-3- 457 



Putting (2) in the form 



(^) 2a3 « - 2. (a^^) . l^ ^- (a^a) - l^ ^ (av) 



dt Id' dt 2d' dt 



we note that putting the left hand side of {/?) equal to zero gives the case of zero gravity. 



Also we have 



±. (d - z) ■= V. 



dt 



This assumes that d is measured from the centre of the Subole to the centre of gravity 

 c' target plate. It might De more consistent with the other assumptions to measure d from the 

 initial position of the plate, in which case rr (d - z) = 0. The values of d obtained from the 

 two assumptions only differ by J V dt which is never more than a few inches, and since the 

 other two equations only involve d itself, and not its derivatives, the difference between the 

 two assumptions is small. 



Experxmental Data , 



Fortunately there became available records of the Sox Model shots detailed below. 

 The diagrarmat ic s;t-up is as shown in Figure 3. m the actual calculations the set-up was 

 simplified to the case of Figure a. It was assumed that the mutual effects of the target and 

 bubble would Be the same whC'ther the target was above the charge or to its side. The conditions 

 of the f-xperiir.ents were:- 



Test U8 : Depth of Charge = 5 feet. 

 Stand-off - 2 feet. 



Charge = 1 oz. of T.N.T. 



Test 50 : Depth of charge = 5 feet. 

 Stand-off = 2i feet. 



Charge = 1 oz. of T.N.T. 



In both cases the equivalent radius of the plate was 8.25 inches. For this charge the 

 Taylor unit of length is 3 feet, and tne Taylor unit of time is 0.39tt seconds. 



description of Tables . 



The inttgration of the equations derived in (aragrdph 3 were carried out under the 

 following conditions:- 



a = 0.016 





 Z. = 7.6 



(3sl-(§sI-» 



/3) V from Test 50 

 ilucS of V used in cases 1/? and 2fi were derived from smoothed graphs of the deflect I 



For .. 



