301 
AN APPROXIMATE CALCULATION OF THE 
PRESSURES PRODUCED BY DETONATING 
LINE CHARGES UNDERWATER 
G. Charlesworth and A, R. Bryant 
December 1943 
Summary 
Calculations have been made of the forms of the pressure-time curves produced by the detonation 
underwater of line charges, on the assumption that the line charge is equivalent to a number of 
elemental sources of pressure such that the pressure due to unit element at a point distant r from 
it is of the form Poe okt. 
F 
The pressures produced by straight line charges at points on the perpendicular bisector and 
also on the axis of the charge in the direction of and in the opposite direction to that of detonation 
have been evaluated. The pressures produced by a circular arc and by an arc of an equiangular spiral 
of charge at the centres of the circle and spiral respectively, have also been calculated, Numerical 
examples have been considered for an arbitrary value of k — 60,000 sec. + and the results have been 
compared with experimental values obtained using Cordtex charges. 
{t is concluded that the theory predicts to a first approximation the form and relative 
magnitudes of the pressure-time curves produced by line charges. It has been noted that the theory 
is limited by tne uncertainty in the values to be assigned to Py and k in any particular case and by 
the breakdown of the simple acoustic approximation at points near the charge. 
Introduction 
The purpose of this note is to attempt to calculate by approximate methods the distribution 
of the pressure effects produced by the explosion underwater of line charges. 
General 
The analysis used may best be illustrated by considering the special case shown in Figure 1, 
where the line OL represents the charge and 0 is the point of initiation. |t is assumed that each 
element of the charge length &x produces at a point p distance r from it a pressure 
p(t) ox 
—— 
where p(t) fs a function of time measured from the instant at which the element was detonated. it 
is also assumed that the pressures are simply additive. 
Let c, be the detonation velocity of the charge 
1 
co be the velocity of sound in water 
> 
where cy cy 
Let t = 0 at the instant of detonation at o 
Consider the effect at time t at a point P due to an element dx distant x from the end of the charge 
at which detonation commences. The element dx produces no effect at P until a time. 
The eevee 
