292 - 10 - 



(a) for R < C6 the question falls to t^e ground, because cavitation either does not 

 occur at all, or only ovtr a small extent of the plate, ana therefore proDably ooes 

 not affoct damage. 



(b) For R > C e, we have two possibilities. \f p^ C^ 9 < u n u' a^h ne may be 

 confident that the effect of diffraction is small, and that cavitation will therefore 

 increase damage. This criterion cannot, however, be satisfied in the "box-nx)del " 

 case D'ut only in the "ship" case, with N of the order of 10 or more. If 



^ C^ R > 4 w N^ o- h diffraction becomes inportant, but incompressible theory 

 refrains a bad approxiitat ion until R beccmes somewhat Urjcr. We ray then compare 

 the results of sections (3-l) and (3.2) to find the effect of cavitation. It 

 seems best to assume complete "follow-up", as it is herd to irragine a mechanism 

 Bx which the plate can leave the water when tne pressure drops to zero, and 

 receive no further damage either from cavitation or diffraction. On this basis 

 we conclude that cavitation will increase damage if the following criteria are 

 sati sf ied:- 



8 N (o 





i 



(3.^* R* -_Vl_, </± f 

 which reduce simply tn the following:- 



f > UlI (ship) (16a) 



C 16 



f > 2JI^ (box model) (l6b) 



C u 



The difference of a factor of '» being due to the absence of the baffle. 



D-j scussion . 



For structures such as a ship's bottom, or panel backed by stiffeners and without any 

 baffle, it will be seen that it needs a rather exceptional set of circumstances for cavitation to 

 make any appreciablp reduction in damage, R must be comparable with C0 for cavitation to be 

 extensive, and yet criterion (l6a) must not be satisfied. This fixes R within fairly narrow 

 limits. In addition N must be small enough for criterion (li*) not to be satisfied, which 

 restricts N to fairly small values. 



For structures such as the Box-model, although it is undoubtedly true that for sufficiently 

 large R cavitation will increase damage, yet (l6b) shows that for a baffled plate there is 

 probably quite an extensive range of values of R for which extensive cavitation occurs and yet 

 reduces dtmage. Further, With N = 1, (no sub-division of pljting) criterion (ll) is never 

 satisfied for any practical size of plate. The range of values of R for which cavitation may be 

 expected to diminish damage seems to include all types of box-model target in common use. 



Conclusion . 



The conclusion, on evidence at present available, appears to be that cavitation would 

 almost certainly increase damage to such a target as a ship's bottom or plate sub-divided by 

 stiffeners, but that it would, in general, reduce damage to targets of the "Box-model" type 

 consisting of a single platu and a baffle. 



References 



