NSWC/WOLTR 76-155 DYNAMICAL MODEL FOR EXPLOSION INJURY TO FISH BY JOHN F. GOERTIMER RESEARCH AND TECHNOLOGY DEPARTMENT 18 DECEMBER 1978 Approved for public release, distribution unlimited NAVAL SURFACE WEAPONS CENTER Dahlgren, Virginia 22448 • Silver Spring, Maryland 20910 en H O H 1-3 UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) REPORT DOCUMENTATION PAGE READ INSTRUCTIONS BEFORE COMPLETING FORM I. REPORT NUMBER NSWC/WOL TR 76-15 5 2. GOVT ACCESSION NO 3. RECIPIENT'S CATALOG NUMBER 4. TITLE (and Subtitle) Dynamical Model for Explosion Injury to Fish 5. TYPE OF REPORT & PERIOD COVERED Final 6. PERFORMING ORG. REPORT NUMBER 7. AUTHORfsJ John F. Goertner 8. CONTRACT OR GRANT NUMBERfl.) 9. PERFORMING ORGANIZATION NAME AND ADDRESS Naval Surface Weapons Center White Oak, Silver Spring, Maryland 20910 10. PROGRAM ELEMENT, PROJECT, TASK AREA & WORK UNIT NUMBERS 63721N; S0400; S040001; CR14CA501 It. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE 18 December 1978 t3. NUMBER OF PAGES 137 14. MONITORING AGENCY NAME ft ADDRESSf// different from Controlling Office) tS. SECURITY CLASS, (ol thle report) UNCLASSIFIED 15«. DECLASSIFI CATION/ DOWN GRADING SCHEDULE 16. DISTRIBUTION STATEMENT (of this Report) Approved for public release, distribution unlimited, 17. DISTRIBUTION STATEMENT (of the abstract entered In Block 20, It different from Report) 18. SUPPLEMENTARY NOTES 19. KEY WORDS (Continue on reverae aide if neceaamry and Identity by block number) Underwater Explosions Swim Bladder Fish Fish-kill Explosion Effects Cavitation Sound Ranging Lethal Ranges 20. ABSTRACT (Continue on reverae aide It neceaamry end Identity by block number) A new method is given for calculating kill probability for bladder fish subjected to the rapidly varying pressure field of an underwater explosion. The method consists of an approximate calculation for the extreme values of compression and extension of the fishes' gas-filled swim bladder in response to the explosion pressure wave. The calculations are made for the damped radial oscillations of a spherical air bubble in water. The kill | probability is then calculated as an experimentally (Cent) DD | JAN 73 1473 EDITION OF I NOV 65 IS OBSOLETE S/N 0 102-014- 6601 UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Dmta Entered) UNCLASSIFIED jLtumTY CLASSIFICATION OF THIS PAGEC*hen Data Entered) determined function of the ratio of maximum to minimum radius during the oscillatory response. For each species of fish the effective bubble radius for the calculations is determined thru correlating the observed injuries with the calculated radius ratio. The method was used to satisfactorily describe dissection results from 1500 Spot and White Perch caged at depths from 5 to 100 feet and subjected to pentolite explosions of from 1 to 70 lbs submerged at depths ranging from 5 to 70 feet. An approxi- mate method for calculating the pressure signature from an underwater explosion subject to surface effects - including cavitation - is given in an appendix. UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGEfH7i»n Dmtm Ent.r.di NSWC/WOL TR 76-155 FOREWORD This report deals with the prediction of explosion injury to fish with swim bladders and is part of a continuing study of the effects of underwater explosions on marine life. Swim bladder fish are parti- cularly vulnerable to explosions, and this group includes the majority of fish with sports and commercial value. This study will result in an improved capability to predict such effects, and will be useful in connection with the testing of new explosives and of warheads at sea. This study is part of the ordnance pollution abatement program of the Naval Sea Systems Command and was supported by SEA TASK SSL 55001/ 19373. The author is indebted to Ermine A. Christian and George A. Young for many valuable suggestions during the course of this work. JULIUS W. ENIG By direction 1/2 NSWC/WOL TR 76-155 CONTENTS Page 1 INTRODUCTION AND SUMMARY 13 2 DYNAMICAL MODEL 14 2 . 1 The Swim Bladder 14 2.2 Preliminary Calculations of Bladder Oscillation .... 14 2.3 Current Method for Calculating Bladder Oscillation 14 3 CORRELATIONS WITH EXPERIMENTAL DATA 2 3 3.1 Summary of Test Data and Computation Results 23 3.2 Observed Injuries to Spot vs Calculated Oscillation Parameter Z 38 3.3 Observed Injuries to White Perch vs Calculated Oscillation Parameter Z 42 3.4 Comparison of Shockwave Impulse and Calculated Bladder Oscillation as Damage Parameters 47 3.5 Discussion of Injury Correlations 49 4 APPLICATIONS 5 3 4 . 