literature. Some of these discrepancies may be due to faulty instrumentation, but 

 real further progress would seem to require that they be explained. Some of our 

 conclusions are contained in Ref. [1], Ch. XI, §2, but N.O.T.S. lost interest in our 

 project before it was completed. Also it was not clear how much experimental data 

 should be declassified, especially as regards the influence of air viscosity. 



Again, and in spite of laborious calculations by Marchet, Miss Vaisey, Brunauer, 

 and Young (see Ref. [1], Ch. X, §9), the axi-symmetric potential-theoretic cavity flow 

 past a disc has never been accurately computed, for any cavitation number Q. Though 

 C D (Q) is now accurately known, the variation in cavity length / as a function l(Q) 

 of Q is not. In these calculations, the free streamline location seems very sensitive 

 to small variations in pressure. Also, the singularity at the known separation point is 

 extremely troublesome, and I wonder if a more careful analysis of the computational 

 implications of this singularity should not take precedence over the still harder prob- 

 lem of locating the unknown separation point on streamlined missiles. 



In the potential-theoretic approximation, this separation point should presumably 

 be assumed to be determined by the axi-symmetric analog of the Brillouin-Villat Sepa- 

 ration Condition (Ref. [1], Ch. VI, §6). But again, the numerical application of this 

 method promises to be extremely difficult. — The situation is much more favorable in the 

 plane case, and I confess to feeling great confidence in the calculations by Zarantonello 

 and myself, referred to by Drs. Cox and Maccoll. 



The theoretical analysis of cavitating flows past yawed solid bodies strikes me 

 as very much harder, except perhaps in the case of long, nearly cylindrical missiles. 

 Moreover it should be remembered that, in hydroballistic applications, the problem is 

 to predict the angle of yaw a and cavitation number Q, whereas these are assumed 

 known in most theoretical analyses. In practice also, / and hence Q{1) depend on the 

 complex mechanism of air entrainment at the rear end of the cavity, described by 

 Drs. Cox and Maccoll. The amount of this air entrainment, and the degree of delay 

 of separation due to boundary layer turbulence and air viscosity, all of which are 

 neglected in the potential-theoretic model, impress me as being extremely difficult to 

 predict. 



In spite of the above difficulties, and the probability of other complications as 

 yet unsuspected, I hope that a determined effort to solve impact and water entry 

 problems will continue. My critical remarks are not intended to discourage further 

 research, but to emphasize the need for distinguishing plausible ideas from reliable 

 methods of prediction. In hydrodynamical theory, this distinction is always essential. 



Ref. 1 : G. Birkhoff and E. H. Zarantonello, "Jets, wakes and cavities," Academic 

 Press, approx. Dec. 1956. 



F. S. Burt 



Dr. Maccoll has taken hydroballistics to cover not the whole field of the hydro- 

 dynamics of underwater weapons but rather the various aspects connected with the 

 entry of an uncontrolled air launched weapon up to and including its fully wetted 

 underwater run. I think this is a perfectly proper view to take and it certainly leaves 

 a sufficiently wide and difficult field to be considered under the heading of hydro- 

 ballistics. 



In the water entry phase, even geometrically simple shapes like the sphere are 

 extremely difficult to deal with theoretically. Unfortunately many of the applications 

 we are interested in for naval use are concerned with the oblique entry of head shapes 

 which are spherical, ogival, or a combination of both. With such head shapes the simi- 

 larity principle that applies to the entry phase of a cone is no longer applicable. The 

 cone is a rather special mathematical case in that during the initial entry phase the situa- 

 tion at a time t is very similar to that at a time t + 8t. Nevertheless, I am very 

 interested to see the data which Dr. Maccoll has presented on the oblique entry of cones. 



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