SURFACE AND OTHER EFFECTS 401 



The observed time, and hence path, difference for any pair requires that 

 the source He on a hyperboloid of revokition around the gauge Une, the 

 intersection with the plane of Fig. 10.2 being a hyperbola as shown. 

 Another pair gives a second hyperboloid intersecting the first in a circle 

 around the line, and the depth and perpendicular distance from the 

 gauge line are therefore determined. Not all of the gauges need be real 

 ones if surface or bottom reflections of the shock wave recorded by any 

 gauge are used, for these correspond to virtual image gauges at points 

 such as A^ above the surface, from which hyperbolas of constant path 

 difference are also obtained, as shown by the dashed curve for the gauge 

 pair AA^ 



It is evident that a vertical array of gauges is only one of many pos- 

 sible arrangements. It is usually the simplest and most accurate for 

 depth measurement, because known vertical distances are more readily 

 established, but tides and current may even so cause displacements 

 from the vertical. Surface image gauges are free from this error, but 

 become inaccurate if there are appreciable waves (bottom image gauges 

 are usually unreliable). The vertical array is obviously indifferent to 

 the horizontal direction of the explosion, and must be supplemented by 

 gauges off the line if this quantity is to be determined. Despite these 

 limitations, the vertical sound ranging system is a proven one, and has 

 been successfully used to measure explosions at depths from 25 to 800 

 feet. 



D. Bubble period measurement. The discussion of Chapter 8 shows 

 that, for a given charge, the period of oscillation of the gas bubble is a 

 simple function of depth. The measurement of this period by the dif- 

 ference in arrival times of shock wave and bubble pulses at a gauge 

 therefore provides a method of depth determination, which has been 

 found to give results of high accuracy when properly used. If the 

 charge is sufficiently far from boundary surfaces, the period T is given 

 by 

 (10.4) T = KW"^/{d + 33)^/6 



where X is a constant characteristic of the explosive, W is the charge 

 weight, and d the depth in feet. Although the constant K is known 

 quite accurately for a number of explosives, it is desirable for good pre- 

 cision to determine it empirically for the charge of interest under the 

 conditions of measurement. This is particularly true if effects of 

 boundary surfaces modify Eq. (10.4) appreciably (see section 8.10). 



As an example of such calibrations, the data of Fig. 10.3 for period 

 versus depth were obtained by firing four 200-pound charges suspended 

 at depths up to 800 feet in 3,000 feet of water. The plot of period versus 

 depth is fitted within experimental error by a function of the form of 

 Eq. (10.4), as shown by the straight line. Points are also plotted in 



