1155 
JHE PRESSURE AND IMPULSE OF SUBMARINE EXPLOSION 
WAVES ON PLATES 
G. I. Taylor 
July 1941 
* * a * * * * * * 
Summary. 
Some work of F.G. Friedlander is summarised which describes the way in which the pressure 
due to reflection of a pulse from an explosion is built up during the passage of the pulse along a 
plane set obliquely to its direction of motion. The pressure ultimately attained at some distance 
from the point where the pulse first strikes the reflecting surface is twice that in the incident 
pulse when that surface is immovable, but when the reflecting surface is not fixed, as when it is 
a steel plate, the motion of the reflecting surface reduces the pressure acting on it. This 
reduction is greater for oblique than for normal incidence. For comparatively thin plates the 
pressure changes to tension in a time which is small compared with the duration of the pulse. 
\f water can support tension the displacement of the plate is small compared with the displacement 
which occurs when no tension can be held, The amount cf tension which water can support for periods 
of the order of 1 millisecond at a free surface can be estimated from observations of the radius of 
the circle over which spray is projected upwards from a submarine explosion. It seems likely that 
this tension could be applied to a surface which is wetted by water but experiments on this subject 
are desirable. 
Though the amount of damage done to a ship must depend on the strength of the structure 
supporting the plate and other factors not included in the present analysis, the results give the 
relationship between weight of charge and distance for a given amount of damage. It is found that 
if water cen support tension the charge weight for given damage is proportional to (distance)3. 
On the other hand if the water is incapable of withstanding any tension, the law of variation of 
Charge weight with distance is not a simple power law. If, however, an attempt were made to 
represent experimental results by means of a formula 
(distance for given damage) = constant x (charge weight)®, 
S would have a value which in the extreme range of charges and plate thicknesses varies from 2 
to 3° In the range covered by charges from 300 to 2,400 1b. of T.N.T. and plate thicknees i inch 
to 6 inches, S varies from 9.38 to 0.54, the mean value of S being 0.46, 
ee 
The reflection of sound waves both in air and water by an infinite rigid plane provides a 
simple mathematical problem. The amplitude of the reflected wave is equal to that of the incident 
wave, so that at the reflecting surface where the pressures due to the incident and reflected waves 
are in phase the pressure in double that due to the incident wave alone. This statement is correct 
whether the incident disturbance is a train of narmonic waves or a single pulse. It is also true 
for all anyles of incidence. 
When the reaction between a plate and’a pulse is considered, certain limitations to the 
simple theory immediately appear. These are due to the two assumptions of the simple theory that 
the reflecting plane is infinite and that it is rigid and fixed. -Neither of these assumptions is 
true when the reflecting plane is a finite flat or bent steel plate, though it is to be expected 
that in the limiting case when the plate is very thick and of very large area the simple theory 
will apply. The object of the present note is to explore the modifications which the reflected 
pulse will experience owing to the finite size and thickness of the plate and to describe the motion 
of the plate in terms of the incident pulse, 
The cecses 
