note we are in a very serious situation with regard to mils dispersion. The argument 

 that you travel a short distance under water so that the errors, though large in mils, 

 are not important, is not sound. When we talk about submarines at very deep depths, 

 and the errors in mils begin to imply large errors in distance, the dynamic forces and 

 moments acting may well be equal in importance to the static ones which we now 

 consider, and, thus, will have to be included for calculations of satisfactory accuracy. 



Recent tests in fully wetted flow indicate that the Magnus forces which are 

 ordinarily completely neglected by the hydrodynamicist, are indeed quite important, 

 and create quite large transverse displacements. It might be expected that in the cavity 

 flow these forces will be important also. 



In other words, what I am saying is we have come a long way, but the 

 knowledge that we now have compared to what we .need in weapons development is 

 poor, and thus we are very far behind indeed. 



Now I might say in that regard, and this my second point, that in reference 

 to the high-speed computers, they may in a sense be our main hope. For example, in 

 connection with the double disk cavity problem in recent work by the Naval Proving 

 Ground (NPG Report No. 1413 by Young, et al.) this problem has been completely 

 coded, and the free boundaries have been determined. 



Now this problem was somewhat unchallenging to some of the people at the 

 Naval Proving Ground, and they felt that it might be interesting to consider the case 

 of a disk travelling at constant velocity in water, and then suddenly stopped, and then 

 attempt, using that Naval Ordnance Research Computer to compute the transient 

 development of the cavity. It is too early to indicate any results. More than a year 

 has been spent just bringing up to date the coding required to attack this formidable 

 problem. 



I might also mention that once you determine your forces and moments on a 

 hydroballistic missile, be they linear or non-linear, you have the problem of determining 

 where the missile will go. Assuming we have these forces, let me say to you, the coding 

 is now available for this same machine to predict the underwater trajectories. 



In summary I would like to suggest two things about which there is an awful 

 lot we don't know: first, transient or dynamic forces and moments, including those 

 of the Magnus type; and secondly, flow and performance problems for which the high 

 speed computing machine, in the final analysis, may be our only hope. 



A. G. Fabula 



This paper gives a valuable summary of recent results and new directions for 

 hydroballistics research. This summary is of especial value because as the authors 

 have indicated, the open literature on the subject is limited and the research establish- 

 ment reports have limited distribution. In an attempt to thank the authors for their 

 excellent work, I would mention certain additional reports — in the order as the subject 

 material of the paper. 



Shock Phase 



In [1], Dergarabedian has summarized the work of Trilling, Owens, and Korkegi 

 on effects of water compressibility in normal impact (two and three dimensions). 

 Basic assumptions of these linearized theories are that the body is rigid and that the 

 ratio of body speed to the speed of sound in the water is much less than one. The 

 more general problem of an elastic body impacting on the surface of a compressible 

 liquid has received some preliminary consideration in [2]. 



Normal Entry 



In connection with the authors' mention of Monaghan's extension of Wagners 

 approximate treatment of normal symmetric wedge impact, it is interesting that related 

 work was done by Bisplinghoff and Doherty [3]. Besides the effect of deadrise on 

 the added mass coefficient, they included the effect on the rise of the free surface. 



236 



