Hammer Shank Ratio

[Phillip Ford]

> 
>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.

>Below are a couple pictures showing a method of checking the hammer
>shank ratio by measuring the weights involved. First is the SW and
>second is a difficult (but doable)  quantity to measure, the actual
>weight of the hammer assembly at the knuckle. The flange is replaced by
>an adapter to the Stanwood kit so as to achieve as solid and friction
>free a measurement as possible. And the wood dowel used to contact the
>knuckle is glued in place to tray so as to remove any influence from it
>moving around. About 50 samples were taken, and compared to a 60 second
>sampling under vibration.... the variation of the samples was at highest
>80,4 grams and at lowest 73.1 grams. About 80 % of the samples were
>right around 76 grams, and the average weight under vibration was at
>about 75 grams, though as soon as the vibration was shut of the scale
>settled at 76.5... which ended up being the picture I took.


I don't understand the purpose of this vibration.

>  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.

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?  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.


>  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?

>  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?

>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/D = 6.28 (suggested by a technical editor informally in private
>correspondence)


I believe this last one was supposed to be A/E = 6.28.


>Its quite obvious which one of these comes out best.

Yes.  Obviously A/D because that simulates what you are measuring. 
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.

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.

>  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.  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?

Phil F


Phillip Ford
Piano Service & Restoration
1777 Yosemite Ave - 215
San Francisco, CA  94124