NSWC/WOL TR 76-155 



^- -1 = EXP | 8.84-160.9 + ^ %^° > for R/R < 25 (D4a) 



— -1 = EXP < -3.264 - 1.098 In 5Z|a. \ f or r / Rq > 25* (D4b) 



To calculate VEL. CORR. Equation D3 must be integrated all the way 

 out to the gage. (This correction does not assume a constant value 

 beyond some arbitrary point, i.e., for this application the shock- 

 wave cannot be considered to be like a sound wave, anywhere.) 



Table D-l summarizes the results of the sound ranging 



computations. The last two columns give the comparisons for the 



time of arrival for the direct Shockwave. The comparison is easily 



understood by subtracting At , from both sides of Equation Dl . 

 2 ^ sound 



The maximum discrepancy is 0.4 milliseconds (Shot 786) or a spatial 

 discrepancy of about 2 feet. 



Tables D-2 thru D-7 list cage and gage locations for the 

 19 75 test series which where calculated by the method of this appendix, 

 The values listed in Tables D-2 thru D-7 were used for the present 

 analysis of the 1973 and 1975 test series data. The distance along 

 the support wire (Column 1) is the nominal or desired depth of the 

 fish cage or pressure gage. The wire angle (Column 2) is the 

 calculated deviation from the vertical of the wire segment attached 

 to the preceding depth coordinate. The cage and gage coordinates 

 (Columns 3 thru 6) are calculated relative to the point on the water 

 surface directly above the charge. Sound speeds were calculated 



from salinity and water temperature at charge depth using Del Grosso's 



13 

 equation. (All the computations described in this appendix were 



done using an HP-65 Programmable Pocket Calculator.) 



*This straight line log-log extrapolation beyond the range of Sternberg and Walker's 

 calculation should be adequate out to at least R/R = 1000. 



13. Del Grosso, V. A., "New Equation for the Speed of Sound in Natural Waters (with 

 Comparisons to Other Equations)", J. Acoust . Soc. Am., October 197*+ 



D-6 



