A History of Research and a Review of Recent Developments

Table 2.6
Underwater explosions 53
(into air) and a reflected pulse which must be added to the original pulse.
Because of the large difference in density and compressibility between air and
water the transmitted pulse pressure will be very small and is usually neglected.
The surface is then taken as undisturbed, which means that the reflected pulse
must be equal and opposite to the initial pulse. This makes calculation of the
effect of downwards reflection very simple, since at any point P it is a
combination of a positive incident pressure at a distance r from the centre of
the explosion and a negative rarefaction or ‘tensile’ pulse originating from an
imaginary point which is at the image of the centre of detonation in the air
immediately above this centre (i.e. the concept of images as used in the reflection
of sound waves). The combination can theoretically produce a sharp decrease
or ‘cut-off’ in the shock at point P, although in practice the decrease is more
gradual.
Reflection of a pressure pulse from the seabed can vary considerably,
depending on the state of the bed surface. On a rocky bottom the main pulse
may give rise to a reflected wave having a peak pressure over half that in the
main pulse; on a soft mud base the reflected pressure could be almost negligible.
In general, the effect of the seabed is positive, leading to additional pressure.
An upper limit to this additional pressure can be found by assuming that
complete reflection occurs and that the concept of images can be used to
calculate total pressure at a given distance from the centre of detonation.
Some examples were given by Cole in ref. [2.22]. Apparently the peak
pressure, impulse and energy flux density 60 ft from a 300 lb TNT charge
fired on a bottom of hard-packed sandy mud, was increased by 10, 23 and
47% over the values observed from a charge at mid-depth. These increases
correspond to increasing the weight of a charge in free water by between 35