Friction Weight=(D-U)/2

[Nancy McMillan]

David Stanwood wrote:

> Why not make an action that has no friction!  Ball bearing knuckles, ball
> bearings in the hammer and wip centers, ball bearing heel cushion, and
ball
> bearing key pivots and guides.  (Of course these would have to be dry ball
> bearings so as not to cause any extra drag)
>
> Now we measure down weight and it turns out to be 35.001 grams and the up
> weight is 34.999 grams.  But since we normally measure up weight and down
> weight to the nearest gram these figures both round out to 35 grams.  So
> with no friction, Up Weight and Down Weight are the same.
>
> Now let's spray mist the ball bearings with a mixture of 80% water and 20%
> alcohol.
> get that water right into those bearing with a liberal soaking!  Let stand
> for one full day do allow for full rust development.
>
> Now remeasure Down Weight and we find it has increased by 13 grams.  It
was
> 35 grams, now it's 48 grams.  13 grams is the additional weight needed to
> overcome the friction in the rusty bearings.  That's why it's called
> Friction Weight.  Now we measure Up Weight and we find that it has
> decreased by 13 grams as a result of the friction in the rusty bearings
and
> now measures 22 grams.
>
> So this 13 grams is called "Friction Weight" and in the real world we find
> it as:
> (D-U)/2.
>
> As you can see in this case, referring to friction as 26 grams doesn't
> really tell you the effect of friction on either Up or Down Weight until
> you divide by two.
>
> Also, the 35 grams in this case,  is referred to as "Balance Weight" and
is
> found as: (D-U)/2

**  David, did you mean BW = (D+U)/2 here? ********************

> In defense of these terms I have to take exception with the comments by
> Mark Abbott Stern in his December 1999 Journal Article "Touchweight &
> Friction"
>
> In his introduction he states:
>
> "The hardest part will be giving up the belief in a widely accepted
> statement: "One half the difference between down weight and up weight is
> the friction of that note." Not entirely true. Repeat --- not true.
> Friction is certainly a part of that value, but there's more to it; there
> is a portion that cannot be reduced by all the lubricants in the world."
>
> He seems to imply that, by using all the lubricants in the world, we have
> eliminated friction and since there is still a difference between up and
> down weight, it must be from some other cause. He goes on to make the case
> that force vectors are the cause of it.
>
> My take on this is that if we reduce friction as much as we can (and this
> is not necessarily desirable) there is still plenty enough friction
> leftover to cause a difference between up weight and down weight.
>
> If we TRULY eliminated friction (Ball bearings) there would be one weight
> placed on the front of the key that would cause it to become balanced.
The
> slightest amount added or subtracted to that weight would cause the key to
> move down or up irregardless of the force vectors within the action.
>
> David Stanwood

Hi David and Mark Abbott Stern, if the latter is a subscriber to the list.

Mark stated in his Dec. 1999 Piano Technicians Journal article  intitled
Touchweight & Friction, "Today's mission is to explode a myth.  Forget that
there are diagrams and even an equation or two. That stuff will be simple."

I didn't find it simple.   Confused would be how I would describe my state
of mind regarding this article.  I had to look up the word vector in my
dictionary, which stated the following definition: "A line representing a
physical quantity that has magnitude and direction in space, as velocity and
acceleration: distinguished from scalar."
The above definition put into the context of a grand piano action  implies
(to me anyway) the line or trajectory that any given part in the action is
embarking on under movement.  It would seem to me the path of a moving
action part translates into an energy loss only when it encounters another
action part and that, in itself,  brings about some magnitude of friction.
My first question then: Is vector really the correct term to be using in
this article?

Given the folded beam design of a piano action and how escapement is
desirable where some of these parts vectors come into play, if the geometry
was "perfect" on an action one would still have what Mark calls vector
losses.  So my second question is: How would one quantify these vector
losses as opposed to friction?  I'm talking about breaking the friction
measurement out from the vector loss measurement. And is it really
necessary?  Doesn't the Stanwood method include solving these problems to a
degree without actually stating it in specific vector terms?

I'm not clear on how the three piece chain description illustrates vectors.
Given Mark's drawing and description of the three piece chain it would seem
that as soon as F2 and F3 had 1 unit of force on them pulling against F1,
which has 2 units of force, an equilibrium would take place.  The chain
really doesn't know it is being pulled in the direction of F1 specifically
at this point so wouldn't all forces in all three directions be equal?

Mark, if your out there can you help me out in understanding your article.
Or any one else that wants to chime in.

Sincerely,

Doug Mahard, Associate