22 
63. Although the oscillation of the bubble had been predictea, little 
significance was attached to bubble motion until World War II when interest 
was revived by the appearance of two important papers, one British, the 
other American; these two papers have formed the basis for most of the 
subsequent theory of bubble motion. An outline of the basic theory in the 
British form is given at Appendix B. Equations B8, B9 and B10 enable the 
bubble motion to be computed. Fig.10 shows graphically the results 
calculated for a small charge of 4.65 lb. of T.N.T. exploded at a depth of 
20 ft. below the sea surface. 
64. The curve 0 ABC in 
fig.e10 shows that the bubble 
first expands to a maximum 
radius of 5 - 6 ft. and then 
contracts to a radius rather 
less than 2 feet before 
commencing to expand again. 
At the same time, the bubble 
tends to rise, at first very 
slowly while the bubble is 
expanding,and then very 
quickly when the bubble 
becomes of small radius again. 
This rise is represented by the 
curve ODEF. 
SEA SURFACE 
20 
DEPTH OF CENTRE 
OF BUBBLE 
RADIUS OF BUBBLE— ft. 
6 
DEPTH OF BUBBLE CENTRE —ft. 
7 RADIUS 65. Using Bernoulli's equation, 
Seats the pressure in the water 
associated with the bubble 
motion is found to be completely 
° o1 o2 o3 o-4 negligible except when the bubble 
TIME — sec. is near its minimum radius. 
The pressure then rises sharply 
to give the effect of a second 
Fige10 - Curves showing calculated explosion emanating from the 
bubble motion position of the bubble at this 
time. The resulting pulse 
will be termed the "first 
bubble pulse". If the pressure at a fixed distance from the bubble be 
considered, the first bubble pulse is relatively feeble compared with the 
original pressure pulse. On the other hand, since the bubble is moving 
upwards, a target point above the original explosion may be relatively close 
to the bubble at its first minimum and the resulting bubble pulse may have 
a damaging effect comparable with that of the original pressure pulse 
emanating from the more distant centre of the original explosion. Fora 
fixed point 6 ft. below the sea surface and 14 ft. directly above a charge 
of 4065 lbs T.N.T. exploded at a depth of 20 ft. the calculated pressure 
in the first bubble pulse is shown in fige 11. 
For comparison it may be noted that the original pressure pulse would have 
a maximum pressure of about 2,000 lb. per sq. in. and a time constant, 4/n 
of about 0.0002 sec. The bubble pulse is thus of much lower pressure but 
has a longer effective duration than the original pulse. 
