What's all this I hear about Inertia ?

[Richard Brekne]

Greetings

    Unfortunately it's not the case in this particular formula because
    of the relationship between BW and FW.  Change one and the other
    changes in the opposite direction in an equal amount.  Increase FW
    (front weight) by 5 and BW (balance weight) decreases by 5 so any
    change in FW or BW will not change the value of R.  You cannot
    change them independently without changing the other in this
    particular formula.  Makes sense too since adding (or subtracting)
    lead to a key certainly doesn't change the action ratio, it just
    decreases the touchweight.   


In the formula, as written, Nick has it right. Thats why I responded to 
the quip about having problems with my math that is was not a math 
problem, but a bit of a brain fart. As written in that post, if you 
change FW  then R changes. That in real life it doesn't work out that 
way simply reveals what Nick was saying in his polite smoothing over of 
my little stumble yesterday. Clearly... if you simply take  R = (BW + FW 
- WW) / SW  as it is and change FW then R changes too. The point Nick 
was making is that you have to KNOW that changing FW means an equal and 
opposite change in BW so that their sum remains the same. This is not 
obvious from the equation in written form. The same thing happens with 
WW for that matter.  Change WW and you have to remeasure or re-calculate 
BW. Nick was pointing out that BW is a dependent variable.  You cant 
just <<change>> BW. You first have to change some physical quantity to 
effect a change in BW.  And of course you dont just see that in this 
kind of equation. Curiously.... if you isolate the same formula for BW 
all this comes pretty clear.
BW = (SW*R) + (WRW*KR) - FW.

Also.... Stanwoods formula is far more useful then just using it in its 
form for solving for R, and I think most folks that use Stanwood 
concepts a lot are only interested in the ratio in terms of comparing it 
to an appropriate set of hammer radius weights. The balance equation is 
also extremely useful as a diagnostic, as David Stanwood himself pointed 
out to me here in Bergen. Once R is established, and both FW's and SW's 
installed... then both key to key friction and BW variations are 
directly identifiable and can be addressed very effectively.  Then too, 
once R is established and SW is decided upon then you can specify the BW 
you want and solve for the required FW.  Rewriting to solve for FW you 
get  FW= (SW*R)+(WRW*KR)-BW.  Since SW, R, WRW and KR are knowns here 
then specifying BW will yield FW.  There are other ways to go forward 
here as well if one wants too.  About the only thing really that is 
usually taken for granted is the WRW. And even there you can get 
creative if you want.... and some do. Suggestions for how to manipulate 
the wood makeup of the whippen to result in less weight...even increased 
<<aerodynamics>>  have all been suggested from time to time.

For my own part... I usually simply take a simple distance ratio... 
hammer motion for key motion. Plug it in as R, a default set of FW's, 
and a SW curve that is appropriate for R, run the numbers and look at 
the resultant BW.  If its reasonably close to what I want for BW then I 
just install without further ado. Then I run my BW and Friction 
diagnostics and adjust individual key ratios and friction values as 
needed to bring the whole action into a dead even balance weight and 
friction condition.  Its the eveness I am most after as in my experience 
that is far more important (given reasonable values for key and hammer 
mass) to the pianist then anything else.  If I find some need to get all 
creative about just how much key leading or hammer mass I need... or 
what kind of ratio I think is called for,  well I can. But I find that 
sticking to somewhere between 5.3-5.7 SWR and using anything between a 
3/4 medium to 1/2 top SW curve with my default leading table ends up 
working just dynamite every time. 

I mentioned plugging in a simple distance ratio as the R in the balance 
equation. This is clearly a different R as I've stated before. Yet they 
are never so far away that the resultant target BW is more then very 
easily and uniformly adjusted for by adding (or subtracting) a couple 
two - three grams of FW when all else is done. Works great, lasts a long 
time.

All this said... and as I stated last time, I look very much forward to 
what David Stanwood has to publish on his <<Ratio of ratios>> concept. 
If there is some  geometric configuration where the SWR and the DR come 
into some kind of coincidence or some optimal ratio between them.... 
then it will be no doubt a very useful contribution to our knowledge base.

Cheers
RicB