SURFACE AND OTHER EFFECTS 399 



served appearance, that the upper surface at least is spray, and the 

 deceleration must be attributed to the drag of the drops of spray. 



10.3. Determination of Depths of Explosion 



A. Dome analysis. The methods of Shaw and Pekeris mentioned in 

 section 10.2 have been extensively applied to measurement of depths of 

 explosions. Critical comparisons have shown that measurements based 

 on the first few frames of motion picture records are very unreliable, but 

 that extrapolation of velocities to zero time gave results with scatter of 

 the order of five per cent. Further tests with charges at a variety of 

 known depths gave calculated peak pressure-distance curves agreeing 

 with piezoelectric gauge measurements to within six per cent. An 

 anomaly was found in that the apparent measured velocities from the 

 first few frames were significantly higher than extrapolation of the 

 smooth curves for later times. The reason for this discrepancy, not ob- 

 served in small charge trials (see section 6.3), is not known. 



Other methods of an empirical nature have been developed by 

 Halverson (43). The first of these is simply measurement of the dome 

 height at an arbitrary fixed time and use of calibrated curves made with 

 charges of the same weight at known depths. A second method elimi- 

 nates the need for either time or a distance scale by employing the ratio 

 of the dome height to its width at the time the first plume from the gas 

 bubble breaks through. As in the first method, calibration curves are 

 obtained by measurements with charges of the same weight at known 

 depths, and it is found that for a given charge this ratio varies with 

 depth to the — 3/2 power. The reason for using ''plume time" as the 

 time of measurement is to provide a simple criterion as to time of meas- 

 urement which gives a calibration sensitive to depth. Simple as it is, 

 the method gives remarkably reproducible values, the only compli- 

 cation being the necessity for empirical calibration. 



B. Shock wave spread. Although the modified dome analysis 

 methods are simple to use, their application becomes difficult or im- 

 possible at great charge depths, because of the smallness of the disturb- 

 ance. Another method based on surface measurements is determination 

 of the rate of spread of the shock wave across the surface, which is often 

 visible at considerable depths. The distance r the front travels across 

 the surface from the point above the charge is given by 



(10.3) r'' = {d + cty - d'' = 2dct + cH^ 



The velocity dr/dt along the surface is thus 



dr d , ct 

 dt r r 



