[pianotech] Action Ratio measuring

[David Love]

Good question.  There are different methods of measuring the action ratios:
top of the key to the bottom of the balance point to the top of the capstan,
hammer flange center to the knuckle contact point of the jack and to the tip
of the hammer, etc.  I do it this way largely because I've been convinced
that this is the proper way to do it.  But I can't give you the precise
engineering argument.  When I play around with my action model, this seems
to yield consistent results.  I'll have to leave it to others to make the
arguments.  Nick Gravagne's class coming at West Pac III would be a good
place to start it sounds like.  

The issue of the relationship between the action ratio and strike weights is
definitely important and you are correct: higher action ratios will work
best with lighter hammers and vice versa.  The reason is because of the
inertia generated in the system that is a function of the relationship
between the action ratio and the amount of weight being lifted (mostly).
While most people consider the primary issue the number of leads in the
keys, that's really a secondary issue.  A system with high inertia  because
of a mismatch between the action ratio and strike weights (let's say a high
ratio with high strike weights) will need a lot of lead to balance the
action at normal levels.  But the high inertia in the system is really more
a product of the relationship between the ratio and the strike weight than
it is a function of the added lead.  That added lead adds to the inertia but
it is not mostly responsible for it.  BTW the inertia can be too low as well
as evidenced by low action ratios with low strike weights.  Not good either.


Fandrich and Rhodes at the convention in Seattle addressed this issue and
the article by Mallory that Nick Gravagne refers to also addresses this.
http://pianobytes.com/ActionAnalysisinertiaa.htm for those who want to delve
into the details.  

One can, however, determine an acceptable relationship between the strike
weight and the action ratio indirectly by using the lead pattern which
results in the so called "Front Weight" of the key, a term used by Stanwood.
I've attached a guide of Front Weight Maximums.  You'll have to review
Stanwood materials to determine how this is measured but basically I use his
platform and a scale.  You can determine the maximum strike weight for any
given note by using the following formula derived from Stanwood's equation
of balance.

(FWmax + BW - 9)/AR = SW max

Or, the front weight maximum plus the balance weight target minus 9 divided
by the action ratio will give you the maximum strike weight for any
particular note.  A better target is about 80% of the Front Weight Maximum

So, for example, if the front weight maximum is 40 (that would be note
number 6 on my chart) and the balance weight target is 38 and the action
ratio is 5.5, then the maximum strike weight for that note will be (40 + 38
- 9)/5.5 = 12.5.  Since the shank contributes about 1.8 grams to the strike
weight (untapered Renner Shank), the hammer should weight no more than 10.7
grams.  Since the better target is 80% of the Front weight then you would
have (32 + 38 - 9)/5.5 = 11 grams.  Subtracting the shank weight the hammer
should weigh 9.2 grams.  You can basically figure out your entire hammer
weight curve using this method along with the FW maximums.  A review of
Stanwood formulas and procedures will help you here.  For those interested,
the number 9 comes from the average contribution of the wippen weight to the
system.  Typically a wippen SW is about 18 grams and its effect is seen
through the key ratio which is typically about .5 (see Stanwoods protocols
for measuring the key ratio by weight).  So the wippen only contributes half
its weight to the system.  As an aside, that's why drilling holes in the
wippen doesn't accomplish much.  For each gram of wood you take out you only
get about half at the key.  

Anyway, enough fun for the morning.  Gotta go to woik.   



David Love
www.davidlovepianos.com


-----Original Message-----
From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On Behalf
Of Brown, David
Sent: Thursday, September 20, 2012 7:30 AM
To: pianotech at ptg.org
Subject: [pianotech] Action Ratio measuring


Well, that is just me being unnecessarily thick! Every representation I had
seen showed measuring diagonally from balance point to key front / capstan.
Thank you , David. Can you do it this way because the  measurement at the
bottom instead of diagonally gives the same results?

If we could also explore a little more- once the action ratio is obtained ,
my understanding is that it is inverse to strike weight, higher ratio drives
lighter hammers better  with fewer touch weight problems and vice versa?

D Brown
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