14 
of rise for the pressure at any point of the order of 107'1 sec. ‘The time 
of rise has yet to be accurately measured but recent work indicates that it 
is at least as small as 1078 sec. Such a time of rise can be regarded as 
instantaneous so far as the ultimate problem of damage to ships is concerned. 
38. It may be finally noted that the energy dissipated as heat in the 
water during the early propagation of the pressure pulse can account for 
about 25% of the total energy of the explosion. The corresponding energy E, 
given in equation 14 which remains in the pressure pulse at large distances 
is also about 25% of the total energy liberated by the explosion. The 
pressure pulse thus only accounts for about 50% of the total energy and the 
remaining 50% is left behind as energy in the gas bubble and kinetic energy 
of motion in the water in the immediate neighbourhood of the explosion. 
This motion will be considered later (para. 62). 
Reflection of pulse at sea surface 
39. The inevitable presence of the sea surface can lead to important 
modifications of the pressure due to an underwater explosion. In 
considering the modification due to reflection of the pressure pulse, it is 
assumed that the explosion is sufficiently deep (about 12 charge diameters 
or more for conventional explosives) for the pressure pulse to behave simply 
as an intense sound pulse on arrival at the sea surface. 
40. When a sound pulse arrives at a boundary between two different media 
it will produce in general a transmitted pulse and a reflected pulse. For 
an underwater pressure pulse arriving at the sea surface there will thus be 
a transmitted pulse or blast in the air and a reflected pulse in the water, 
this latter being additional to the original pulse. However, owing to the 
large difference between both the density and the compressibility of air and 
water, the pressure of the transmitted blast in the air is very small 
compared with the pressure in the underwater pulse and it is a very good 
approximation to neglect this transmitted pulse. The sea surface can thus 
be taken as a surface where the pressure effectively remains undisturbed 
and for this to be true the pressure in the reflected pulse at the surface 
must be equal but of opposite sign to the pressure at the surface due to 
the original pulse. 
4A. The pressure at any point below the surface due to the combined 
original and reflected pulses can be conveniently calculated by using the 
concept of images. In fig.5, E represents the explosion centre at a 
depth d below the sea surface A B and E' the image of E in the Plane A B. 
The pressure pulse sent out from E can then be taken as given by equation 1 
where the distance r is measured from E. The reflected pulse can 
similarly be considered to originate simltaneously from B' and to 
contribute a pressure, p' where p’ is given by 
pts - p/rtt(t - =') Keb p ewer Laces Mises dvaeoen Cea) 
where r' denotes the distance from E‘'. The reflection of the pressure 
pulse at the sea surface as a tensile pulse corresponds in effect to an 
equal but "negative" explosion at E‘. The pressure at P due to both the 
incident and reflected pulses will then be given by 
p =/* rt - 2) -2 f(t - 2) sedis aeiee: Ui wise Setelete he Cale) 
