SURFACE AND OTHER EFFECTS 421 



necessitate developing a theory appropriate to the bubble pulse pressure- 

 time curve. 



The calculations outlined above for circumstances when cavitation 

 occurs are clearly idealized, as they take no account of differences in 

 character of the loading at different points on the diaphragm and further 

 involve approximations in analysis of the spreading of the reloading 

 wave. More refined analytical treatments would evidently be difficult 

 to carry out. The significant result in the idealized case is the relation 

 of damage to absorption of energy from the incident wave if cavitation 

 occurs, and it is not unreasonable to expect that at least qualitatively 

 similar results would be obtained from such treatment. 



The analytical treatments for damage to circular diaphragms which 

 have been given here are based largely on theories developed by Kirkwood 

 and by Kirkwood and Richardson.^ A comprehensive discussion of 

 damage to circular diaphragms and plates, which treats similar prob- 

 lems in more detail than has been possible here, has been given by 

 Kennard (57). The reports of these workers should be consulted for 

 more complete analytical developments. A number of experimental 

 investigations under varying conditions have been carried out at several 

 laboratories. Among these may be mentioned experiments on 10 inch 

 plates by Hudson (48) at the Taylor Model Basin, on 21 inch plates 

 (Goranson (41)), and Modugno gauges (see section 5.3), and on 3.3 

 inch diameter diaphragm gauges by Fye and Eldridge at Woods Hole 

 (39). Another important series of investigations has been carried out 

 by the British Admiralty Department of Naval Construction and by 

 the Road Research Laboratory, employing box models with rectangular 

 air-backed steel plates having areas of several square feet.^ The dis- 

 cussion of these and other larger scale damage trials is beyond the scope 

 of the present development, which has for its purpose only an indication 

 of the factors which must be involved in an understanding and evalu- 

 ation of such experimental work. 



10.7. General Considerations in Underwater Explosion Damage 



The discussion of the last three sections shows that damage from 

 underwater explosions involves a number of factors, which depend both 

 on the pressure waves and the nature of the structure. As a result, no 

 single answer could be given to the question as to what characteristic of 

 underwater explosions is decisive in causing damage, even if our knowl- 

 edge of the subject were complete. Enough of the phenomena are 

 sufficiently well understood, however, that some useful generahzations 

 can be stated. Most of these conclusions can be understood in terms of, 



8 Reports of these calculations are given in References (61) and (62) . 

 ^ The work along these lines is presented in a series of reports too long to be 

 listed here; many of them have been listed as Undex Reports (115). 



