Key Leads and Inertia

[Bill Ballard]

At 10:05 PM -0400 6/10/03, Mark Davidson wrote:
>I wouldn't say that static balancing is meaningless, but for Stanwood's
>system to work, you have to have smooth weights AND smooth geometry.  I think
>the latter is understood, but not necessarily emphasized enough.  Without
>smooth geometry, the system falls apart pretty quickly.

Actually I like a system which is based on both smooth weight AND 
geometry. Kinda like laying an ET in which the 3ds/6ths and 4ths/5ths 
all find themselves smooth. The system I first learned seemed to 
imply that friction problems could be dealt with by weight.

>For instance, add two equal weights to a key, one in front of the balance
>rail and one behind, such that the FW is not changed.  Correct me if
>I'm wrong (like you wouldn't) but I don't think any of Stanwood's
>measurements can detect the presence of those weights.  But
>adding those weights violates the "smooth geometry" assumption

I don't understand how the geometry gets changed by adding 
"canceling" weights. Yes, the FW measurement would not detect this 
maneuver, but there is nothing in Stanwood's Metrology which would 
lead one in that direction. As you point out, it's a blind spot. 
Indeed the purpose of smooth (and appropriate) SWs is so that the 
front of the key doesn't have to get loaded up with unnecessary 
weight.

Not to say that adding weights to both sides of the key 
simultaneously is useless. It did prove to be the answer for Rick 
Baldassin, on one particular occasion.

>First, the keys are the heaviest moving part of the action, but
>unfortunately have the most irregular geometry (I'm talking about
>the rest of the key, notthe leads).  Each key is a different shape,
>black keys different from white keys, different widths, etc.  So the
>"smooth geometry" assumption holds up least well in the keys, which
>have the most weight.  This isunfortunate.

No quite so. Most of David's measurements are based on taring 
(zeroing the meter). Take for example that lever of "most irregular 
geometry", the key. Most of the irregularities you mention occur on 
the front half of the key. When we measure FW, what we are measuring 
is actually how much heavier the front half of the key is than the 
back half. One thing which we expect to find in the front half of the 
key is lead, but the other things you mention (difference between the 
nats and sharps, between a D and G key) are also in the front half of 
the key. They may not be made of lead, but because they're in the 
front half of the key, they're contributing to why the front half of 
the key is heavier than the back.

>Second, the thing we ultimately want to measure is really key acceleration.
>Yet there is NO direct measurement of acceleration.

I'm surprised that nobody has mentioned the optical velocity sensors 
which the digital player mechanisms are based on. I wouldn't happen 
to know how many points in he key/hammer stroke the Disklavier system 
measures velocity, but to measure acceleration, you really need only 
one velocity, the terminal one. That plus the time interval gives you 
acceleration.

But If there has been anything constant in Stephen Birkett's beacon, 
it is the importance of the slope. It's a flatter slope which tells 
us that an action will become increasing more tiresome under forceful 
play. I wouldn't be interested in reading acceleration unless I had 
the corresponding force figure which produced this acceleration. At 
that point, I probably want a pair of them (so's I knew what the 
slope was).

>This suggestion has the immediate problem that you are once again
>adding weight some of which is used to overcome friction.  Smooth or
>very low friction would be required for this to work well, and some
>experimenting to determine how much of the additional weight goes
>toward friction unevenness vs. inertial unevenness.

Yes, lease, by all means, let's separate weight and friction. But I 
don't think your experiment should be bothered with escapement weight 
(the 800# gorilla in the minimal sound). It would demonstrate what it 
wants to simply by arriving at the string, whether that motion 
included an escapement. But your experiment still does concern itself 
with the soft zone, and the area which concerns Stephen , Richard and 
Phillip is the "outfield" of the hard zone.

>Suggestion 2 is to find a way to directly measure the rotational inertia
>of the keys.  That's hard, but not impossible.

Richard is pressing ahead as hard as he can on this. But I haven't 
heard Stephen mention yet that modeling it (so that you even know how 
to measure it) requires a university lab full of equipment and a 
funded grant. (I remember when he was approaching the PTG Foundation 
to underwrite such a project.) I gather it does qualify as rocket 
science. I also don't think that making the pianists happy requires 
rocket science. (Pianists can always be bought off with a really good 
voicing.)

Then we'll be able to load onto the capstan, the rotational inertia 
of the rep and shank (with hammer).

>Then add weights to smooth out both balance weight and key inertia.

Personally, I'd bet that Stephen has already worked this out, and 
that Richard will be the next to.

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

"We mustn't underestimate our power of teamwork."
     ...........Bob Davis RPT, pianotech '97
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