To all that have followed this thread: After revisiting the recent exchanges RE action ratios it is occurs to me that too much emphasis has been placed on aftertouch (AT). To briefly recap, Pfeiffer's stated relationship of EQ 1: W / S = the product of the RAs / EAs was my beginning point. This basic relationship was also restated in reverse as: EQ 2: (keyout/key in) x (wippen out/wippen in) x (shank out/shank in) = (blow distance - letoff) / (key dip-aftertouch). Both formulas imply the same thing; that the ratio of the leverage arms as configured in the key, whip and hammer shank will always be reflected in the key dip as it relates to hammer rise at the point of letoff. We do not have a single term or expression for "hammer rise at the point of letoff". What I did was to rearrange Pfeiffer's EQ 1 and solve for S, which is dip, regardless of AT; which is what the term (key dip-aftertouch) implies. EQ 3: S = (V x Ra x N x W) / (H x Rs x K) (*See below for factor designations) EQ 3 example with assigned values was S = (245 x 67 x 18.25 x 44) / (126 x 94 x 141) = 7.89 What this states is that 7.89 mm of dip is required to raise the hammer 44 mm. AT begins the moment that the jack tender makes contact with the letoff button and completes when the key bottoms out on the punching. But for the sake of these relationships it is proper to focus on the amount of dip required to raise the hammer to the point of letoff. Thus, the ratio of the (key leverages) to that of the (engaged dip and related hammer rise) will be equal. In the case above, 44 / 7.89 = 5.58, and this equals the Action Ratio. And so, the leverage ratio = 5.58, and this ratio is reflected exactly in the ratio of hammer rise to key dip, without regard to AT. Now why bother to think this way? Because it encourages us to remember that any changes made to the key leverages are going to be reflected in the dip; and this dip is going to be required to raise the hammer the required distance to the point of letoff. RE Aftertouch: in the above EQ 3 example, factor S (or calculated dip) equals 7.9 mm. Thus if total regulation dip is not to exceed, say, 10.7 mm, then AT must fully occur by using up the difference between required dip (S) and the limit of 10.7. The difference is 2.8 mm. Clearly this is plenty; in fact the regulated dip would likely be less than 10.7. David Love wondered if an informative relationship can be found RE a useful ratio or percentage of overall hammer rise (OHR as calculated without regard to letoff) as it relates to standard blow and dip specs. Or stated another way, how many mms are required after S has been achieved to safely complete AT. I feel certain the relationship can be uncovered. RE Pfeiffer in general: no useful understanding of Pfeiffer's work can be had until the overall goal of his work is appreciated. At the drawing board, and when designing new actions from scratch, Pfeiffer sought to create a conjugate (gearing) relationship of the six levers in question (two in the key, two in the whip, and two in the shank). In brief, this conjugate relationship is intended to minimize friction by creating a "rolling" rather than "sliding" friction at half-stroke and thus "minimize the slide path" of the contacting profiles (capstan, whip heel, etc.) For most modern actions today, the layout of the balancier and knuckle prevent such conjugation from taking place, at least at that interface. But the Langer action as appears in Pfeiffer's book The Piano Hammer (page 110) admits of such an arrangement due to the flattened and re-angled top portion of the balancier; ditto RE the Bender action page 84. There is a ton more which could be said of Pfeiffer's work. *********************************************** Designations per Pfeiffer: W = (hammer travel - let off) S = (key dip required to lift the hammer to the point of letoff) H = rear key lever arm resistance (key out) Rs = whippen lever arm resistance (whippen out) K = hammer lever long arm resistance (hammer out) V = front key lever effort (key in) Ra = whippen lever arm effort (whippen in) N = hammer lever short arm effort (hammer in) Nick Gravagne, RPT Piano Technicians Guild Member Society Manufacturing Engineers Voice Mail 928-476-4143 _____ -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://ptg.org/pipermail/pianotech.php/attachments/20100112/c8cd350e/attachment-0001.htm>
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