Where's the engineer?

[Bill Ballard]

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On Sun, 15 Apr 2001, "Mike Spalding" <mjbkspal@execpc.com> wrote:

>  > Wouldn't the calculation of the sideways force need to include the
>  > speaking length?
>
>The sideways force is determined by the string tension, and the angle that
>the wire makes as it goes around the pin.  The offset divided by the
>distance between pins is a good approximation of the the angle.  But any
>other method for determining the angle would work just as well.

After Ron Nossman's quick nudge, I figured out my difficulty. You're 
speaking of the deflection as only being one right triangle, I'd been 
seeing two, which of course there are. But imagine it this way. If 
you take two segments, one 7/8" long and the other 8" long, and if in 
each, you make a deflection of .131" 3/4" in from one end, it'll be 
the 7/8" segment which will be the harder one to deflect. Even though 
they'll both be being deflection at a point 3/4" down from one end, 
the crucial detail is that one of them will be having its deflection 
done 1/8" from the other end and the other 7-1/4". As you use the 
opposite side of these right triangles to measure the deflecting 
forces, the right triangles with the 3/4" adjacent sides will both 
yield the same forces resisting deflection. But of the complementary 
right triangles, the one with the 1/8" adjacent side with require a 
far greater force to achieve the deflection whose opposite side 
equals .131" than the triangle with the 7-1/4" adjacent side. In fact 
the deflecting force will always be determined by the complementary 
triangle with the shorter adjacent side, as its deflection angle will 
be greater than that of its partner's triangle. And on any piano a 
3/4" distance across a bridge will always be shorter than any 
speaking length to be found on that piano. (You'd have to get up to 
F9, I b'lieve, and most pianos stop at C8.)

>There is a limit to theoretical analysis, and with pianos we get 
>there pretty quickly.  While I
>enjoy examining problems this way, I think there is equal or greater value
>in sharing our experiences with real pianos - what did we try and how did it
>work.

Speaking about the empirical measurements which engineers prefer, a 
few years back I dreamed of a way of measuring the total friction 
barrier presented by the bridge to the string, that is, its pair of 
staggered, slanted pins and the wooden surface between them. This 
would quite likely be a two person job. With some sort of frequency 
counter, particularly one cap[able of identifying the frequency of 
the short high tone to be found on the other side of the bridge, 
measure and hold the starting frequency of both the speaking length 
and the back length of the string path. Then with a tuning hammer, 
start changing the tension of the string path while continuing to 
pluck on the back length until either your ear or the frequency 
counter registers a change there. At that point immediately freeze 
your motion with the tuning hammer, and quickly record the frequency 
in both speaking length and back sections. Convert frequency into 
tension (via length and constants). Hopefully if your reactions are 
fast enough, you will have captured the exact change of tension which 
will have overcome the friction barrier at the bridge. I now remember 
that this also involved checking for an initial tension differential 
between these two segments, by seeing whether the ratio of their 
frequencies matched the ratio of their segment lengths. This would 
enter into the equation whether the change in speaking length tension 
required to overcome the friction barrier of the bridge would be 
raised or lowered by such an already existing tension differential on 
either side of the bridge.

Bill Ballard RPT
NH Chapter, P.T.G.

"We mustn't underestimate our power of teamwork."
     ...........Bob Davis RPT, pianotech '97
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