orientation with the radial direction. The location of the penetration 

 and girth welds are shown in Figure 13 to the same scale as the contour 



plots o 



DISCUSSION 



To determine the maximum loca]. radius of curvature, it is necessary 

 to obtain the maximum out-of-roundness A over a critical arc length. This 

 value may be obtained using the contour maps (Figure 12) and the scales 

 presented in Figure 14. These scales have been drawn to overcome the 

 mapping problem. Each scale contains two curves; the inner curve covers an 

 arc length of 16.6 in., the outer curve an arc length of 19.4 in. The 

 critical arc length may be calculated by Equation [10]. Assuming a thick- 

 ness of 1.33 in. and a ratio R-, /R of lo05, the critical, arc length is 18.0 

 in., which is midway between the curves presented in Figure 14. Areas of 

 maximum out-of-roundness may be determined by placing Figure 14 over Figure 

 12 and rotating the scal-es . The values for the deviations from sphericity 



6 and fi (see Figure 4) are determined across any "diameter" of a scale 

 at a point midway between the two curves. The deviation 5 is determined 

 at the center of each scale. The location of points with relatively large 

 values of out-of-roundness A may be found in this manner. 



Using the hull thickness measurements presented in P'igure 10 and 

 the curves presented in Figure 5, further refinements can be made in 

 determining the critical, arc length. A sample calculation sheet is shown 



in Figure 15. Values of A . h , and R, /R were determined for several locations 



a 1 



on each of the three hulls. Some of these values are shown in Table 1„ 

 The maximum ratio of R /r for the three hulls was 1.05. This demonstrates 

 the accuracy with which these hulls were fabricated and provides a guide- 

 line for reasonable tolerances for similarly fabricated steel vehicles. 

 For example. Figure 5 indicates that a steel hull 2 3/4 in. thick and an 

 out-of-roundness A of 0.107 in. would also have a ratio R, /R of 1.05 o It 

 is important to remember that the out-of-roundness is defined over a critical 

 arc length „ 



The collapse depths of the three ALVIN pressure hulls were cal- 

 culated using a critical local geometry„ A minimum ratio of hull thickness 



27 



