254 -8- 



of the gas. This would reduce the pressure inside the gas 

 and also the pressvire in the water. To obtain the optlmun 

 pressure, therefore, this bubble must be motionless at the 

 time of Its mlnlmara size. 



For an appraisal of the value of stabilization, the 

 damage due to the secondary pulse must be studied. All 

 theories of damage show that for a pressure pulse which 

 lasts long relative to the time constant of the structvire 

 to be damaged, the damage is approximately proportional to 

 the peak pressure and not to the Impulse or energy. Since 

 the duration of the secondary pulse is approximately twenty 

 times that of the shock wave, it would seem that maximizing 

 the peak pressure of the secondary pulse increases the damage* 



3, The location of the mine . 



Let *V be the weight of the explosive in pounds, 

 (the nvunerical values refer to T.N.T. for which the charac- 

 teristic constants were available to the authors), D the 

 distance in feet from the bottom of the sea to a point 33 

 feet above sea level (allowing for the pressure of the atmos- 

 phere), and B the distance in feet from the center of the 

 mine to the sea bed. The problem is to determine the best 

 value for B if W and D are given. This is more easily 

 expressed in terms of the non-dimensional quantities which 

 are used In part II. For the unit of length select 



(1.1) L = 13.2^1 ft.. 



•which represents (approximately) the maximum radius of the 



« This argument Is not completely rigorous since contri- 

 butions to the pressure In the water occur from the motion 

 of the water as well as from the gas pressure Inside the 

 bubble. The fact that the gas pressure is the more Important 

 contribution arises from the mathematical analysis of the 

 interplay of the two effects. 



