217 



APPESDIX B . 



As a numerical example of tne possible effect of fixing a target let us consider a sphere 

 of raaius 5 feet subjected to the pressure pulse from a charge of 5 lbs. T.N.T. with its centre 

 of gravity at 15 inches from the nearest point of tha sphere. This case has been chosen as 

 simulating the case of a half-scale Cylindrical target for which no difference in damage was found 

 whether tne target was suspended or resting on the bottom. The sphere has been chosen to have 

 approximately the same volume as the Cylindrical target and we assume it just waterborne. The 

 numerical values of constants for this case are tnen 



x ■= 1.25 k = 3/2 



q =■ 5 m = /J/a (BI) 



and since q (X - l) = 1.25 it should be noted that the case is one of a relatively close explosion 

 where the present analysis, while it cannot give an accurate estimate, snould give the correct 

 order of maximum bodily velocity. 



Using the values for sea-water of 



p = 611 lbs. /cubic feet 

 9 



c = 1900 feet/ second (B2) 



and tne experimental relation for T.N.T., 

 _ 7^1/3 



tons/square inch (83) 



° D 



where W is weight of charge in lbs. and D is distance in feet we find, since 0=5, 



V = 63 feet/second (BU) 







Using the values given by (Bl) and (BU) we then find by using equation (25) that the 

 maximum bodily velocity is 



"max ■ •^° ^0 " '^"^ '^et/second (85) 



It nay be noted that the bodily displacoucnt of the sphere, as given by equation (27), during 

 the time in which tne pressure pulse cormunicates such a velocity is .13 inches which easily satisfies 

 the assumption of the analysis that It is snail relative to the radius (5 feet) of the sphere. 



Thus, if the Cylindrical target had been strong enough to withstand the explosion without 

 dishing, we should have expected the pressure pulse to give it a maximum bodily velocity of order 

 13 fetl/second while in the presence of dishing the maximum velocity would tend if anything to be 

 of lower order. 



In order to consider whether a bodily velocity of this order is likely to affect tlie datrage 

 we note that the major damage was fairly concfintrated near the charge and we then calculate the 

 velocity given initially to the plating nearest the charge by using the results in the repurt 

 "The pressure and impulse of submarine explosion wnvfjs jh plates", assuming the plating leaves the 

 water; for plating 0.U5 inches thick we then obtain o plating velxity of 380 feet/seccnd. 



The energy conmunicated by the pressure pulse is thus mainly concentrated in the form of 

 high plate velocity, of order 100 feet/secona maximum, over tne near portion of the target while on 

 the other hand the total coimiunicated impulse will only produce a bodily velocity of order 

 13 feet/second. 



Owing to the concentrated nature of the blow there seems little possibility of the 

 conditions on the back half of the target, i.e. whether fixed or opposed purely by its own and water 

 inertia, being of any importance until afttr most of the energy has already been absorbed by dishing 

 at the front of the target. 



This conclusion is in agreement with tne experimental results of which it is not, of course, a 

 full explanation since the kinetic wave and pulsating gas nubble effects have not been considered but 

 it seems probable that tnose effects, if of any importance, were also too concentrated to be affected 

 by conditions on the back of the target. 



