Knuckle Size (was Re: All in a row)

[David Love]

Bill:

I appreciate the time you took to respond.  Letting the hammer set dictate
the SW curve makes complete sense now that I think about it.  Steinway
hammers, for example, are generally heavy at the upper end and forcing them
to conform to a predetermined curve, as suggested by Stanwood's published
zones, can require some razor blade and table saw gymnastics that may, in
fact, be unnecessary.

I have not been using a smart chart, rather I have been setting the curve
using my own calculations based on a manipulation of Stanwood's formulas and
guided by his FW maximums, but you have given me some ideas.  I can see that
if you start with a curve dictated by the particular hammer set, then you
would have to alter the front weight curve to maintain even SWR's while
keeping the FW's below his published maximums.  But that is not hard to do
by simply running calculations on some samples and determining where the
FW's should start at the low end of the scale for a given BW.  In the case
of a Steinway hammer, as mentioned above, that would mean FW's at the low
end of the scale would start below maximums and rise nearer to maximums as
you went up the scale.  If you were determined not to exceed them at any
point then you would only need to plot the 2 curves altering the SWR's
around the "sweet spot" via a mix and match of KR and knuckle radius to see
where to begin.  If, as you said, you needed to push the BW too high, or the
SWR too low then you could consider adding assist springs or, I suppose,
lowering the SW.

I have had a tendency to think of the curve represented by the FW maximums
as the ideal curve.  I am beginning to think that as long as the slope
remains within a range, as long as there are no irregularities, and as long
as the inertia transitions smoothly from bottom to top, that the piano will
feel fine.

A discussion of the problems of understanding the relationship between
weight and distance based leverage and which includes an analysis of
vertical and horizontal vectors is something I would like to hear.
Hopefully, that will happen on another day.

Thanks again.

David Love


Original Message -----
From: "Bill Ballard" <yardbird@pop.vermontel.net>
To: <pianotech@ptg.org>
Sent: November 11, 2001 8:49 PM
Subject: Re: Knuckle Size (was Re: All in a row)


