488 -"- 



of deflection and that as a mean value it is reasonable to assume A^ = 31. «. Ve can thus 

 calculate the ratio S'^^/S^ from the formula 



1") = ''- ^ 



i 15.8 w 



m '■■ 



to obtain the values given in the last column of Table 1, 



The combined error in i'J\ "^ue to errors In S '^ and errors in estimating 3^ are considered 

 to be at most lO* *ith the exceptiorrs of Shots 236 and 209, for which the error may be as much as y!%. 



(l) General comparison of theory and experiment . 



The values of S" /S in Table 1 have been plotted against w in Figure 3, and it will be 

 mm ''' . /p • 



seen that in spite of a considerable scatter there is a definite indication that S'^^/S^ increases 



as w decreases (3 statistical check indicating that this is significant) and varies in general in 



much the way that the theory predicts. Some of the scatter is undoubtedly due to the possible 



experimental error in S" /S discussed in the previous section; in particular the value S'^^/S^^ 



= 1.07 for Shot 2 21 must err from this cause since by definition S^^^ ^ S'^. However, the 



experimental results cover a large variety of shots with differing charge conditions and plate 



thicknesses, so that even if S' /S could be accurately measured a considerable scatter is in any 



case conceivable due to variations in type of loiding and of (T^ - T )/T from shot to shot. 



Thus the curves drawn in Fijure 3 correspond to the theoretical curves of Figure 2 with 

 W = 1,0" and * = 1.89" and since they bracket the experimental pointSiall scatter could be due 

 purely to variation in type of loading from shot to shot. Since the second pulse due to bubble 

 collapse Is of much longer effective duration than the initial shock wave, such a variation in type 

 of loading is quite feasible from shot to shot depending on the relative contributions to damage 

 of shock-wave and second pulse. 



Now if we put W = 1° or W = 1.89" in equation (109) with Hab = 3220 square inches and 

 K = 25 from equation (l3l), we then find that (T^ - ''',)/''' = 0,008. Thus, if we assume the scatter 

 In Figure 3 to be due primarily to variation in type of loading between Instantaneous Impulse and 

 H(t), we should then expect (T^ - ''■j)/T^ to be about li for all shots. 



However, we cannot rule out the possibility that the scatter may be equally or more dependent 

 on a variation of (T - T )//T from shot to shot. 



Since, as previously stated, the shapes of the two curves (a) and (b) in Figure 2 are virtually 

 the same, we can Interpret the curves in Figure 3 not only as W = 1", w = 1.89" corresponding to 

 different lading and same (T - '^,)/'^q, but also as W = l", W = 1.89" for pure impulse loading 

 corresponding from equation (1D9) (with K = 25, lab = 3220 square inches) to (T - T ) /T = 0,008 

 and 0,028, Similarly, we could interpret these curves in Figure 3 as W, = l", V. = 1.89" corresponding 

 to H(t) loading with (T - T,)/''' = 0,002 and 0,008. Conversely, it follows that, provided the type 

 of loading is such as to give a theoretical curve in Figure 2 lying between curves (a) and (b), then 

 the values of (T - T,)/''' for all shots are deduced to lie in the range 0.002 to 0,026, Further, 

 the upper estiireite of this range would only bo increased for other types of loading if these could 

 give a curve lying to the left of curve (a) in Figure 2, This does not seem possible since the 

 instantaneous impulse is the most suoden loading we can assume and we should expect, as indicated by 

 the relative positions of curves (a) and (b) , that the less sudden the loading the greater the 

 tendency for pull-in as opposed to plate stretching, i,e., the more the curve lies to the right In 

 Figure 2, Thus, our upper estimate of 0,028 based on pure impulse should be a true upper estimate 

 for all types of loading. On the other hand, our lower limit of C.002 based on H(t) loading is so 

 small that It is relatively unimportant that even lower estimates could be obtained by assuming types 

 of loading giving curves lying to the right of curve (b) in Figure 2, 



We thus estimate that, whatever the type of loading actually occurring, the values of 

 (T - T )/T for all shots lie in a range from virtually zero to about 0,03. This latter is based 

 on a probable mean value K = 25 but even if we assume K = 40, which is probably too large (see 

 A.i«), our estimates of (Tj, - ^I'^^n still remain small, being less than 0.05, This implies, of 

 course, the relatively small variation of less than 5J in T /T from target to target. This Is not 

 unreasonable if the main resistance to pull-in is the resistanc? against the plate stretching at the 



bolt-holes ...., 



