- 11 - 141 



displacement due to the pressure wave. The pressures au'. to the succeeding bubble expansion can, 

 so far as their effect on the plate Is concerned, probably be considered as thoujh applied statically, 

 though this is not quite certain because the pressure due to the first contraction of the bubble 

 doss rise in time l^ss than T. 



Com parison of calculated and observed di splacements . 



The average energy aosorbed by the plate per unit volume must be equal to the average kinetic 

 energy per unit volumo given to it by the pressure wave. From (tu), (43) and (UO) therefore, 



5.76 (0.495)^ h^P/b^ = "/.IS X 10 orgs/c.c. 



Using P = 20 tons/square inch = 3.09 x 10 dynes/sq.cn. and b = 3 feet = 91.4 cm., I find 



h^ = 14.5 sq.cin. or h = 3.6 cm. = 1.5 m. (47) 



The observed value for the plate in the experiment was 1.15 inches 

 and for a similar plate but with R.O.X./T.N.T. 33 explosive it | («8) 



was 1.41 inches 



In the case of these two experiments the plate was set vertically with the explosive at 

 the same level. The bubble might be expected to broak surface before again contracting in both 

 cases so that the subsequent pressure due to the contraction and second expansion would not be 

 expected to appear in any cas'?, but even if the plate and explosive were at such a depth tnat it 

 would occur, it would not produce an effect comparable with tnat which occurs between t = 0.275 

 seconds and t = 0.30 seconds when the plate is placed horizontally 14 feet above the explosive. 



The effect of a static pressure applied to the air-backed plate is accorfling to (Ul) to 

 produce a maximum displacement 



h = 0.179 



0.179(36 X 2.54)^p 



20(1.54 X 10'')(0.173 X 2.54) 



where P Is taken as 20 tons/square Inch and d = 0.173 inches. Thus the plate would be dished 

 I.IOU cm. per atmos. of applied pressure. 



Since the plate has already been dished to 3.8 cm. by the pressure wave, it will be seen 

 from Figure 3 that the pressure due to the kinetic wave which follows immediately after the pressure 

 wave and which has a maximum pressure of about 2 atmos. cannot increase the dishing and Is therefore 

 Ineffective in doing further damage to the plate. 



Plates, which were placed in a horizontal position 14 feet above the charge, were, according 

 to the present analysis, subjected to a long continued pressure which was calculated to begin at 

 about t = 0.275 seconds, rise rapidly to a sharp peak, drop to about 11 atmos. and then fall off 

 gradually till at about t = 0.3O or 0.31 seconds it is again only one or two atmospheres. 



The conditions determining the thickness and intensity of the pulse at t = 0.2 78 seconds 

 (when the bubble reaches its minimum value) are not likely to be In fact as they are described In 

 the theory, because the bubble in collapsing will probably be far from spherical. It may well be, 

 however, tnat tne larye and loiia-cont inu=u pressure which occurs ottween t = 0.278 and t = O.30 

 seconds, i.e. during the second expansion, will be produced in the actual explosion because there 

 Is a strong tendency for the bubble to become spherical while expanding". It will be seen in 

 Figure 3 tnat a pressure of 9.4 atmos. Is nreintained for a duration of r = 2.54 milliseconds. 

 Thus the maximum displacement of the plate is likely to be at least equal to 



h = (1.104 x 10.0) = 11 cm. = 4.3 inches 



The observed maximum displacement was 



h = 4.35 inches 



This close agreement is almost certainly purely accidental. 



