[pianotech] Action Ratios Recap

[David Love]

BTW the practical application of the SBR is that much like the PR can be
interpreted to mean that with a PR of 5.5, 1 mm of key dip will produce 5.5
mm of hammer rise, if the SBR is 5.5 then 1 gram of added SW will produce
5.5 grams of added BW.  By direct relationship this can be translated to the
impact on the FW.  

David Love
www.davidlovepianos.com

-----Original Message-----
From: David Love [mailto:davidlovepianos at comcast.net] 
Sent: Sunday, January 17, 2010 9:40 AM
To: 'pianotech at ptg.org'
Subject: RE: [pianotech] Action Ratios Recap

Nick:

In response to your post (below) and another post inquiring about the
Stanwood method:



First I'd be interested to know which different methods yielded which
results.  Second, and in response to a previous inquiry you made about
Stanwood's SBR.  Stanwood's equation of balance is written as:  

balance weight + front weight = wippen weight x the key ratio + the strike
weight x the strike ratio.

The SBR can be isolated as follows:

SBR = (BW + FW - (WSW*KR))/SW

The terms defined as:

BW = balance weight
FW = Front Weight
WSW = Wippen strike weight
KR = key ratio (expressed as a fraction, a key lever with a 2:1 ratio would
be expressed as .5)
SW = Strike weight

This is all published material, btw.  If I have written something
incorrectly then I'm sure someone will bring it up.  I'll leave it to you to
be familiar with how the measurements are taken but the SBR reflects, among
other things, the efficiency with which the action lifts weight.  The
equation of balance being used to fine tune the front weights but also gives
an indication as to what the strike weights can be given an action with a
certain SBR without creating problems with excessive front weights (too much
lead).  This is a useful tool in setting up or correcting problem action to
determine just what your target weights should and can be.  It is less
helpful in establishing action regulating parameters.

Given what you have written below and the difficulty of determining the
exact action ratio by measurement due to different measurement protocols
and, perhaps, the difficulty of measuring accurately.  This gives a second
option for determining how the action is performing in terms of weight
efficiency and will let you know very quickly if you are likely to have a
problem.  As I mentioned, it won't give you any indication of how the action
will regulate necessarily.  But the method of determining the actual
regulation specs by distance formulas has its own problems as we can see.
Assuming one can calculate the theoretical action specifications, even to
multiple decimal places, how that action actually regulates will vary based
on how the arcs scribed by each lever intersect (whether they intersect in
one distinct point or two points, and to what degree the interface between
these two levers falls on or near that point referred to colloquially as the
line of convergence and written about in Bob Hopf's article on action
elevations.  The actual efficiency (practical output) of this product of
levers, therefore, might vary usually in the form of some degree of loss of
efficiency.  The transfer of energy, which is in effect what happens between
these levers, must be less than 100% efficient because of some degree of
sliding motion that necessarily takes place.  The degree to which that
sliding takes place will cause a drop in actual output from the measured and
calculated ratio.  I guess that's a statement/question.


Interestingly, the ratios as calculated by products (as you have referred to
them and hereafter know as PR) and the SBR yield slightly different numbers
though both express a relationship between input and output.  Stanwood has
recently pointed out that when comparing the ratios as a ratio of ratios
(PR/SBR) that "better" performing actions seem to produce a number >= 1.
Why that is, I'm not sure but I'm interested to know if anyone can answer or
speculate as to why that might be so.  

Using both methods, I find, is necessary to insure the most predictable
result and avoid unexpected results and it may be that the numbers need to
be considered separately and simply don't integrate.  Some kind of unified
theory and practical way to integrate the two would be a worthwhile goal
otherwise.   

David Love
www.davidlovepianos.com



Nick Gravagne wrote:

> I have long thought that we yet lack a consistent and unified approach
> to the subject. I recently evaluated a Young Chang action by physically
> measuring the lever arms using three different methods, resulting in
> three different ARs of 5.9, 5.7 and 4.6. The AR that mostly agrees to
> the actual measurement (a bit tricky to do) of dip and subsequent hammer
> rise is the 5.7 AR.