70 56 



The pressure to be used in calculating the deflection will be the 

 maximum pressure in the incident wave when the dimensions of the entire tar- 

 get are small as compared with the length of the wave in the water, or twice 

 the maximum pressure if the diaphragm is surrounded by a large rigid baffle. 



2. The impulse J pdt should determine damage when (a) cavitation does 

 not occur and (b) the time of action of the pressure is much less than the 

 swing time of the structure, or !'„« T, . For a diaphragm of radius a Inches 

 this should hold for a charge of o^/lOO pounds or less. 



This case is exemplified by Case 1 as previously described, and in 

 particular in Equation [77]- In Case 1 the diffraction time was also assumed 

 to be relatively short; but the statement Just made concerning the impulse 

 should hold independently of the diffraction time. For the influence of dif- 

 fraction Is confined to the relief pressure, as represented by the integral 

 in Equation [l6], and the relief pressure in turn is determined by the motion 

 of the diaphragm Itself. Thus the whole motion depends upon the initial ve- 

 locities given to the structure by the Incident wave; and since the wave, by 

 assumption, acts only during a small part of the swing time of the structure, 

 the initial velocities produced by it are proportional to the impulse, inde- 

 pendently of the maximum pressure or the duration of the wave. 



The variation with Wand R should be as described for Case 1 in the 

 last section. To a first approximation, the set deflection z should be given 

 by 



2 



z = B^ [95] 



where B is almost constant for a given structure, provided the elastic range 

 can be neglected. 



This case will probably not arise often, howe/er, because of the 

 common intervention of cavitation. 



3. The energy carried by the wave, jp^dt/pc, does not appear in any 

 simple damage formula obtained from the present dynamical analysis. The 

 energy should be significant whenever circumstances are such that little re- 

 flection of the wave occurs; but such cases are not easy to define precisely. 

 More generally, the energy will be the significant quantity if, for any rea- 

 son, the plastic work stands in a fixed ratio to the energy brought up by the 

 wave. Since the incident energy varies in proportion to the charge weight W 

 and roughly as ^/R^, the deflection, which is nearly proportional to the 

 square root of the plastic work, will then vary as WpR, or 



. = C^ [96] 



