At A.R.L. we had at one time extremely high hopes of Trilling's theory which 

 Dr. Maccoll has mentioned but we now suspect that no theory which fails to take 

 account of the deformation of the free surface can satisfactorily predict the horizontal 

 component of force in oblique entry. We have recently done a recalculation for the 

 oblique entry of a sphere using an approximation to an oblate spheroid rather than a 

 prolate ellipsoid. The general trend of the drag coefficient for horizontal and vertical 

 components seem to agree generally with that obtained by the Trilling method. That 

 is to say that the vertical component is much the same as that obtained at vertical 

 entry rising to a maximum of 0.8 to 0.9 at some time after an immersion of about 

 I4 th of the radius below the undisturbed free surface, whilst the horizontal compo- 

 nent of the force rises much more slowly. 



Recently Hobbs, Backdon and Woodley at the National Bureau of Standards 

 have produced some measurements of impact force on spheres at oblique entry. One 

 of the results they obtained was for a 4 in. diameter sphere with an entry angle of 

 51°. Comparing the vertical and horizontal coefficients of drag they obtained with 

 those predicted by Trilling's method, it can be seen that although the vertical compo- 

 nents are of the right order, the horizontal components are way off in the time scale. 

 At A.R.L. we are of the opinion that in calculating the horizontal force in oblique 

 entry the free surface deformation has to be taken into account, whereas Trilling's 

 method is only possible because the deformation of the free surface is ignored. 

 Admittedly, satisfactory experimental data on impact forces during oblique entry are 

 not numerous. In this connection, we at A.R.L. are in the early stages of a programme 

 of whip measurements at model scale. A related programme of axial deceleration 

 measurements, for which we have no spare effort at the moment, would ideally comple- 

 ment the whip measurements: between them they would provide much useful data 

 on the impulse imparted to a weapon during the entry phase. 



The recent work by A.R.D.E. on the lift on the nose of an inclined body on 

 a fully developed cavity is extremely interesting. They are to be congratulated on their 

 "strip theory" and their application of the Munk-Jones slender body theory to cavity- 

 running missiles. A recent A.R.L. report No. ARL/R1/G/HY/18/1 entitled "Water 

 Tunnel Boundary Effects on Axially Symmetric Fully Developed Cavities" by I. J. 

 Campbell and G. E. Thomas, dealing with the special case of such a cavity near a 

 solid boundary such as a water tunnel wall, may be of some interest. We are also 

 hoping to devote some effort to such forces in connection with the problems of stability 

 in the cavity stage and, in view of the difficulties of making such measurements in 

 water tunnels of our type, we are planning an experimental programme for our large 

 rotating arm which seems to offer a number of advantages for this type of work. 



I can confirm that the application of Vandrey's method to the calculation of 

 the pressure distribution on fully wetted bodies of revolution does indeed involve much 

 complicated labour and at A.R.L. we are in the process of programming the method 

 for a high speed computing machine. The evolution at A.R.D.E. of a similar method 

 for application to cavities is very interesting. 



/. D. Nicolaides 



I had really only two remarks to make. One, I think that the timeliness and 

 importance of this paper certainly should be recognizable to all who read the newspapers 

 these days, and it is no breach of security to point out that the underwater weapons 

 are beginning to gain on the pure air-flight weapons, and this problem of water entry 

 and underwater motion is extremely important. 



You will recognize with supersonic aircraft drops and rocket shoots, we are into 

 areas in which we are now hardly thinking about in terms of water entry velocity. 



Now I certainly acknowledge the many outstanding items which you included 

 in your paper, particularly the lift force at angles of inclination, but these are indeed 

 steady state phenomena, for the most part, and when one compares the accuracy of 

 performance computations for missiles under water with missiles in the air, you will 



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