16 



The target will usually be Idealized In the form of a plate or diaphragm, 

 initially plane, backed by air at a pressure equal to the hydrostatic pres- 

 sure. Only non-contact explosions are considered in this report. 



In view of the complexity of the phenomena, the analytical results 

 will first be described in general terms for the case that is most common in 

 practice. Some of the ideas developed in this discussion will be made the 

 basis for the classification of other cases that may arise. After a few re- 

 marks on the role of the Bernoulli effect, the analytical methods will then 

 be described. This will be followed by the discussion of other cases and a 

 more detailed treatment of certain phases of the damaging process. The clos- 

 ing sections of the report will give some formulas for the deflection of a 

 diaphragm, a discussion of the features of the pressure wave that determine 

 damage, and an application of the formulas to some of the available data. 



Many of the appropriate analytical methods for dealing with these 

 problems have already been published in other reports, a number of which are 

 listed in pages 62 to 6U, but for convenience a rather complete and syste- 

 matic mathematical treatment is included as an appendix to this report. 



PART 1 . DESCRIPTION OF A COMMON CASE PRESENTED FOR ORIENTATION 



THE WAVES OP PRESSURE PRODUCED BY A NON-CONTACT UNDERWATER EXPLOSION 



When a charge is detonated under water, it produces effects upon 

 structures submerged in the water only by producing pressures in the water. 

 The distribution of this pressure will be influenced by the associated motion 

 of the water - indeed, it is transmitted by such motion - and motion of the 

 structure itself will in turn modify the pressure in the water. A complete 

 description of the action by the water on the structure can be given, how- 

 ever, in terms of the pressures acting upon the surfaces of that structure. 



In the primary pulse of pressure produced by the detonation, the 

 pressure rises almost Instantly to a high value and then decreases. The rate 

 of decrease diminishes, however, so that the time graph of the pressure pulse 

 has a long "tail." This is illustrated in Figure 1, which has reference to a 

 300-pound charge of TNT 50 feet away, and in Figure 2, which is reproduced 

 from an oscillogram given by a pressure gage at a distance of 17 inches from 

 a charge of 1 ounce of tetryl. 



The high-pressure part, sometimes called the A-phase or the shock 

 wave, is of such short duration that it takes the form of a distinct wave of 

 pressure traveling through the water at finite speed. In the tall or B-phase, 

 on the other hand, the relative rate of change of pressure Is much slower, 

 and the pressure in the water soon comes to stand in a definite relation to 

 the simultaneous motion of the expanding gas globe. The appearance of wave 

 propagation thus disappears in this phase, and the pressure and the motion 



