>Gentlemen, and Ladies too, if any of you are following this discussion >among us fellows: Jim, Interesting data you sent. Thanks. >The results speak for >themselves. If we are interested in stiffness - vs - weight, the round >tapered shank is definitely superior to the non-tapered octagonal shaft. It's not clear to me wny that would necessarily be desirable for a hammer shank. Stiffness control, for sure, but the weight really doesn't contribute much per se, given the mass of the hammer head hung out at the end of it. On the other hand, stiffness increases roughly as the fourth power of radius (with tinkering for geometry of the cross section), since moment of inertia does, and that factor includes the effect of the square of the radius on mass already. >Little is gained by the octagonal shape Unfortunately a comparison is difficult with the shanks you tested, due to the added complication of the taper on the round shank. That will certainly make a huge difference as you noticed, regardless of the "octagonality" question. >, and much stiffness is lost by not >having a larger cross section near the knuckle. We are dealing here with a >lever, not a structural beam. It is actually a beam acting in the capacity of a lever. Beams are not necessarily supported at two ends like a floor board. There are cantilever beams that are clamped at one end, and over-hanging beams supported at some intermediate point. Beam theory is applicable to a hammer shank. The lever aspect just provides the input loading which is to be applied to the shank (beam). >Whatever you might or might not say about >Steinway, New York, they obviously have the right idea here. The shank is >stiff where it needs to be stiff, and light where it needs to be light. >That design make good sense to me. That's a different question. It depends on the objective. The thin shank people would not agree that stiffness is the desirable factor. We can certainly conclude that Steinway shanks are stiffer, based on your observations, and I agree it's due to the tapering. Stiffness changes pretty sharply as you increase the "radius". When comparing round and octagon we need to agree on the relative sizes to make sure it's apples and apples. Say the circular section is converted into an octagon, so the points are at the same radius as the original circle. To get the same stiffness from the octagon you'd need only to increase the radius by 5%, which isn't very much. Or, looking at it another way, taking a circular non-tapered shank and reducing it to an octagon section reduces the stiffness by about a not insignificant 15%. Small changes to shank cross-section can have dramatic effects on stiffness, with observable changes to tone, hence the shank-wars that surface from time to time. Ever talked to a fly rod maker about cross-section? We piano makers are tame in that company. Stephen -- Dr Stephen Birkett Associate Professor Department of Systems Design Engineering University of Waterloo Waterloo, Ontario Canada N2L 3G1 Davis Building Room 2617 tel: 519-888-4567 Ext. 3792 PianoTech Lab Ext. 7115 mailto: sbirkett[at]real.uwaterloo.ca http://real.uwaterloo.ca/~sbirkett
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