Leverage and Dip

[David Love]

Bill:

You're right in that the formula is not very practical in it's application.
However, measuring the action ratio by comparing key travel to hammer travel
is useful and need only be measured to the point of jack contact with the
let-off button to give a usable number.  In fact, I've gone to using this as
a preliminary measure rather than the multiple samples method that, I
believe, we both use.  The method for measurement requires calipers but can
be done very easily on the bench or in a customer's home.  Depress the key
to a known quantity using calipers in the locked position secured under the
key frame.  While holding that steady with one hand measure the distance the
hammer has travel upward when compared with it's neighbor.  Divide hammer
travel by key travel and you have the action ratio.  Take measurements at
each end of the key board and in the middle and you have a fairly good sense
of what's going on.  Figure the action ratio will change by .4 for each mm
change in the knuckle placement or for each 2 mm change in the capstan
placement.  You can use these figures to estimate the change required to get
the targeted ratio.  Try samples using Stanwood formulas to calculate
SW-FW-BW relationships to see if you are on target.

I have found that targeting a specific action ratio works best for me.  Once
there I know the range of what I can accomplish given a certain hammer set
and targeted FW maximum level and balance weight.  I am finding that setting
the ratio up at 5.75 gives me the regulation specs that I want: .390 dip and
1.75 blow or the equivalent in metric.  For instruments requiring longer
blow distances I aim for 5.85.  By plugging this number into the Stanwood
equation it is very easy to calculate the hammer weights I will need
beforehand and I can specify with hammer manufacturers the unbored,
untapered weight of the hammers.  On a concert instrument that means I will
have to push up the balance weight or FW closer to maximums to accommodate a
slightly heavier hammer and slightly higher ratio.

As far as R.B.'s question goes, I think it is better to determine what
action ratio sets up for the dip and blow distance that you need and go from
there.  Unless you feel compelled to wander outside of those parameters for
some reason, you want monster hammers, or you are changing hammers only on a
system where changing the geometry is not in the scope of the job, this
allows for consistency from job to job and eliminates much of the futzing.

David Love

---- Original Message -----
From: "Bill Ballard" <yardbird@pop.vermontel.net>
To: "Pianotech" <pianotech@ptg.org>
Sent: October 02, 2002 9:45 PM
Subject: Re: Leverage and Dip


At 8:06 PM -0700 10/2/02, David Love wrote:
>The action ratio not only refers to the relationship between change in
>weight at the hammer and the resultant change in weight at the key, it also
>refers to the relationship between key travel and hammer travel.  A quick
>way to calculate the action ratio is by measuring how far the hammer
travels
>for a given amount of key travel.

Or measuring angular rotation of the key and hammer strike point.
It's a little tricker but it allows you to take shorter sample of the
stroke, say, cropping out escapement and after-touch. Just a note of
spice up the discussion.

>The formula that would be useful to you is:
>
>(Blow Distance - Letoff) / (Key Dip - Aftertouch) = action ratio

That's a nice formula. may I clarify that a little? The dip and the
blow both have one thing in common, a period of their arc when
escapement is occurring (i mean by this the actual scraping out from
under the knuckle). "(Blow Distance - Letoff)" seems to suggest the
highest the hammer is lifted by the jack below it, which would
include measuring through the break into aftertouch.

Would that mean that the motion of the hammer during the entire
(however brief) period of escapement, was worth entering into the
formula? I think not, The escapement is a period of decimated
vertical motion, hovering on disappearance.

I'd much rather eliminate it, and I'm prepared to balance the
equation so as to eliminate it. That means, stopping the sample of
the dip right at the point where the key (at the front-most position
in the lever train) first encounters the resistance of escapement.
That way both arcs are cropped of areas of uncertainty. The equation
is also balanced.

Unfortunately, RicB has asked us to use the entire dip and not a more
abridged measurement of it, as mine is. So how do we figure in those
missing amounts of travel? Well, they're in two parts. The
aftertouch, you might as well dial in. The wild card in this is the
portion of the key's stroke during which escapement is occurring.
That depends on jack's leverage ratio, modulated by the rep's ratio.

I haven't gone out to the shop and measured anything yet, but I
suspect that as the leverage shrinks (and the dip needs to increase
for a constant blow) the portion of the key's arc during escapement
is amplified. Inverse relationship. So Rick's problem is one more of,
if his leverage is too high (and dip has to be reduced) will he still
want the same size aftertouch? Or will he want to maintain the same
proportions among the three components of the key's arc?

Only the Shadow Knows..........

Bill Ballard RPT
NH Chapter, P.T.G.

"All it takes is running your hands across the black granite at the
Vietnam Memorial to understand what mistakes do
     ........... Sen. Lincoln Chaffee, Senate Foreign Relations Comm.,
9/26/02
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