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Studies on the Gas Bubble Resulting From 

 Underwater Explosions 



ON THE BEST LOCATION OF A MINE NEAR THE SEA BED 



At the request of the David Taylor Model Basin of 

 the Bureau of Ships and of Division Re 2 of the Bureau of 

 Ordnance, a aeries of investigations has been undertaken 

 by the New York University Group of the Applied Mathematics 

 Panel of the N.D.R.C* with the object of analyzing the 

 phenomena associated with the gas bubble produced by an 

 underwater explosion. 



The present study, carried out by Dr. Max Shiffman 

 and Dr. Bernard Friedman, with the cooperation of the 

 Mathematical Tables Project in the extensive numerical work, 

 is concerned with the following problem: If a mine of given 

 weight of explosive is to be placed near the sea bed, what 

 position should it have to cause maximum damage to a target 

 at the surface? 



It seems appropriate to make a few introductory re- 

 marks about the broader research program of which this report 

 Is a part. Often the destructive effect of an underwater 

 explosion is not wholly due to the high presstire shock of the 

 explosion. After the initial shock wave has passed with 

 enormous speed, a comparatively slow pulsation of the gas 

 bubble (consisting of the burned gases) takes place. In the 

 second and sometimes even third pulse of this motion of the 

 bubble, a pressure pulse of considerable strength is emitted. 

 While the peak of the shock pressure from the explosion is 

 far above tliat of the later pulses (in typical cases, six 

 to ten times the pressure of the second pulse), .the duration 

 of these later pulses is much longer (about twenty times as 



