[CAUT] Shank Strike Weights

[Ric Brekne]

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Hi Alan

Thanks for the welcome.  Been rather swamped with work these past months 
and have only been able to contribute sporadically on pianotech. 

As for the Stanwood FW's.  Let me first say I also respect Stanwoods 
work and appreciate what his thinking has led to.  That said, the 
Stanwood formula as written is the only thing that is patent protected. 
In other words, you can calculate Front Weights all you want as long as 
you dont use his formula, or a derivative of it.  Even that probably 
wouldnt hold up in a legal confrontation....but heck... why bother 
fighting it in the first place.

Its important to know that the Stanwood formula is really a cute bypass 
of needing to calculate the acurate ratio for the whippen and hammer 
shank levers individually in the exact position they are when the action 
is in balance.  He only needs the key ratio to find the overall ratio, 
because of the way he uses Balance Weight in the formula.  If you use 
simple Archemides rules for combining levers you simply come up with  
           

    Action Weight  = ((SW x HR x WR) + WW )

The weight felt at the front of the key is the Action Weight times the 
Key Ratio so the whole thing becomes

    (((SW x HR x WR) + WW ) * KR)

Which is a direct derivative of the basic d1 * W1 = d2 * W2 as applied 
to three levers Action Weight is what you need to balance with FW and 
BW.  i.e.

    FW + BW =  (((SW x HR x WR) + WW ) * KR)

Calculating FW's from here is a snap and perfectly legal as this formula 
is essentially 2500 years or so old.  The hitch is that you need to also 
calculate individually and correctly the correct ratio for the hammer 
shank and whippen individually in their positions when the action is at 
half stroke.  Rather tricky it would seem.... but you can by pass that 
problem again by a good approximation.  You end up close enough that 
your target balance weight is within 1-2 grams of your resulting one and 
since any error applies to the whole action uniformly, you can simply go 
back and add or subtract exactly that much of FW as needed... if you 
even bother.  

I personally have absolutly no problem using this approach anytime I 
wish.  Davids way is  more accurate and I respect his patent 
completely.  But this way is plenty accurate enough and really a bit 
quicker as you only need to measure one key and dont need to rely on 
your BW measuring techniques... which btw can be shown to vary rather 
widely from person to person.

Food for thought anyways.

Cheers Alan
RicB






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