At 10:22 -0600 14/1/10, Porritt, David wrote: >In a piano you could state that the ratio is 5.5 at the start of the >stroke, but it might be 5.7 or so by the end of the stroke. Neither >measuring system takes that into account so their answers are >different. At 10:45 -0700 14/1/10, Nick Gravagne wrote: >For example, an AR of 5.5 implies a 5.5 to 1 ratio, meaning that a >keystroke of 1 mm will cause a hammer rise of 5.5 mm; and 10 mm dip >causes a 55 mm rise in the hammer. Pfeiffer understood that, >strictly speaking, losses occur, but he deemed them not serious >enough for our purposes. I pointed out in my last post that the "losses", which you say Pfeiffer deemed insignificant are in fact very important, and even more so in the upright action which he deals with most. What is certain is that the designers of the great actions, such as Herz, Herrburger etc. knew exactly what they were doing and would have dismissed Pfeiffer's approximations as the scribblings of an amateur. What is the point of using approximations when it is possible to calculate the ratios at every point in the action at every slightest increment in the key-dip? My posting of 10th Jan, which nobody has even commented on, though it is the only posting in the thread that that provides a factual calculation without any woolly approximations, deals with the ratio of key-dip to perpendicular rise at the capstan averaged over a range of 8 mm. It is this average, or end-result, that is most useful for practical purposes, but of course the instantaneous ratio varies as the angles change. There are "losses" due a) to circular motion and b) even in the finest design, to sliding motion. The ratio key-dip:capstan-top rise increases as the touch depth increases, because the perpendicular rise of the capstan-top (the y componentof its path) diminishes as the horizontal or x component of its path increases. By contrast, as the intermediate lever (wippen) moves upwards, the x component of the lever heel's path diminishes with respect to the y component as the line from the lever centre to the lever heel approaches the horizontal, and an even greater difference takes place at the hammer:jack/cradle juncture, owing not only to the great differences in lengths and consequent great changes in angle but also to the variation in losses due to sliding motion. So much for the discursive presentation of the question. All that is then needed to produce the exact quantities involved in a particular action is to take precise measurements and apply the necessary trigonometrical calculations. JD
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