NSWC/WOL TR 76-155 



Calculation of DTNEG from Time-of-Flight of Water Layer . 

 The duration, DTNEG, of the negative phase corresponds to the 

 duration of bulk cavitation in the neighborhood of the fish. For 

 this study the duration of cavitation was calculated at the point on 

 the reflected ray at depth y (closure depth) given by Equation C7 . 

 Figure C3 shows the geometry of the problem. To get a first approxi- 

 mation to the duration of bulk cavitation at this point we used 

 Walker and Gordon's result for time of flight of a water layer of 

 thickness, y , decelerating (falling back) due to gravity and atmo- 

 spheric pressure 



2 • PMAX ♦ 6 



TFLIGHT = —7 . . C . _ L C nAmM (C12) 



pg (y + k) + PATM 



where PMAX and 9 are the Shockwave peak pressure and decay constant 



at the closure point (x ,y ) , 



and 



k = 



e r 



c z 



DOB 



and 



c = sound speed in water 



R = slant range from charge to point of reflection at 



water surface 

 DOB = depth of burst. 



11 / Walker, R. R. , and J. D. Gordon, 1966, "A Study of the Bulk Cavitation Caused 

 by Underwater Explosions", David Taylor Model Basin Report 1896, pl8 , 

 Equation 5. Note, however, that we used an empirical equation (CT) to calculate 

 the closure depth rather than Walker and Gordon's result. 



C-8 



