Likewise Monaghan (1949) extended the work of Wagner by approximating to the 

 entry of a wedge by the flow past an expanding prism. 



In addition to the above, a number of model flows have been investigated by 

 comparatively easy analytical methods and are usually found to be in fairly good 

 agreement with experimental data. In this connection mention may be made of some 

 war-time work at the California Institute of Technology on the potential flow about 

 a spherical bowl as the basic pattern for the vertical entry of a sphere (Fig. 3(a)). In 

 this model the p = contour is taken to be the free surface. Although the condition 

 of continuity is not satisfied in this model, most of the physical features of the actual 

 problem appear to be reproduced. A similar treatment has been that carried out 

 recently by Coombs at Fort Halstead for an expanding hollow wedge (Fig. 3(b)). 

 Although infinite velocities are present at the rims of both these models, these singu- 

 larities are outside the field of practical interest. 



b. Oblique Entry. With oblique entry the problem is further complicated by 

 the presence of an additional independent coordinate and for this reason little work has 

 been carried out in this field. Trilling (1950) has devised a technique for calculating 

 approximately the forces on a body of arbitrary shape during the early stages of 

 submersion. He estimates the hydrodynamic forces on the body at a number of 

 depths of penetration by considering the impulsive motion of half a general ellipsoid 

 having the same depth of penetration, the same length and the same submerged 

 volumes as the actual body. Trilling applied his method to the case of the water entry 

 of a sphere at an angle of 45 degs. to the water surface and obtained for the vertical 

 and horizontal components of the drag the results shown in Fig. 4. It will be seen 



2 



6 



OS 



0-4 

 X= Y /R 

 Figure 4. Variation of drag coefficient with depth for 45' oblique entry of sphere. 



219 



