500 - « - 



11,2 The trajectory of the centre of the bubble : A detailed comparison is difficult unless a 

 calculation is made in detail for each separate case. Lieutenant Campbell does not give any figures 

 for the trajectory of the bubble in the presence of the free surface only. Wright, Campbell and Senior 

 give a detailed trajectory, but in their work the effect of the bottom of the tank must have been 

 appreciable, it being only about 2i feet below the charge, (the free surface being li feet above it). 

 They find that during the first expansion phase, there Is (as predicted by theory) a definite attraction 

 of the bubble towards the free surface, repulsion setting in during the contracting stage. using the 

 Road Research Laboratory formulae and considering the effect of the free surface only, they find good 

 agreement for both the total depression of the centre of the bubble up to the f i rst'minimum but not for 

 the velocity of the centre of the bubble at this point. we have seen that the formulae used would give 

 a numerically too large value for the rise or fall of the centre, and the close agreement actually found 

 may be due to the mutual cancellation of this error with the fact that the effect of the bottom was 

 neglected. The situation regarding the vertical velocity at'minimum is not so clear, the agreement being 

 very poor. Wright, Campbell ana Senior give in error a theoretical maximum velocity of 6i*.5 feet per 

 second compared with an observed value of 64 feet per second, the correct theoretical figure being 

 6U5 feet/second. The explanation of this large discrepancy is probably similar to that of similar 

 disagreements found by Lieutenant Campbell discussed below. 



A comparison can also be made with Lieutenant Campbell's results on the bubble near a vertical wall. 

 The horizontal motion due to this will then be approximately independent of the vertical motion due to 

 gravity plus the effect of the free surface and bottom. we use the data in his Table 2 and Figures 20 

 and 21. we need first of all an estimate of the energy given to the water by a No. 8 cap (apart from the 

 energy appearing as a shock wave). This is best obtained from the maximum radius of the bubble, which is 

 given by him as 5.05 inches (average) which corresponds almost exactly to the figure to be expected for 

 0.6 gram of T.N.T. In the cases where the wall is so near that the bubble touches it before reaching its 

 maximum radius, the rraxlmum volume is considerably less, than in the cases where it forms a complete sphere. 

 The reason for this Is not very clear, but it is possible that energy is carried away as a compressional 

 wave in the steel of the wall, to a greater extent than it is in the water. Anyway, theory cannot 5t 

 present be applied to these cases where the bubble actually touches the walls except to the limiting one 

 where the charge is fired in actual contact with the wall. This case will be discussed later on. we 

 make the calculations for 0.6 gram of T.N.T. on the basis of the approximate formulae, dividing the figures 

 for the rise of the bubble under gravity by a factor of 1.6 in order to bring the approximate formulae 

 into line with the detailed calculations. The remaining approximations are used as they stand. 



Table II. Comparison of Lieutenant Campbell's results with theory . 



0.6 gram of T.N.T. }0 Inches below free surface, and at various distances 

 from rigid wal 1 . 



