added impetus to experimental studies of water entry, especially in view of the diffi- 

 culties Dr. Maccoll has pointed out that exist in the theory. 



There are several questions that I would like to ask Dr. Maccoll. First, what 

 test facilities does he consider best for studies of the various phases of hydroballistics 

 that he has outlined? My second question arises from his mention of the gravity effects 

 on the quasi-steady cavity phase — that is, the effects causing the rolling up of the rear 

 of the cavity into two hollow-core vortices, I would like to know whether he knows of 

 any tests that show a Froude number effect on the drag of a cavitating body, and if 

 so, is the drag reduced or increased by such effects? My last question concerns the 

 role of water entry theory in the development of hydroballistic missiles. I would 

 like to hear Dr. Maccoll's opinion of the role water entry theory plays in such a 

 development. 



REFERENCES 



1. Levy, J., "On Modeling the Oblique Entry Into Water of Air-Launches Missiles," Calif. 



Inst, of Tech. Hydrodynamics Lab. Rept. No. E-12.19, August 1956. 



2. Waugh, J. G., "Water-Entry Pitch Modeling With One-to-One Froude and Cavitation 



Number Scaling," U. S. Naval Ordnance Test Station, Underwater Ordnance Depart- 

 ment Internal Report, IDP 221, 8 July 1955. 



/. W. Maccoll 



These contributions represent a valuable extension to the topics discussed in 

 the paper, and draw attention to some subjects, such as water exit, unsteady flow, and 

 dynamics of an underwater body which it was not possible to deal with in the time 

 available. 



The remarks by Professor Birkhoff and Mr. Nicolaides serve to emphasise 

 the computational difficulties of even the simplest potential-theoretic flows, and under- 

 line the need for a closer mathematical and physical understanding of the separation 

 phenomenon. 



The remarks by Dr. Berger and Mr. Fabula on the experimental work on 

 water entry modelling at the California Institute of Technology and the Naval Ordnance 

 Test Station are of great interest. An extension of this work to the high speeds associ- 

 ated with rocket entry would be of great practical use. Dr. Berger's question on test 

 facilities is rather difficult to answer briefly, except perhaps to mention that in the 

 experimental field there is a need for detailed measurements of pressure distributions 

 during the water entry phase, and, in general, for work on high speed water entry, 

 in which the main problem is that of controlling the entry conditions. For steady flow 

 problems there is already an impressive and varied array of cavitation tunnels and 

 rotating arm facilities in existence. 



The authors know of no tests which show a marked Froude number effect on 

 drag at the low cavitation numbers at which vortex rolling-up takes place; it is unlikely 

 that the flow over the head of a body will be very much affected by conditions at the 

 rear of a cavity. Security requirements unfortunately preclude a full answer to Dr. 

 Berger's question on the role of water entry theory in the development of hydrobal- 

 listic missiles; the remarks by Mr. Burt and Mr. Nicolaides point out the need for a 

 great deal more work in this field before theory can be applied with confidence to the 

 problem of water entry of missiles. 



In conclusion the authors wish to thank Mr. Fabula, Dr. Berger and others 

 taking part in the discussion for drawing attention to additional work which had 

 escaped their attention. 



239 



