
mm blocks,  will tell me if an action has a higher ratio at the beginning 
of a hammerstroke (bad progression), or if the beginning ratio is lower than 
the final, (good progression).  <<

Dale writes:
<<  The use of smaller  than a 6 mm block takes  us in the direction of 
action  acceleration. >>

Exactly.  I have found that an action in which the ratio increases as the 
hammer travels feels better. I call this "rising rate geometry".  Whereas I 
haven't always been able to detect this effect by the Steinway patented 
"accelerated action" half round in creating this, I have found that whenever the capstan 
contact patch reaches the so-called 'magic line' at the point of escapement, 
the rising rate geometry is there.  
    I wrote in a much earlier post, that this set-up allows the initial 
acceleration of the action from an at rest position to be assisted by a lower ratio 
and as the hammer's inertia is overcome, the action progresses into a higher 
ratio.  The effect is the same as having a low gear on a car's transmission 
for moving away from a standstill, and a higher gear for greatly increased speed 
after the car is moving.  
   Consider the finger to be the 'motor', and it makes sense, (at least, to 
me), that a rising rate geometry allows maximum power with the least amount of 
effort. The same phenomenon exists at the intersection of the knuckle and 
jack, controlled, to a large degree by the size of the knuckle.  It seems that the 
larger the knuckle, the more rise in the rate,(but I haven't been able to 
reduce the other variables to ascertain how much change can be ascribed to 
knuckle size). 

    As far as confusing the method of determining ratio between this and 
Stanwood's, I don't use David's procedures for arriving at my relationship between 
SW and FW.  I use a visually determined curve drawn atop the charting of my 
FW's.  Where that curve orginates is in my choice of SW, which depends on the 
size of the piano, the intended venue, and the subjective desires of the 
pianist.  There are limits to how high FW can go without bringing in unavoidable and 
undesirable inertial results which, in some configurations, may force the SW 
lower than optimum.  How much keydip can be used will limit the amount of 
ratio available, given a set hammer blow.  I strongly prefer to limit key dip to 
.400" and I like no more than . 30" aftertouch.   

     Case in point. (here is the puzzle part)
      I am currently preparing to rehammer and reshank a 10 year old D which 
has a very high string height and a very low ratio (4.9). At 1 7/8 blow, the 
shanks are almost 1/2" off the cushions.   This action currently has 17 mm 
knuckle distance, SW in the upper middle range, FW in the average range, and 
ridiculously low DW of 50 gr. in the bass, 44 gr in the area of note 25, and 40-42 
gr. from note 32 on up.  BW on A0 is 40, tapering down to 33 at note 73.  
      I could elect to reduce the FW, keeping all other things near the same. 
However, this would not address how high the hammers are off the rest 
cushions.  It would not increase the power,either.  What would you do? 
( I already have a plan of action, which entails three changes, but will be 
interested in other's interpretation.)  

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