445 



THE ATTRACTION OF AN UNDERWATER EXPLOSION 

 BUBBLE TO A RIGID DISC 



A. R. Bryant 



February. 1945 . 



Summar y. 



The attraction of an explosion DuOble towards a rigid disc has been calculated for two 

 important cases, viz. (l) the disc fixed, (2) the disc moving along the 1 ifle joi-ning disc and explosion 

 centre. The case in which only part of the disc is moving has been treated in an Appendix. 



For the fixed disc the attraction falls off more rapidly with distance than the attraction of 

 an infinite rigid plane. At one disc radius the attraction is one half that of the infinite rigid 

 plane at the same distance. At one disc diameter the attraction is one seventh that of the infinite 

 rigid plane. 



The attraction of the moving disc depends on both its velocity and acceleration. That part 

 of the attraction vhich is due to its motion falls off more rapidly with increasing distance than the 

 part due to its rigidity. 



It is suggested that the attraction of a bubble to a rigid disc is a reasonable approximation 

 to the practical case of a target like a Box Model. It is pointed out that the motion of the Box Model 

 as a whole due to the explosion pressures may have an appreciable influence on the displacement of the 

 bubble. 



Introduction .. 



In considering the damage to finite targets caused by underwater explosions it is desirable to 

 calculate, at least approximately, the displacement of the bubble towards or away from the target. 

 So far the only finite rigid surface whose attraction has been calculated is the sphere. For targets 

 like the D.N.C. box model, or the "drum" model used in the U.S.A., where a target plate is surrounded 

 by a rigid "skirt" or baffle of finite extent, it is suggested that the attraction of an explosion 

 bubble to a rigid disc would be a better spproximat ion to the experiment ':1 conditions than the 

 attraction to a sphere. The problem of s rigid disc is treated in the following note. 



The following assumptions have been made:- 



(1) The bubble remains spherical throughout its motion. 



(2) The maximum radius of the bubble is small compared to its distance from the disc. 



(3) The vrlocity of displacement of the bubble is small and its contribution to the 

 attractive forces is neglected. 



The Attraction of an Exp Lo sion Subtle to a .'ixed Rigid Disc . 



The metho..' if calculating the attraction of a fixed rigid disc is as follows. A point source 

 of unit strength is placed at the explosion centre. A potential <P2 'S found which, when added to the 

 potential <p^ due to the point source, gives the correct boundary condition over the surface of the 

 disc. This potential may be regarded as due to image sources "induced" by the original point source. 

 The required "attraction coefficient" is then the value at the explosion centre of the space gradient 

 - ^ , where x is positive in a direction away from the disc along the axis of symmetry. It was shown 

 in an earlier paper' that the velocity of the bubble towards the surface at any time is the product 



of two 



' "A Simplified theory of the Effect of Surfaces on the Motion of an Explosion Bubble." 



