7. Wayland, H. "Scale Factors in Water Entry." NAVORD Report 978 (NOTS 105), 



April 1947. 



8. Birkhoff, G. and R. Isaacs. "Transient Cavities in Air-Water Entry." NAVORD Report 



1490, January 1951. 



9. Weible, A. (Forschunganstalt Graf Zeppelin). "Penetration Resistance of Bodies with 



Various Head Forms at Perpendicular Impact on Water." Naval Research Laboratory 

 Translation No. 286, February 1952. 



H. M. Berger 



We have heard a very comprehensive review of the state of the art in the 

 theory of water entry and it was interesting to hear in particular of the recent work 

 at ARDE on steady state cavitation. I would like to point out that one of the prob- 

 lems in hydroballistics that was not mentioned and which has received practically no 

 theoretical attention in the past is that of water exit. It seems to me that this is a 

 fertile problem for a theoretical treatment. Many of the difficult problems that plague 

 us when we attempt to analyze water entry are not present in water exit, and therefore, 

 I believe that a theoretical approach could contribute a great deal to an analysis of the 

 forces that arise during water exit. 



I have just a few brief remarks to make about the state of the experimental 

 work in this field. Concurrent with the effort to develop an adequate theory for water 

 entry that has been outlined by Dr. Maccoll has been an extensive experimental program. 

 However, early in the history of water entry studies, those working in the field realized 

 that the modeling techniques they were using did not model important full scale effects 

 such as the sudden accelerations experienced when the missile strikes the water. Con- 

 sequently the experimental program divided into two parts — one, a full scale investiga- 

 tion of water entry characteristics of particular missiles — the other, an investigation of 

 the scaling laws. Also, much attention was given to the development of adequate instru- 

 mentation for both full scale and model tests. 



Recently, studies have been carried out by Levy at the California Institute of 

 Technology [1] and Waugh at the Naval Ordnance Test Station [2] that have shown 

 that with both Froude and cavitation number modeling, good agreement can be 

 obtained with full scale water entry tests. 



Levy concludes that for the range of Froude numbers and cavitation numbers 

 that are within the prototype range: 



1. "The behavior of the model with regard to trajectory, inclination, time to 

 tail slap, and drag during cavity motion depends much more on the cavitation number 

 than on the Froude number." 



2. "Model tests in which the cavitation number is considerably greater than that 

 of the prototype may yield a model behavior that is completely different from that of 

 the prototype." 



3. "Within the range of parameters that are encountered in prototype opera- 

 tion, the behavior of the missile is nearly independent of Froude number. This means 

 that good results may be expected in most cases by using cavitation scaling alone. This 

 is not meant to imply that the cavitation criterion is the only one that need be con- 

 sidered. It is known that under some conditions water entry phenomena are affected 

 by gravity, viscosity and surface tension. However, cavitation scaling does not specify 

 the operating conditions of the model except by establishing a functional relation 

 between speed and pressure. 



Therefore, it should be possible to avoid these other complications by proper 

 choice of variables." 



Dr. Waugh has told me that preliminary tests that he has made show that with gas 

 density modeling, in addition to Froude and cavitation modeling, the cavity shape and 

 closure can be accurately reproduced by model tests. The above results should give 



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