Phillip Ford wrote: > > > >Folks > > > >I keep being bothered by the differing conventions for measuring the > >ratio of the hammer shank. From the Law of Levers we know that the ratio > >is the same whether its weight, speed, or distance we are looking at. > > As long as you are measuring all of these at the same spot. No.. the ratio is determined by three point that we are to identify. These do not just move around nor are we at liberty to just decide where we want to measure them. They are constant and define the leverage. The point of input force, the point of output, and the fulcrum. > > I don't understand the purpose of this vibration. For the same reasons that UW and DW measurements require a bit of vibration (ie light banging on the action).. to relieve some of the frictional component. Its just a double check in this case. And it checked out quite well. > > > > All in all > >it seems pretty reasonable that in this case the established ratio is > >76.5 / 10.1 which gives a ratio of 7.57 for this hammer shank assembly. > > I'm not sure that I understand why you want to know this ratio. Because the convention for measuring hammer shank ratio is critical to the resulting overall action ratio. Agreement on what that is, is neccessary if any meaningfull discussion about action ratio questions is to take place. The recent discussions about whether an action can be regulated at a 5.0 R illustrates that. Two camps argueing against each other seeming unaware that they were talking about two completely different Ratios. > Given the parameters that you've established I agree that this particular ratio is 7.57. I question whether this is useful for anything. When the shank is parallel to the scale platform and the support under the knuckle is vertical then this ratio is 7.57. This doesn't represent a configuration of any real piano action so in what way is this useful? THis was the first experiement, I am going to try a few different things along the lines you suggest, tho I might point out that in a well regulated grand, the hammer shank is indeed perpendicular to the jack, which represents the input force element. So the weight of the hammer shank assembly does sit perpendicular to the support. This changes to some degree through the key stroke for sure, tho for a good deal of that the average will be position will be perpendicular. > In a real action the support for the knuckle is being applied perpendicular to a line between the whippen center and the whippen/knuckle contact point. So, when the hammer shank is horizontal, the force applied by the whippen at the contact point will be less than 76.5g since the moment arm, or lever arm, is 21.64 mm - see D below, assuming that the contact point is on the magic line at this moment. This number seems more relevant to what is happening in a real action. By the time the shank is horizontal the jack is well out of the picture. If the jack is regulated just on the B+ side then it will be on average perpendicular with the shank through the first part of the stroke. The action ratio surely has no meaning after the point of jack contact with the jack tender. While the figure of 21,64 does admitedtly seem to be the rightone, it does not conform to either this way of measureing weight (and it should in anycase), nor does it yeild an overall Ratio that conforms to the SW ratio... and it should there too. This tells me that there is something wrong with useing that length. Or perhaps better said... it says that useing this length means you are measureing a different ratio relationship then what is measured by the SW ratio method. My purpose is to find that way of measureing arms that yeilds the same Ratio figure for the reasons stated above. > > > Now the interesting part of all this comes when you compare the > >different conventions for finding the ratio by measuring lever arm > >distances. Remember that whatever method is chosen simply must conform > >reasonably to the ratio established above. > > Why? Because they clearly demonstrate which of the present conventions closest conforms to the SW ratio. You plug any of these into the total action equation, and check that against what you come up with by measureing the SW ratio and you will see what I mean. Terry Farrel did a simple and similiar comparison on this earlier on as well including the idea of comparing key travel to hammer travel. His results pointed in exactly the same direction. > > So first .... some distances. > > > >--From center of hammer shank diameter to knuckle contact point 13 mm > >A) From middle of center pin to middle of hammer molding straight down > >the shank -- 136 mm > >B) From middle of center pin to center of gravity point on the hammer > >142 mm > > How did you establish this? Quick and dirty... the hammer was removed from the shank and I found the point of balance. I might point out this is a convention I never have used personally. Just following directions as to how to find it. > > >C) From middle of center pin to tip of hammer 148 mm > >D) From middle of center pin to middle of knuckle molding -- 17.3 mm > >E) From middle of center pin to knuckle contact point 21,64 calculated > >as root (17,3^2 + 13^2) > > > >Now lets take a look at which convention most closely conforms to the > >already established ratio. > > > >A/D = 7.86 (given by Vincent RPT) > >B/D = 8.21 (discussed informally on the PTD list) > >B/E = 6.56 (I ran into this one in Stockholm last year in informal > >discussions) > >C/E = 6.84 (given by Overs) > >A/E = 6.28 (suggested by a technical editor informally in private > >correspondence) > > I believe this last one was supposed to be A/E = 6.28. Yes,, thank you.. a typo on my part. > > > >Its quite obvious which one of these comes out best. > > Yes. Obviously A/D because that simulates what you are measuring. Actually... thats the part that confuses me... the point of input force is indeed 21.64 mm away from the fulcrum.. that is to say IF the point of contact between knuckle and jack top is indeed the point of input force. I would have expected to read closer to that on the scale... but I didnt. > > Whether that simulates something in a real action and is useful for anything is another question. For your setup, and based on the numbers that you provided, I suggest that there is another number F=horizontal distance from hammer center to spot where tail contacts scale platform when shank is horizontal. This number would be 131 mm. F/D = 7.57. Grin... yet another convention for measureing the hammershank ratio. I like it !... who knows ? > > > One of the shortcomings of this method of measuring SW is that the contact points of the tails can be somewhat inconsistent. A better setup would probably be to have a support for the hammer shank at a fixed and known distance from the hammer center. I believe that this would provide more reliable and consistent readings. An interesting refinement, tho this was a rough first run through. The dowel was glued in place so it was fixed alright, and its diameter was the same as the knuckles and it was slightly rounded at the top so its actual surface contact with the knuckle was about the same as a jack top... tho round. The dowel was placed directly under the middle of the knuckle so I think I have a pretty good ball park result here. Tho I am not taking anything for granted for sure. > > > > But what is most > >interesting is the degree of deviation from those that conform poorly. > > >From this the initial conclusion is inescapable, that the method > >Vincent gives for measuring lever arms is the most dependable. > > > >I intend to further refine the weight measurement method, and supplement > >it with a contrivance for moving the assembly at the knuckle a given > >distance and comparing that to the distance the hammer moves. > > > >Fun eh ??? > > > >Cheers > > > >RicB > > We are talking about static balances here. The sum of the forces must be zero and the sum of the moments must be zero. So, the sum of the moments about the hammer center must be zero. The force acting on the hammer, shank, and knuckle assembly is gravity (in other words a downward force, and always a downward force, regardless of hammer position or shank angle) at the CG of this entire assembly. This CG will probably not be on the hammer but in toward the hammer center by some amount depending on shank and knuckle weight. Ah... yet ANOTHER distance to be checked out. You mean the CG for the whole hammer shank assembly, not just the load on the hammer shank. > The moment arm is perpendicular to the force vector - the horizontal distance from a vertical line through the CG to the hammer center. The balancing force is the force being applied to the knuckle and is being applied perpendicular to a line between the whippen center and the contact point. The moment arm is the perpendicular distance from this force vector to the hammer center. So, as I see it, to establish your true ratio you need a couple of new! > parameters: > > G=Perpendicular distance from hammer center to whippen force vector > > H=Horizontal distance from hammer center to CG of hammer/shank assembly > > The ratio would be H/G. > > Now, in the particular case of the hammer shank being horizontal and the whippen/knuckle contact point being on the magic line at that moment, then this would be fairly close to A/E given above. > > More fun, eh? Yep... the point is Phil... to find that method of measuring lever arm distances, that yeilds as close as possible a result to the SW Ratio. Agreement on a common understanding of this SW ratio is important for reasons already mentioned. Thanks for the thought fuel ! RicB > > > Phil F > > Phillip Ford > Piano Service & Restoration > 1777 Yosemite Ave - 215 > San Francisco, CA 94124 > _______________________________________________ > pianotech list info: https://www.moypiano.com/resources/#archives -- Richard Brekne RPT, N.P.T.F. UiB, Bergen, Norway mailto:rbrekne@broadpark.no http://home.broadpark.no/~rbrekne/ricmain.html
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