Ron N. wrote....
"The Great International Math on Keys book,
> available in Garage Sales everywhere, supplied the Trig and vector
stuff"
Oh yeah I used to have that book. Who would have guessed a book
written for calculators could be used for computers. I hope I
didn't sell it at my Great Garage Moving Sale.
I would have to figure out how to measure angles of bearing, but I
think I can find distance, as a deflection from straight line. I
would assume/presume, this distance should be measured after tension
is established.
The problem I would like to solve is similar to; " a piano string at
a tenion of 180 pounds is pushed up 1/8 " by the bridge. What is the
pressure of the wire on the bridge.? "
On reflection, I am wondering if it might not be easier to measure
angle. I think we all have the "rocker" type bearing guage and using
it over the years one gets a sense of, "yes there is bearing, ah this
piano has a little more/less that the last one in this section." But
that doesn't fit into a vector equation.
There are two more gages listed in APSCO, but the description does
tell what they read out. I like the dial type #16397 (p 11) as this
seems to be the one used in player pianos to determine travel
distance in valves, for which I can use. But I think it will give
diff readings for string bearings if placed on diff parts of the
string. The other guage, called "Lowell Down-bearing Gage I have
no idea how it works. "The degree of bearing is translated easily
into "fall" per inch of string length. The bubble gage simplifies
calculation of the degree of downbearing. Detailed instructions
furnished." The cost....... what a hassel to look up.....$`132.00
retail . Hmm the dial guage is only $64.00 retail, (before discount
to the trade)
Well "degree of down bearing" I thinks means some kind of angle and
I think that is what Ron has posted....(degrees,, not radians?). So
if one can measure angle, this might be more accurate than deflection
distance, because that (deflection distance) is a little more
difficult to determine on a loaded board, with all the strings,
bridge pins, I almost said bitch pins, swagger, narrow aliquoit
blocks or what ever the heck they are called. (if they are even used)
But I like Ron's chart as he gives a whole compass so one can make a
guess if he/she can't get to the nth degree.
So according to his chart if there were angle of bearing of 1.7 I
would multiply .0296675 times the tension? Ummm that would
be.......5.340743210973477652347655 pounds : ) of down pressure for
that string at 180 pounds of tension. So for my small elephant, good
sized cow, or however large a horse is at 1400 lbs, the angle would
have to be........2.2 approx. to produce a load of aprox 1400 on the
sb if the strings were at an average of 180 lbs tension. 2.3 produces
7.2 lbs of down pressure from a string at 180 lbs tension. Exact
fugures, oops figures to be posted, as .1 in the angle makes a
significant diff. Don't know how to get close to a .1 angle in
measuring, and want to make sure I did the calculations right on
"example" problems. In the meantime it would be intersting to convert
Travis's rule of thumb for bearing (unloaded) of a dime, nickle and
quarter through the sections, to down pressure. But I think the
measurements of distance of deflection must be taken after tension is
applied.
So after spending all of this time rambling here, I wonder if Ron
can come up with a chart that shows the down pressure for distance
the string is deflected? Some one of us will have to put in the
time, I guess it is my turn,,but sometimes I am slower than an
elephant.
Thanks for the calcualtions and tables Ron. I don't have turbo
pascal installed, but do have 3 hours credit from a
university...(four years ago, so figure out what is left from not
using it for that long) However if the equations can be posted, I
might could convert them to a spread sheet style that could be cut
and pasted into most brands, especially MS Works for Windows, Quatro
Pro and and 1 2 3.
Richard Ihavenotyetbeguntoramble.
> From: Ron Nossaman <nossaman@SOUTHWIND.NET>
> To: pianotech@ptg.org
> Subject: Downbearing/Unsubscribe
> Date: Friday, June 20, 1997 8:28 PM
>
> Hi all (that's left),
Is that left brained, left handed, left of center, or left here?
Takes a left brained person to ask that>?
>
>
> I've worked up a downbearing
> poundage figgurer-outer chart. The Great International Math on Keys
book,
> available in Garage Sales everywhere, supplied the Trig and vector
stuff. I
> whipped up a Turbo Pascal program to print this sucker out for
whoever can
> use it. Look it over and see if you can make sense of it. Also,
check the
> figures against your own information and see that I didn't screw
something
> up. Shift happens.
>
>
>
>
> Measure angle difference between string segments on either side of
the
> bridge. Multiply times tension for downbearing weight.
> Ron Nossaman June, 1997
>
> Angle Bearing Angle Bearing Angle Bearing
> 0.1 0.00174542 3.4 0.05933258 6.7 0.11687053
> 0.2 0.00349075 3.5 0.06107712 6.8 0.11861284
> 0.3 0.00523608 3.6 0.06282161 6.9 0.12035505
> 0.4 0.0069814 3.7 0.06456605 7.0 0.12209717
> 0.5 0.00872671 3.8 0.06631045 7.1 0.1238392
> 0.6 0.01047202 3.9 0.06805479 7.2 0.12558113
> 0.7 0.01221732 4.0 0.06979908 7.3 0.12732297
> 0.8 0.01396261 4.1 0.07154332 7.4 0.12906471
> 0.9 0.01570789 4.2 0.07328751 7.5 0.13080635
> 1.0 0.01745316 4.3 0.07503164 7.6 0.13254789
> 1.1 0.01919842 4.4 0.07677571 7.7 0.13428933
> 1.2 0.02094366 4.5 0.07851972 7.8 0.13603067
> 1.3 0.02268889 4.6 0.08026368 7.9 0.13777191
> 1.4 0.02443409 4.7 0.08200757 8.0 0.13951304
> 1.5 0.02617928 4.8 0.0837514 8.1 0.14125406
> 1.6 0.02792445 4.9 0.08549516 8.2 0.14299498
> 1.7 0.0296696 5.0 0.08723887 8.3 0.14473579
> 1.8 0.03141473 5.1 0.0889825 8.4 0.14647648
> 1.9 0.03315983 5.2 0.09072607 8.5 0.14821707
> 2.0 0.03490491 5.3 0.09246956 8.6 0.14995754
> 2.1 0.03664996 5.4 0.09421299 8.7 0.1516979
> 2.2 0.03839498 5.5 0.09595635 8.8 0.15343815
> 2.3 0.04013997 5.6 0.09769963 8.9 0.15517827
> 2.4 0.04188493 5.7 0.09944284 9.0 0.15691828
> 2.5 0.04362986 5.8 0.10118597 9.1 0.15865817
> 2.6 0.04537476 5.9 0.10292903 9.2 0.16039794
> 2.7 0.04711962 6.0 0.104672 9.3 0.16213758
> 2.8 0.04886445 6.1 0.1064149 9.4 0.16387711
> 2.9 0.05060924 6.2 0.10815772 9.5 0.1656165
> 3.0 0.05235399 6.3 0.10990045 9.6 0.16735577
> 3.1 0.0540987 6.4 0.1116431 9.7 0.16909492
> 3.2 0.05584337 6.5 0.11338567 9.8 0.17083393
> 3.3 0.057588 6.6 0.11512814 9.9 0.17257282
>
>
> Ron Nossaman
>
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