Bill writes: << The inefficiency enters when the radius of the pivoting moves away from normal (perpendicular) to the direction you want the payload to go. I agree. Though I think there are various philosophies inre the "magic line" that are in contention with one another. (see below) >>Say (in a grand action) The back lever arm of the key will move in an angular fashion, At the moment when that lever arm is horizontal,the vertical vector will be 100% and the horizontal, 0%. Optimum efficiency, right? The further that lever arm swings upwards from perpendicular to the desired motion, the more the more the horizontal vector picks up at the expense of the vertical vector. << 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. 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"?? 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. 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. This is why. My thinking is that friction is speed dependant. 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. 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). 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. The actions tend to feel like there is a lot of control and power. 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. 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. 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. >>What an extreme example of action inefficiency? How 'bout a vertical action with wood dowels on tall wires.<< Agreed, however, I have a 1890 Steinway upright that plays like silk. Players rave over it, and there are them tall wires and all! >>Usually the matter of inclination is settled by how well the keyboard is going to fit within the case parts, and these ideal of efficiency of angular motion are left behind in the dust. >> I have seen the same thing. Sadly, it is often the case that to make some simple changes requires that we also address the underlevers' installation, and suddenly it begins to look like a lot of work! Regards, Ed Foote RPT http://www.uk-piano.org/edfoote/index.html www.uk-piano.org/edfoote/well_tempered_piano.html
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