Balance Weight and Ratios

[Dennis Johnson]

At  8:55 AM 2/20/96 -0700, stanwood wrote:
>BALANCE WEIGHT factors out the friction!!
>
>It's the
>BALANCE WEIGHT!!
_______________________


This may be a good opportunity to beg a little more elaboration as to the
nature of balance weight measurements. Previous discussion has been great,
but I still have questions.

It is clear that the amount of balance weight added to the rear tells us
specifically how much heavier the front half of the key is. However, I have
also noticed that the value for friction taken from balance weight
measurements may slightly increase over what that value was from normal
touchweight measurements. I found that friction values as taken from
balance weight measurements increased with low leverage shanks, but
slightly decreased with high leverage shanks. This would seem to indicate
that friction is increased by reduction in shank leverage more than it is
reduced by reduction in strike weight. Is the mass that is zeroed out, as
opposed to friction?

I can easily picture that the process of taking balance weight is really an
effort to reduce key and wip ratios to the front half of a simple lever
with its fulcrum at the hammer center pin. But specifically, "how does this
factor out friction"?  Why doesn't the value for friction taken from
Balance weight measurement decrease more than it does with high leverage
shanks and why does it increase with low leverage shanks (about .5 grams)?

__________

I have also had some thoughts on the differences between strike and motion
ratios. It would seem that the differences observed between these two
ratios lie in whatever friction wasn't factored out and/or minor
discrepencies in measurments. I believe that if we could also take balance
weight measurments to the nearest .1 gram these ratios would come out
closer than they do.

An even greater reduction in the differences betweeen SWR and SMR however,
can be achieved by measuring the back half of key ratio from point W to P
(see Pheiffer, this is value h). This is a line from the balance hole
straight up to the capstan contact point as opposed to the protion of a
straight line taken from the center of touchweights at the key front. If
this method were adopted though, our key ratio standard would change from
.5 to about .53.

For those who like loose metaphors, I see that SWR is to SMR as fine tuning
is to theoretically correct calculations without regard to inharmonicity (a
blank page on the SAT). There is no motion involved in measuring SMR. In
Pheiffer's book it is called Transmission ratio. Or, to state it in terms
of Downweight, this is what I get:



SWR/SMR = DW/(SW)(SMR)

This equation in this form actually says more, I think, than its reduced form:

(SW)(SWR) = DW

which says not much at all.



Thank you for any comments.



Dennis Johnson
johnsond@stolaf.edu


P.S.  When you measure SW from original old parts with worn, overcentering
hammers, do you still set the shank level for weighing?