Don A. Gilmore, mechanical engineer, Kansas City, is exactly right. I used the wrong words. I should have said "property" instead of "quantity", and I should have said "acceleration" instead of "velocity". Also, the moment of inertia is proportional to the square of the radius about the center of rotation, or the pivot, but that relates back to the change in velocity, whether it be acceleration or deceleration. So my first statement was not so far off after all. Other than that, I'm saying the same thing Don is, and I'm also sticking to my guns about the point I'm trying to make. You can go through the whole tedious process of calculating the moments of inertia of the entire action, and adding it all up. You can also treat the whole thing as a compound lever system, which it is, the shank ratio, the wippen ratio, the key ratio, etc. You can't use any nice formula for it, because it is a compound lever system, and these pieces all have irregular shapes, sizes, and mass distributions. You will have to take it piece by piece by piece. With the exception of the extreme high treble, when you are done, you will find that the hammer head out on the end of the shank dominates the picture with respect to the moment of inertia, and as someone said, there is not much you can do about that, assuming the hammer has optimum mass in the first place. You can reduce the moment of inertia of the keys by moving the leads closer to the centers, but you will have to use more lead to get the touch weight you want, and you will be putting more holes nearer the centers of the keys, and that will weaken them. In the low bass, you will have keys with lots of lead. When you are all done, you will find that you have not accomplished very much for the total moment of inertia of the whole action, because it's the hammer heads out on the ends of the shanks that are dominating it. In the extreme high treble, you don't have this problem anyway. I used to weigh off keys by concentrating the leads toward the centers in order to reduce the moment of inertia of the keys, but I came to the conclusion that it was just not worth it, and I quit doing it that way. That's the point I was making, and I am sticking with it. Merry Christmas, Jim Ellis
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