595 



snail bubbles at the miniraum. The radius values used in Fig. 9 were obtained 

 by estimating the total vola-ie of gas present at any instant and then 

 comnuting the radius of an equivalent sphere. Figure 6, v/Mch includes 

 data frooi two sizes of charge, shows that for a scale range of apDroximately 

 2:1 it is possible to reoresent the radius-time curve for a given explosive 

 at a fixed depth in non-dimensional form. Although data from a wide range 

 of explosive weights at a given depth were not available, it is believed 

 that these non-dimensional curves will represent any size of charge in fra* 

 water. 



The shape of the composite curves resembles that of a curtate cycloid* 



(the curve traced out by a point on the spoke of a wheel which is rolling 



along a straight line in a plane) . The equation of a c\u*tate cycloid in 

 rectangular, paranetric form is: 



A " m - n cos «P 

 T = ma - n sin •. m > n > (l-l) 



The constants m and n in this equation must be chosen so that A « Awn and 

 T = Ti for 9 equal to TT and 2fT respectively, and so that A/A^j fits the 

 composite curves at ^ equal to 2TK It should be noted that for f equal 

 to 2Tf, A/Ajji is identically Ani^Ajj]_. If this ratio is represented by the 

 syinbol q, Eq. (l-l) becomes: 





If one plots Eq. (1-2) with q taken as 0.25 along with the composite 

 curve for TNT at 300 ft, it can be seen that the equation has been made to 

 fit the data at f equal to If and ZTT', but that it predicts a value of A/Ajjj 

 which is too low for intermediate values of ^ . This situation can be 

 remedied if one writes the equations in the form: 



* Various authorities disagree as to the distinction between a prolate and 

 a curtate cycloid. The author prefers the definition given above. 



- 39 - 



