Hi Frank good post And...IMO a heavier stick is also usually a stiffer stick & one resulting in less key bending & action saturation plus it transfers hammer energy more efficiently. Dale Frank writes This thread has taken off in different directions. Good advice has been offered for other approaches to solving the specific original problem. Still I cannot leave the issue of key leads and moments of inertia without further comment. I hate to even use the term "inertia." It is moments of inertia in piano action considerations. William Monroe wrote: heavier key stick would "resist" that initial change of direction that starts the key moving (and all subsequent changes in direction) more than a lighter key stick, right? Wrong! .... if you accept as a precondition that you must end up with a reasonable touch weight. In fact the opposite is true. A heavier key with the same static balance characteristics will have less moments of inertia than a lighter key. It doesn't make sense intuitively, but again, we are talking about moments of inertia, not linear inertia. Let's put it in more familiar units and unrealistic round numbers, to make it easier to calculate. Suppose we have a 1lb. weight added at 10 inches from the fulcrum. yielding a perfect DW, unrealistic numbers, but easy to calculate. That represents 10 in/lb of torque (10in x1lb) to achieve the desired static balance and DW. Then suppose we put a 2lb weight at 5 in. from the fulcrum in an identical key just next to it. The torque is the same, 10in/lb (2lb x 5in). The static balance and DW are both the same. The moments of inertia are not the same. In the first case, moments of inertia (MR^2) is 100 (!lb x 10in x10in). In the second, it is 50 (2lb x 5in x 5 in). Which key will depress more easily, and which will return more quickly .... the one with a value of 50 or 100 for moments of inertia? There is a secondary benefit to twice the weight at half the distance. It is far less likely that the added weight at half the distance will achieve the acceleration of gravity, than half the weight at twice the distance. In the first key, with the weight added near the end of the key, the added weight will likely achieve the acceleration of gravity at a volume level of mf. At higher volumes, the added weight become counterproductive. In the second key, the weight is added closer to the fulcrum and it is more likely that one could play fff before the added weight accelerates to the acceleration of gravity. In the first key, the added weight begins to work against you at high volume levels. In the second case, you can produce the maximum volume that the acoustic sytem is capable of delivering before the added weight begins to work against you. Frank Emerson -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://ptg.org/pipermail/pianotech.php/attachments/20100108/d81d5ebc/attachment.htm>
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