William R. Monroe wrote: >I would disagree however, with the assessment that inertia only comes into play until.......[acceleration of gravity]. OK, "comes into play" is a poor choice of words. The point is that the positive influence of gravity, acting upon the lead weight assists the key's downward movement to a greater extent than the negative influence of inertia, until the acceleration of gravity is achieved, at which point there remains only the negative influence of inertia. Or, better put ... At some point approaching the acceleration of gravity, the balance tips toward inertia having the greater influence. We tend to think of inertia as being equivalent to mass, which is true in linear motion, but not in rotational motion, which is moments of inertia, Mass x Radius^2, radius being the distance from the axis of rotation to the center of gravity of the added mass. A certain amount of torque (MxR) is required to achieve a static balance that will yield a given DW. For a key in the mid-range of the keyboard, you can add as little as 9 grams, in the form of a lead plate just under the keyfront cover, or as much as 65 grams in the form of a single ob-oval lead mass near the balance rail. In both cases the torque is the same, as is the DW. There is an infinite number of possibilities between these two extremes that would also yield the same torque. One might think that 65 grams adds more inertia than 9 grams. In this case, not so. If torque is MxR, and moments of inertia is MxR^2, or MxRxR or TxR, the only factor to determine the difference in moments of inertia is R. The greater the value of R, the greater the moments of inertia, assuming that we remain within the parameter of retaining the required torque and DW. In order to reduce inertia and retain a reasonable DW, one must add weight at a shorter distance. To only remove weight without adding more weight, closer to the axis of rotation, is counterproductive. Frank Emerson -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://ptg.org/pipermail/pianotech.php/attachments/20100106/0c14e4ac/attachment-0001.htm>
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