> At 9:07 AM -0800 11/11/01, David Love wrote:
> >Bill:I may not have stated my question clearly.  I was wondering
> >about preferred
> >flange center to knuckle core distance (16mm, 17mm?) that you combine
with
> >.51 key ratio.  Do you have a preference and let the SWR fall where it
will
> >making adjustments by altering the hammer weight?  Or do you vary your
> >selection of the knuckle radius depending on the overall leverage of the
> >system and the hammer weight.
>
> No, I don't have a preference which is based on knuckle mounting
> distance. How that fits into my "hanging" of the action is minimal. I
> just figure that any hammer set can be pushed only so far towards an
> envisioned SW curve, so if a given set of hammers is committed to a
> particular action, the the SW curve is going to fall in a certain
> workable range. Those of you who do this stuff know what workable
> means.
>
> Thus Strike Weights are a starting point, a given. The Front Weights
> are the end point. How one draws the line from start to finish is
> proprietary but it means various contact points in the action will
> have to move to produce the particular SWR which will allow the SWs
> to be counterbalance with comfortable FWs (which, remember, are a
> good representation  of the level of inertia in the action) at an
> acceptable balance weight.
>
> But in the effort to properly balance (or hang) a set of SWs, both
> the key and the hammershank need to pitch in. Which is why, unless I
> have good reason not to (and that does happen) I simply assume that
> the business of properly hanging that action will be a lot easier if
> I start out with 17mm knuckle mounting distances.
>
>
> >The reason I ask is that I have found a trend in combinations of KR and
> >knuckle radii.  Depending on choice of hammer weight (a factor not to be
> >glossed over lightly) it would seem that a 16mm knuckle works with KR's
up
> >to .50; 16.5mm up to .52 - .53; 17mm up to .55, 18mm up to .60 or so.  (I
> >realize that there is also the wippen lever to consider as well which
will
> >change as the KR changes.)
>
> Six of one , half dozen of the other. A shorter knuckle mounting
> distance asks for a lower key ratio, and via versa. No surprise here.
>
> >The knuckle radius doesn't seem to really have a place in the Stanwood
> >formulas:  R = (BW + FW - (KR x WW)) / SW can be manipulated
algebraically
> >to isolate different variables.  But the knuckle radius remains out of
the
> >formula loop except to the extent that it impacts BW and therefore will
> >change R (Strike weight Ratio).
>
> You're right, and if you look at anyone's model, you're sure to find
> something left out. Consider this. Suppose you replace a 16mm/10mm
> (mountingdistance/knuckle dia.) with a 17mm/11mm shank. The knuckle
> has moved away from the shank center by 1mm, thus reducing its
> ability to amplify the SWs, but it has also grown taller by 1mm,
> driving the jack-knuckle contact point even lower from level. (This
> is the issue which Ron Overs so neatly dispatched with his action
> design.) Taking a shank at level, moving the knuckle 1mm out will
> reduce its overall leverage. The extra height of the knuckle will
> certainly make the shank leverage shrink just a bit more, and we
> should be thankful for this. But dropping the shank down from level
> to its normal point of rest above the bumper felts, the knuckle
> contact point is pushed even further down from level and further into
> the neighborhood where rotation produces horizontal motion (friction)
> instead of vertical (payload lift).
>
> It gets comlicated and there are more trde-offs than any of us care to
admit.
>
> >His formula also does not address distance leverages, that I can see,
except
> >to the extent that a certain range of SWR's will result in acceptable
> >regulation perimeters.
>
> You got that right. The actions's leverage is not being measured by
> distance but by weight.
>
> >Do you, when setting up an action, aim for a
> >particular distance leverage, i.e. a range of dip/blow combinations,
force
> >leverage, or both?
>
> If you want to look at it from that angle, then calculating the
> lowest SWR is easy. Measured the highest you can raise the hammerline
> and still slide the action in and out. Measure the deepest dip you
> can lay in without setting the sharps too unreasonably high above the
> naturals. That's the lowest overall leverage ratio which will allow
> for a reasonable regulation of the action. Remember, this is a
> measure of the action based on distance.
>
> >Where do you prefer to take your compromises from?  For
> >example, if you want to put on a very heavy hammer and don't want to use
> >assist springs, you can achieve an acceptable front weight within a range
of
> >SWR's.  But depending on the SWR chosen, your regulation specs will vary
> >somewhat.
>
> Why would I want to put on a heavy set of hammers which required
> amounts of front weight which really should be balanced by assist
> springs (to avoid the inevitably excessive FWs), and then not choose
> the help of rep assist springs.
>
> >Personally, I try to set my FW's below maximum by 10-15%, and
> >select KR/knuckle radius combinations that give me a .390 - .400 key dip
> >with normal blow distance.  The resulting SWR will dictate the SW zone.
>
> I don't let SWR dictate the SW zone.  I let the set of hammers set
> the SW zone. Then, instead of letting the specification of ".390 -
> .400 key dip with normal blow distance" (really, the specification
> for a particular SWR) dictate the SW, I let the SW and FW curves
> dictate the SWR. We're agreed that the FW curve should be specified
> (in your case, from the Smart Chart, I presume, and in David
> Stanwood's case, something proprietary.) We probably also agree that
> there should be a sweet spot for the SWR. For my part, I'm not happy
> to go below a 5.5 SWR. If the combination of SW/FW curve asks that
> SWR drives below that, I let the Balance Weight float upwards, and
> when that gets out of range, I put assist spring reps into the
> equation.
>
> But this example assumed a set of hammers which were rhinoceros sized
> and excluded the option of spring balancing.
>
> >It's not always possible to do that, sometimes the hammer of choice
forces a
> >compromise somewhere.  Maybe the more precise question is do you find
that
> >SWR always has a direct relationship to distance leverage and, if so, is
> >there a preferred SWR?
>
> Sure there is a preferred SWR, I've stated mine. As far as a direct
> relationship between SWR (weight based) and distance based leverage,
> there may be. But my model for distance based action leverage would
> have to include the losses in pure lift due to the inclination of
> levers. I admire any who has built their own spreadsheet models, but
> when I build mine, it will clean up this slight inaccuracy. A
> customer of mine has an engineering degree from MIT and has just
> retired up here to teaching math and physics at his old prep school.
> I described this problem of tracking the ratio of horizontal and
> vertical vectors of contact points between levers, and he said,
> "Piece of cake, the motion of cams." If I didn't have to tune pianos
> to pay bills, I'd take off a Friday afternoon and put together a
> model with him. He's ready.
>
> But as to a clear relationship between the weight and distance based
> readings of action leverage, I'm assuming that they'll be there, I
> can't guarantee as to how straightforward that relationship will be.
>
> Bill Ballard RPT
> NH Chapter, P.T.G.
>
> "I go, two plus like, three is pretty much totally five. Whatever"
>      ...........The new math
> +++++++++++++++++++++