> > >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. But you have just decided where you want to measure them. The SW as you're measuring it is with support under the tail of the hammer. This is not where the force is applied. The force is applied at the CG of the hammer/shank assembly. The point at which you are measuring is not under the hammer CG, the assembly CG, or the hammer centerline. I would say that it is arbitrary. I don't see that as a problem as long as you can do something useful with the information. I would say that we are at liberty to decide where we want to measure. As I mentioned before it might make more sense to measure at a point say 120mm out from the hammer center. Then you would always be consistent. The tail contact point is going to be different for every hammer. I don't see that one of these measuring points is more arbitrary than the other. As long as the number that you get from this measurement can be used to derive something that you want to know, then that point is workable. The point that I was trying to make is that if you are talking about a weight, or force, balance then it probably makes sense to talk about the points where forces are applied: The hammer/shank CG and the knuckle contact point. If you are talking about movement, or distances, then it probably makes more sense to talk about the points where you care about the movement: the hammer strike point and the knuckle contact point. These are different sets of points so the 'ratios' that you derive in the two cases will be different. Just because something is a lever doesn't mean that the leverage ratio is going to be the same at every point along the lever. You pick different points on the lever and you get different numbers. > > > 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. Perhaps I'm behind the curve. I'm not familiar with hammer shank ratio. Is this what you're calling the ratio of SW to weight measured vertically at the knuckle? I had assumed that we were talking about Stanwood methodology, but I don't find this ratio in the Stanwood articles that I have. Am I overlooking something? Perhaps you can enlighten me about how this particular ratio that you're talking about is used to derive an action ratio. By the way, what are you calling the measurement that you take vertically at the knuckle? > > 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. The position of the jack relative to the hammer shank has no bearing on the direction of the force being applied at the jack contact point, just as the angle of the hammer head and hammer shank have no bearing on the direction of travel of the hammer strike point. The jack contact point is moving in a circle about the whippen center. The force vector at the contact point is perpendicular to a line between the whippen center and the contact point, regardless of the jack angle. At no point in the whippen travel is this line even close to horizontal. Therefore the force vector is never close to vertical, as it is the way you're measuring it with your setup. As I said before, this is not a problem if you can do something useful with the information. Even if it doesn't simulate what is going on in the real action, if the number that you get can be used to derive an action ratio, then it's useful. >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) I wouldn't expect it to since you're measuring at a point 17.3mm out from the hammer center, not 21.64mm. If you were to set up your scale so that the dowel is at the angle of the force vector and 21.64mm from the hammer center then the resulting ratio should agree with your measurement. >, nor does it yeild an overall Ratio that conforms to the SW ratio... and >it should there too. I don't understand what you mean by an overall ratio that conforms to the SW ratio. >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. OK. Perhaps your explanation of how you intend to use this number will make things more clear to me. > > > > > 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. I'm confused. The SW Ratio as I understand it is the ratio of the SW to the upward force at the key (at the measuring point). In order for this ratio that you're measuring to be the same, then the force down at the knuckle would have to be the same as the force up at the key. Why would you expect these to be the same? The force at the knuckle is acting through the whippen on the key. I wouldn't expect there to be a 1:1 correspondence. > > >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. Buy your point of force input is not at 21.64mm, it's at 17.3mm. The horizontal distance from your force vector (which is vertical) to the hammer center is 17.3mm. If your dowel were angled to simulate the direction of the force vector in the action, then the horizontal distance from this force vector to the hammer center would be 21.64mm (assuming that your dowel was perpendicular to the magic line). > > 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. Yes, the CG of the whole hammer shank assembly, That's what the action is moving, not just the hammer, and that is where the summation of gravity forces on the assembly is being applied, not at the center of the hammer. For the example that you gave, you could have a vertical force at the knuckle of 76.5g with an assembly weighing 10.6g at a CG 125mm from the hammer center or an assembly weighing 10.2g at a CG 130mm from the hammer center. Statically, both of these will be balanced by the 76.5g force applied vertically at the knuckle. But dynamically the inertias of these two assemblies will be different, so the hammer strike point acceleration is going to be different. >.......... >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. > >RicB I would say that it's important to find a formula based on measured values that yields a correct R so that you can understand how changing the knuckle location affects the R. If you can do this with one measurement on the hammer shank then fine. But I think you might have to combine this measurement with other measurements from the whippen in some way to get the result that you want. Phil F Phillip Ford Piano Service & Restoration 1777 Yosemite Ave - 215 San Francisco, CA 94124
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