Key Excursion

[william ballard]

On Apr 18, 2006, at 11:59 AM, A440A at aol.com wrote:
> I don't know that "horizontal" actually addresses the interaction with
> the whippen's arc.  If the whippen was also horizontal at the same  
> time as
> the key, then yes, we get 100 % efficiency for that micro interval  
> where it is
> all lined up.

"Horizontal" actually doesn't exist in a grand action, with the  
possible exception of the long lever arm of the hammershank.  At  
rest, running at near level from the hammer center to the hammer  
strike point. The short lever arm of the shank running down to the  
knuckle is 50-60º, about the worst in the grand action.

> I am a little foggy on the exact meaning of  "upwards from pe
> rpendicular to the desired motion" because I am not sure if desired  
> motion is indicated
> as straight up or not.  Maybe my problem is trying to link  
> horizontal and
> "upwards from perpendicular"??

I should have been a little clearer, just having gotten back from  
seeing " V for Vendetta" at the local big-screen. Yes, the desired  
motion for the output of this lever system is straight upwards: the  
hammer at rest to the hammer at strike. The desired motion is  
vertical and perpendicular to that, horizontal, is what we'd like all  
these levers to be.

On Apr 17, 2006, at 10:31 PM, william ballard wrote:
> .....angular motion introduces a kind of inefficiency which we  
> wouldn't have to have if the motion were purely linear. (Imagine  
> the hammer mounted on the end of a piston.)


On Apr 18, 2006, at 11:59 AM, A440A at aol.com wrote:
>  As to the "magic line" approach to setting up actions; as both  
> levers,
> (key and whippen) pass through the coincident point, (the point at  
> which a line
> intersects both action centers as well as the contact patch),   
> there is the
> minimum amount of friction and the maximum amount of energy  
> transferred.

I should point out that what I'm talking about (breaking down angular  
motion into horizontal and vertical vectors) is a separate matter  
from the alignment with magic lines (all three of them). Separate but  
simultaneous. The former can be visualized as a diameter line  
rotating within its circle, that line being a single lever. If you  
want to go up, the greatest vertical motion is would be when the  
lever is horizontal. Etc.) The latter concerns two levers, and where   
their smoothest conjunction lies, so that one won't be digging into  
the other.

> Where do we optimally want this point to occur?  I agree with Bill,  
> I like the
> actions that allow this to occur at let-off.

I'm not sure I stated a preference, but I won't let that hold back a  
perfectly good discussion. Actually with either the above former and  
latter aspects of design, there is a particular orientation for  
optimum efficiency. You're about to say it belongs at one end of the  
stroke and not the other. I'd say that if you put it in the middle of  
the stroke, your maximum friction with be half of what it would be at  
either end of the stroke. But let's move forward with your point.

> This is why.
>      My thinking is that friction is speed dependant.

The component of friction due to inertial forces is; that due to  
gravitational force should be constant. More to the point however,  
the inertial component of friction is acceleration-dependent. Once  
the key has hit cruising speed, the inertial resistance and its  
resulting friction shrinks dramatically.

> At the beginning of the key-stroke, when the "wiping speed" (WS),  
> is low, the friction is minimal,
> even though the geometry is at its most inefficient.

By "wiping speed" do you men the extent to which two levers slide  
against each other, as oppose to one lifting the other? Coming from  
either of the above-mentioned situation (breakdown of angular motion  
of a singular lever, or "hitting the magic line"). .

> In an action that has its
> coincident point occuring at let-off,  WS will slow geometrically  
> as the key
> is depressed, continually dropping through the keystroke, finally  
> reaching
> zero at the point of maximum key velocity and control, (let-off).

Sounds like you're only considering the latter. There still remains a  
WS from the former, even though of the three levers, the key is the  
closest to level.

> Compare two examples:
>      1.  The first situation describes a "rising-rate" geometry.   
> If the
> conicident point is at let-off, then there is an effective increase  
> in the key
> ratio occurring during the key stroke, ie. for a given increment of  
> key movement,
> the hammer moves more later in the stroke than at the beginning.  
> This creates
> an effective "first gear" in getting the action started.  At the  
> same time,
> the WS will be decreasing in step with increasing acceleration of  
> the action
> parts.

I'd bet that while the key may still be picking up speed at the end  
of the stroke, the acceleration at the end is a fraction of what it  
is at the beginning.

> The actions tend to feel like there is a lot of control and power.

Agreed. With the initial inertial forces (both direct and frictional)  
out of the way at the beginning of the stroke, and with increasing  
efficiency as you approach the magic line, the pianist would sense  
that her/his strength was "buying more" and the wrestling match with  
opposing forces for control of that power is far less.

>      2.  If the action has the coincident point at rest, then from  
> there on,
> each incremental movement of the key produces less hammer movement,  
> while at
> the same time suffering from constantly increasing friction.  The  
> combination
> of increasing friction and constantly decreasing action ratio makes  
> for poor
> response.   These actions often feel weak, unresponsive and often  
> hard to
> control.

Agreed, the converse.

> Setting the action up so that the coincident point occurs mid stroke
> might be a way of avoiding # 2. and is thus the factory standard  
> approach. I
> don't know if they consider the advantage of rising rates in  
> determining the
> action lay-out.  Production tolerances and balance sheets may make  
> it a moot point,
> and avoiding #2 is more important that that last 2% of performance.

Keep in mind that whatever advantage may be enjoyed by the proper  
timing of the coincident point in the keystroke, the second magic  
line to be hit, runs from the rep center to the shank center. With  
the current style of shank short lever (ie., the full circle barrel  
hung from the underside of the shank), that never gets close to  
coincident by the end of the stroke. Even more out to lunch is the  
fact the when the jack starts to pivot (heck, scrape) out from under  
knuckle, the lever driving the knuckle has switched from the 1:0.95  
ratio rep to a 2:1 jack. The jack itself is barely 20º off vertical  
and moving towards vertical as it pivots. While we want the jack to  
slide out horizontally, this is also the direction which will produce  
the greatest friction (ie., the direction perpendicular to the force  
of gravity.

> The Steinway accelerated action is, in theory, designed to create a
> rising rate during the down stroke.  However, whatever changes can  
> be effected
> by the curvature underthe balance hole are not as big as what can  
> be had by
> getting the whippen and key working together.

Which makes me think, has anyone every tried using David Stanwood's  
key ratio measurement to detect a KR change from beginning to end of  
an Accelerated Action key. Although David's KR measurement is a  
static one, the two ends of the stroke could be simulated by leaning  
the balance pin in his set-up.

> Agreed, however, I have a 1890 Steinway upright that plays like silk.
> Players rave over it, and there are them tall wires and all!

No mystery there. Vertical actions are a different animal. The weight  
of an upright piano hammer is mounted on a (nearly) vertical shank,  
and is thus supported by center pin. The weight of a grand hammer is  
out at the end of a (nearly) horizontal shank, and is supported by a  
short lever arm 1/7 its length. Also, as a vertical jack pulls out  
from under the butt, it's moving away from the butt center decreasing  
the leverage and the way weight is perceived. As a grand shank pulls  
out, it's moving towards the butt center.

Lots to think about.

Mr. Bill

".......true more in general than specifically"
     ...........Lenny Bruce, spoofing a radio discussion of the  
Hebrew roots of Calypso music
+++++++++++++++++++++