A History of Research and a Review of Recent Developments

52
The detonation of explosive charges
By 1942 the UK Ministry of Home Security had established a co-ordinating
committee on shock waves, and G.I.Taylor [2.34] reported to this body on
the vertical motion of a spherical bubble and the pressure surrounding it. He
presented calculated values for the radius and the height of the centre of the
bubble for a range of charge weights in a non-dimensional form. A.R.Bryant
[2.35] took Taylor’s non-dimensional analysis and produced a series of
approximate formulae that involved simple calculations, for example:
Period of the first oscillation:
T=4.32W 1/3 /(d+33) 5/6 ,
(2.22)
(W in lb, d in feet)
His calculations for peak pressure p 0 in psi, duration in seconds, and distance
R from the detonation point in feet are given in Table 2.6.
There are further fundamental areas of physical behaviour that must be
mentioned: the reflection of the underwater shock wave downwards from the
free surface of the water; the reflection upwards from the bottom of the sea,
lake or river; and the generation of surface waves. In considering surface
reflection, it is usually assumed that the explosion is sufficiently deep for the
pressure pulse to behave as an intense sound pulse. This means that the depth
is at least 12 charge diameters. At the surface there will be a transmitted pulse
Figure 2.20 Bubble periods against depth for 0.55 lb Tetryl charges (from Ewing
and Crary, ref. 2.32).