- 5 - 449 



_ a dv 

 " - 9 ^ 



a is the factor in the first Dracket in (13) which has been plotted In Figure 3. 

 Amplication to r'ox Mod.'.l Experiments . 



In Box Model and similar experiments where the target is slung in such a way that it is free 

 to move as a whole under the influence of the explosion pressures acting on it, the effect of such 

 movement on the dis placement of the bubble may be estimated by nuans of equation (13). The following 

 approximate numerical example suggests that this effect trey be of r^al importance. 



The area of the target plate and "skirt" of the R.R.L. box model ts 5 square feet, i.e. for 

 the purposes of using equation (l3) the equivalent disc would have a radius of 1.25 feet. Consider 

 the case of a 1 oz. charge, 3 feet deep, fired at a distance of 1.5 feet from the target plate. it 

 will be supposed that the effect of the explosion pressures on the box model as a whole is to give it 

 an initial velocity away from the explosion centre which is rapidly reduced to zero by the drag forces 

 in the water. 



It is not practicabl- with present knowledge to calculate the initial velocity and the deceleration, 

 but in order to estimate the importance of the effect arbitrary values will be assumed. Let it be 

 assumed that the box model is brought to rest by the drag forces with a uniform deceleration of tg, and 

 that it comes to rest in 50 milliseconds. This corresponds to an initial velocity of 6.H feet/sccond 

 and a total displacement of t>ie box of 1.9 inches. These two latter figures do not seem unreasonable 

 for a box model slung at the same horizontal level ^s the charge. 



The displacement of the bubble d ue to the motion of the box model alone may Be calculated from '% 



(13). The overall displacement is away from the box and is found to bt aPproxirately one half the " 



rise of the bubble under the influence of gravity at the end of the first oscillation. I.e. it is II 



displaced about 5 inches. n 



2 



strictly speaking equation (13) only holds for cases where the maximum bubble radius is small I ' 'jijj 



compared to the distance from the disc, and this condition is considerably exceeded In the numerical ' ink 



example above. The example does, however, suggest the desirability, either of measuring the overall "^ 



movement of the 'jx model so that this effect nay be estitrtitcd, or of fixing the box model so rigidly " 

 that the effect becomes negligible. 



Conclusions . 



(1) The attraction of a fixed rigid disc for an explosion bubble has ceen calculated and is found 

 to decrease rapidly with distance. If the explosion centre is one radius distance from the 

 disc the attraction is one half that of an Infinite rigid wall at the same distance. At a 

 distance of one disc diameter the attraction ic only one seventh of that due to an infinite 

 wall at the S':me distarice. 



(2) Tht- attraction of a rigid disc moving towards or jway from the explosion centre has been 

 calculated. The effects due to the motion of the disc fall off with increasing distance more 

 rapidly than the attraction from a stationary rigid disc.' Both the velocity and the 

 acceleration of the oisc give terms in the equation for the velocity of the explosion bubble 

 towards the disc. 



(3) It is pointed out that in experiments with box mode.ls or similar targets with flat plates 

 surrounded by rigid f1an,es the foregoing analysis Is relevant. In particular the motion 

 of the box model as a whole due to the explosion may have an appreciable influence on the 

 displacement of the explosion bubble. 



