Action Ratio, was: More off the wall stuff

[Richard Brekne]

Yes yes Isaac

But this is an unneccessary complication for our purposes in describing
action leverage.... and indeed no method of  measuring ratio that I know
of even comes close to addressing these... nor do we need it to.

If we want to set up and action we want to do two things. We want to
allign the geometry as close to as optimal as is possible, and we want
to
decide the overal action ratio characteristics. This can also includes
different combinations of the individual levers ratios I suppose, but I
havent gotten into designing and action from scratch yet.

While its true that leverage changes through the keystroke, its also
true
that one can take the mean value of all these possible discrete points
on
that leverage curve and come up with a meaningfull description of the
actions general ratio characteristics. This mean will correspond nicely
to
Stanwoods formula, and to Terrys method of looking a key travel vs
hammer
travel. I cant see that use of the Balance equation does anything more
then finding that same mean value.

Take the following re expression of the Stanwood formula which I worked
out a couple weeks back.

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

The only unfamiliar terms here should be HR (hammer shank ratio) and WR
(whippen ratio). This is really what the Stanwood equation expresses.
And
its pure Archimedes with the three weight parameters worked in. Reduced
all the way down its just  d1 * W1 = d2 * W2

follow :
((SW x HR x WR) + WW) x KR = (SW x R) + (KR x WW)

 … divide both sides by KR
(SW x HR x WR) + WW = ((SW x R) + (KR x WW)) / KR

...simply the right side of the equality
(SW x HR x WR) + WW  =  (SW x R) / KR + WW

……subtract WW from both sides.
SW x HR x WR = (SW x R ) / KR

…… multiply both sides by KR
SW x HR x WR x KR  =  SW x R

 ……. and finnally dividing both sides by SW.

HR X WR X KR = R

You see ?

This means of course that Frontweights can be solved for by the
following
instead of the Stanwood formula for those who know what to do with such
things.

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


Anyways....Since consistancy between the for mentioned three
perspectives
is neccessary to begin with, and because consistancy is a good idea when
exchanging data about different actions.... ie... we need to make sure
we
are all taking about the same ratio.... I think its best to measure the
action ratio as I have mentioned before. Which means the Hammershank
ratio
is taken from the centerpin straight down the shank, the distance to the
middle of the moulding divided by the distance to the middle of the
knuckle core.

Thats my present understanding of things anyways.


Cheers

RicB

Isaac OLEG wrote:

> Dear Richard,
>
> Do you mean distance leverage and force leverage are suppose to change
> the same at the same time ?
>
> and that the only difference that we can find between the 2 is induced
> by friction change or mass distribution change ?
>
> Confusion is that lever laws apply to levers (fixed lengths) and  tell
> us about force direction.
>
> The lever's lengths is changing at the whippen/capstan, depending of
> the configuration.
>
> The contact line between the parts in the piano  action is a tangent
> following a path, the leverage is changing accordingly of the change
> of the lever's length during the travel.
>
> Indeed David's method of measuring is not totally static, as geometry
> method is, because it takes in account the result of these different
> levers, that is what I wanted to say.
>
> That is how I understand it anyway, does not mean we can't use any of
> the above methods...
>
> Let's take a piano key, for instance, a very slight change in it's
> attack angle change its leverage enough to be noticed by a change in
> DW even if the leverage is only better at the beginning at the stroke.
>
> Cheers yourself , and take care of the !!!!!!!
>
> Isaac OLEG
>
> Entretien et reparation de pianos.
>
> PianoTech
> 17 rue de Choisy
> 94400 VITRY sur SEINE
> FRANCE
> tel : 033 01 47 18 06 98
> fax : 033 01 47 18 06 90
> cell: 06 60 42 58 77
>
> > -----Message d'origine-----
> > De : Richard Brekne [mailto:Richard.Brekne@grieg.uib.no]
> > Envoye : dimanche 19 janvier 2003 13:45
> > A : oleg-i@wanadoo.fr; Pianotech
> > Objet : Re: Action Ratio, was: More off the wall stuff
> >
> >
> > Where does all this mystery come from  ?
> >
> > Davids formula is just another way of applying the law of
> > leverages. Its
> > easy enough to factor out the weight components of the equation and
> > arrive at a more simple and straightforward equality for the action
> > ratio. This is, and can never be anything else then the
> > product of the
> > ratios of the three levers.
> >
> > There has to be consistancy between weight, distance, and speed in a
> > levers ratio. Whatever the ratio of any given lever is, its
> > has the same
> > effect on these three. This is basic to the law of levers.
> >
> > Any ratio that results in something else has simply got to
> > be a measure
> > of something else. Could be a valuable something else in another
> > context, but just so..
> >
> > Cheers
> >
> > RicB
> >
> >
> > Isaac OLEG wrote:
> >
> > > Terry,
> > >
> > > The drawback of this method is that the leverage is
> > changing  during
> > > the stroke (more or less depending of the action setup, kind of
> > > whippen, etc...
> > >
> > > At this moment seems to me that only David's method gives
> > an evened
> > > appreciation of what goes on for all the stroke.
> > >
> > > Regards
> > >
> > > Isaac OLEG
> > >
> >
> > --
> > Richard Brekne
> > RPT, N.P.T.F.
> > UiB, Bergen, Norway
> > mailto:rbrekne@broadpark.no
> > http://home.broadpark.no/~rbrekne/ricmain.html
> >
> >
> >

--
Richard Brekne
RPT, N.P.T.F.
UiB, Bergen, Norway
mailto:rbrekne@broadpark.no
http://home.broadpark.no/~rbrekne/ricmain.html