Bubble Gauge Calibration

[Ron Nossaman]

Hi Del, and all

The 17' increment makes sense in this context, and corresponds nicely to the
downbearing/angle chart I posted a while back. It's tacked on below if you
didn't see it the first time through. I know it goes ridiculously high, but
it filled the page. <G>  I'll whomp up another one to fit the calibration of
the Lowell gauge when I get a minute.

With the Baldwin gauge at 17' increments, and the Lowell gauge at 11'15" we
*now* know that, when following Baldwin's process for establishing bearing
with the Lowell gauge, we need to increase the bubble deflection
measurements by 50%. Where the Baldwin gauge reads two graduations @34' of
angle, the Lowell must read three for (nearly) the same angle (33'45"). Or
are the Baldwin procedural specs currently established to accommodate the
Lowell gauge? See what I mean? We could speculate about this kind of
nonsense for years. If downbearing specs were given in degrees of angle, and
the calibration of the gauges used to establish or measure these angles were
known, we just might have some hope of figuring out what we're talking
about. Now we've got the ammunition, thanks. 

Ron Nossaman




Measure angle difference between string segments on either side of the
bridge. Multiply corresponding bearing factor 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      




At 06:20 PM 7/26/97 -0700, you wrote:
>If memory serves, the Baldwin bubble gauge vial is calibrated in
>increments that indicate 17 minutes of arc. I think this gauge was
>designed by Harold Conklin and he set up the calibration this way to
>make it easier to translate string deflection into string downforce
>against the bridge. 
>
>Using this gauge, if the bubble is zeroed on the speaking portion of the
>string and it indicates a positive deflection of one gradation line (or
>17 minutes of arc) on the back scale portion of the string, the
>downforce of that string against the bridge will be 0.5% of the scale
>tension of that string. (The length of the backscale does not matter,
>only the angle of deflection.) Two gradation lines indicates 1.0%
>downforce, etc. I.e., if a single string has a scale tension of 170
>pounds and the gauge indicates two gradation lines of positive
>deflection, the downforce of that string against the bridge will be 1.70
>pounds. If the total scale tension of the piano were 40,000 pounds and
>the bubble gauge indicated two gradation lines of deflection on each
>string the total downforce would be 400 pounds.
>
>I'll leave it to the mathematicians among us to figure out what the
>gradation lines of the Lowell bubble vial indicate.
>
>ddf
>
>
 Ron Nossaman