180 
IV. EFFECTS OF PRESSURE WAVES 20 
2. SMALL TARGETS 
the incident wave itself, and this pressure can be treated as static. Paradoxical as 
it may seem, parts of a small target may undergo displacements many times larger than 
the displacements of the water particles in the undisturbed wave. A particle of wat- 
er is accelerated, first, forward as the pressure rises to its maximum, then backward 
as the pressure sinks, the pressure gradient being now reversed, and in the end the 
water is left at rest except for motion due to the afterflow. If part of the target 
is movable, however, it experiences a positive impulse of magnitude }pdt and so may 
be left in rapid motion by the passage of the wave. The water will follow this local 
motion of the target approximately according to the laws of non-compressive flow, 
provided the velocities involved do not become excessive. 
In this way, for example, displacements of the piston of Hilliar's gauges 
could occur amounting to several inches, without causing much distortion of the pres- 
sure in the water, although the displacement produced by the wave in unobstructed wat- 
er should have been only a fraction of an inch. 
To take another example, suppose a wave like that at 50 feet from 300 pounds 
of TNT passes over a light, hollow metal sphere of 6 inches diameter; the maximum 
pressure of 1700 pounds per square inch is far more than enough to crush the sphere. 
The resistance of the metal will, therefore, play only a minor role in determining 
the initial phase of the motion. If we neglect this resistance altogether, it is 
easily calculated from Equation [6] in Appendix II that the water will start rushing 
toward the center of the sphere with a velocity of over 300 feet per second. The 
local motion involved is on a small scale as compared with the 5-foot effective length 
of the wave. The inward motion will continue until the kinetic energy of the water 
has been spent in deforming the sphere. 
We may consider also the 31-inch mine case shown in Figure 64 of Hilliar's 
report (1). At a distance of 126 feet, a 1600-pound charge of amatol would produce a 
maximum pressure of about 
1600)! 
12 
13000 = 1180 pounds per square inch 
and hence a maximum water velocity of 
ue 160 - 17 feet per second 
From Hilliar's Figure 1 it can be calculated that the total (observed) impulse from 
300 pounds at 50 feet is equivalent to the maximum pressure acting for 0.85 milli- 
second. The time for the larger charge would be 0.85 x (1600/300) ° = 1.48 millisecond; 
and 0.00148 x 17 foot per second x 12 = 0.3 inch for the displacement of the unob- 
structed water. Yet the mine case is indented at least 15 inches. Even an object 
31 inches in diameter should be small enough relative to a wave 5 to 10 feet long for 
the small-target theory to be partially applicable. 
It may be of interest to consider the afterflow, also. An upper limit can 
be set to the displacement produced by it in unobstructed water in the following way. 
