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THEORETICAL ANALYSIS OF THE DISHING OF SIX INCH 

 DIAMETER COPPER DIAPHRAGM GAUGES BY UNDERWATER 

 EXPLOSIONS 



E. N. Fox and W. T. Rollo 



Admiralty Undex Works 



Summary . 



An empirical analysis of the results of the dishing of 36 six-Inch diameter copper 

 diaphragm gauges is given. From this analysis an empirical formula connecting weight of charge, 

 distance of gauge from charge and the volume of dishing Is derived. 



A theoretical analysis is undertaken assuming the diaphragms defom plastically Into a 

 parabolic shape under the action of the primary pressure pulse behaving as a small amplitude 

 plane wave, the pressure decaying exponentially with time. Fran the relatively poor agreement 

 between experimental and theoretical volumes of dishing it Is concluded that the basic assumptions 

 and/or data must err considerably in one or more respects. Before any further refinements of 

 the basic theoretical analysis are attempted it Is recamiended that controlled experiments should 

 be carried out to check first whether the discrepancy depends primarily on inaccuracies In the 

 assumed data and form of the incident pressure pulse. 



Introduction , 



in the past, six inch diameter copper diaphragm gauges have been extensively used, mainly 

 for comparing the underwater damaging efficiencies of various explosives. Little attempt, however, 

 has been made to determine the physical entity measured by the gaug^ this latter being regarded 

 as an empirical 'damage gauge" fron the point of view of comparing explosives. As there is now 

 available a considerable mass of data obtained by the use of these gauges it seemed opportune 

 to attempt a theoretical analysis. The results of this analysis are now presented In this report. 



Experimental data and empi rjcal analy si s . 



The results of the dishing of 36 gauges are given in Table 1, these results having been 

 obtained in numerous trials some of which were carried out primarily to compare the underwater 

 damaging efficiencies of various explosives, others to compare different qualities of steel In 

 Box Models and others to compare the efficiency of riveted targets with ttet of welded targets. 

 Only the results of shots in which T.N.T. was used arc analysed In this report. 



As several empirical formulae of the power-law type, i.e. 



V = KvP'/tr (1) 



where V = volume of dish in cubic inches, 



w = weight of charge in lbs. 



D = distance of gauge from charge- In feet. 



K, a and being constants, have been used in the past, It seemed advisable to obtain ai 

 empirical formula of this type from the analysis of as many results as are available at present. 

 Expressed logarithmically equation (l) may be written 



Log V • Log K + a Log W - /S Log (2) 



and 



