the instrument is designed to measure the distance from a central point 

 inside the sphere to any point on its inside surface. This central point 

 should coincide closely with the center of the sphere. It is possible to 

 take the readings obtained from the instrument and then, utilizing the 

 high-speed computer facilities of the Applied Mathematics Laboratory at the 

 Model Basin, to calculate the theoretical location of the center of the 

 sphere relative to the actuaJ. position of the instrument. Departures from 

 sphericity may then be calculated by a computer relative to the theo- 

 retical center of the sphere. This was not done for the ALVIN spheres 

 since it was possible to locate the instrument with sufficient accuracy 

 (within 0.050 in.) by taking readings on the Ames dial gage and adjusting 

 the position of the instrument by means of the vertical adjustment screw 

 and the horizontal adjustment holes shown in Figure 11. Small variations 

 between the theoretical center of the sphere and the position of the in- 

 strument would have a negligible effect on the local curvature over a 

 criticcil arc length. The instrument can rotate 350 deg about the horizontal 

 pivot points, and the adjustable arm can rotate 180 deg about the vertical 

 pivot point. 



Over 1200 measurements were taken on each hull to ensure that at 

 least five readings were taken over a critical arc length. Additional 

 readings were taken in the areas of the welds to locate points of maximum 

 deviations. The Ames dial gage was calibrated for each hull by the use of 

 inside micrometers. Deviations were then measured and computed relative to 

 the nominal inside radius. 



RESULTS OF MEASUREMENTS 



Measured deviations from the nominal inside radius are plotted in 

 the form of contour maps in Figure 12. Inward deviations are plotted as 

 minus contours. The radial scale used in all drawings is constant. The 

 solid circles in the figures represent a complete hemisphere, and the radial 

 scale may be determined by measuring the diameter of this circle. This 

 measured diameter represents one-half the inside circumference of the 

 sphere. This is done for accuracy in analyzing the data. As is the case 

 with the problem of mapping, however, the scale in all other directions 

 varies, depending on the distance from the center of the plot and the 



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