1 Fish-Kill Contours 53 4.2 Kill Probabilities as a Function of Depth for Different Sized Fish 57 4.3 Total Fish-Kill and its Spatial Distribution 59 REFERENCES 6 3 LIST OF SYMBOLS 6 APPENDIX A RESPONSE OF GAS BLADDER TO UNDERWATER EXPLOSION PRESSURES: SQUARE STEP APPROXIMATION A-l APPENDIX B METHOD FOR CALCULATING GAS BLADDER RESPONSE TO EXPLOSION PRESSURE WAVE B-l APPENDIX C APPROXIMATE METHOD FOR CALCULATING THE PRESSURE- TIME SIGNATURE C-l APPENDIX D LOCATION OF FISH CAGES BY SOUND RANGING D-l APPENDIX E NOTE ON FISH CLOSE TO THE WATER SURFACE E-l NSWC/WOL TR 76-155 ILLUSTRATIONS Figure Page 2.1.1 Body Tracing of Spot 15 2.1.2 Swim Bladder Removed from Spot 16 2.1.3 Body Tracing of White Perch 17 2.3.1 Bladder Pressure and Size as a Function of Time 18 2.3.2 Approximating Step Wave for Calculating Oscillatory Response 21 3.1.1 Sketch Showing Calculated Pressure-Time Signature 33 3.1.2 Sketch Depicting Injury Code for Evaluating Visible Fish Damage 37 3.2.1 Observed Injuries to Spot as a Function of Z 39 3.2.2 Observed Cumulative Injury to Spot as a Function of Z 41 3.3.1 Observed Injuries to White Perch as a Function of Z 4 3 3.3.2 Observed Cumulative Injury to White Perch as a Function of Z 45 3.3.3 Observed Cumulative Injury as a Function of Z - Spot and White Perch Combined Data 4 6 3.4.1 Correlations of Level 3 Injuries for Spot and White Perch with Impulse Damage Parameter and with Bladder Oscillation Parameter 48 3.5.1 Sketch Illustrating Bubble Response to a Pressure Wave of Very Short Duration 51 4.1.1 Region of Greater than 50% Kill for 18 cm Spot - 32 KG Pentolite at 9 M Depth 54 4.1.2 Regions of Greater than 10%, 50%, and 90% Kill for 21.5 cm White Perch - 32 KG Pentolite at 9 M Depth 56 4.2.1 Predicted Kill Probabilities as a Function of Depth for Different Size Fish - 32 KG Charge at 9 M Depth - Horizontal Range: 91 Meters 58 NSWC/WOL TR 76-155 TABLES Table Page 3.1.1 Applied Pressure Parameters and Bladder Oscillation Response for Spot 24 3.1.2 Applied Pressure Parameters and Bladder Oscillation Response for White Perch 26 3.1.3 Observed Injuries for Spot and Calculated Oscillation Parameter Z 28 3.1.4 Observed Injuries for White Perch and Calculated Oscillation Parameter Z 30 3.1.5 Code for Evaluating Visible Fish Damage 36 3.2.1 Averaged Observed Injury Probability for Spot as a Function of Calculated Oscillation Parameter Z 40 3.3.1 Averaged Observed Injury Probability for White Perch as a Function of Calculated Oscillation Parameter Z 44 4.1.1 Bladder Oscillation Parameter Z as a Function of Fishes' Depth and Horizontal Range 55 4.3.1 Bladder Oscillation Parameter and Kill Probability as a Function of Fishes' Depth and Horizontal Range 60 4.3.2 Fish Present and Number Killed as a Function of Water Depth and Horizontal Range 61 NSWC/WOL 76-155 LIST OF SYMBOLS A Swimbladder or bubble radius A. Bladder or bubble radius corresponding to ambient pressure p. (A.) Bladder or bubble radius corresponding to zero depth, i.e., one atmosphere pressure A Bladder or bubble radius at "equilibrium" (radius after oscillation has damped out, Equation A-19) A., or AMAX Maximum bubble radius M A or AMIN Minimum bubble radius m A , t , V , P Radius, time, volume, and internal air pressure c c c ' c n n n n when ambient pressure jump from p to Pn+i occurs P„„ Bubble internal air pressure at maximum size M c P or PMIN Bubble internal air pressure at minimum size m r P Bubble internal air pressure at "equilibrium" o (= Pn) AMmr VMm, PMm Bubble radius, volume, or internal air pressure at either extremum of the bubble oscillation (Appendixes A and B) NSWC/WOL TR 76-155 P Ambient water pressure = constant = p.. p, , o rr 1 ?2 p. Initial value of ambient water pressure p n value of ambient water pressure = constant ^n c P(A) Air pressure inside bubble of radius A V(A) Volume of bubble of radius A E(A) Internal energy of air inside bubble Y Total energy of oscillating bubble (Equation Al) Y. Initial value of total energy of at-rest bubble Y n value of total energy of oscillating bubble n n = constant (Equations A7 , A10, B15) Y n value of total energy of non-oscillating equilibrium bubble (Equation E17) Y' Y - Y = oscillation energy of bubble (Equation B18) n n n P Density of water = constant y Exponent in adiabatic P-V relationship = 1.4 (for air) a Dimensionless bubble radius = A/L Fork length of fish - length measured from most anterior part of head to deepest point of notch in tailfin NSWC/WOL TR 76-155 L Length scale factor (Equation A-5) t1 Dimensionless time = t/c C Time scale factor (Equation A-6) T, T1 Bubble period of oscillation and dimensionless bubble period T T' Equilibrium bubble period and dimensionless equilibrium bubble period (for vanishingly small oscillations about the equilibrium radius, Equation B-9) k Bubble oscillation parameter (Equations A-4 and A-13) P parameter used in Appendix A to compute I P0(Y-1) other bubble oscillation parameters, where P., is the r Mm internal pressure at either extremum of the bladder oscillation -100 In AMIN/A. (Equation 3.1.3) 100 In AMAX/A.^ (Equation 3.1.4) X + Y = 100 In AMAX/AMIN = Bladder Oscillation Parameter (damage parameter used for fish-kill and injury correlations) - (Equation 3.1.5) 80 In I/M1' 3 J = Impulse Damage Parameter (damage parameter used for fish-kill and injury correlations) In Natural logarithm 8 NSWC/WOL TR 76-155 Impulse of positive portion of pressure wave in psi-mec M Mass of fish in grams '50% Value of Bladder Oscillation Parameter corresponding to 50% kill probability TPOS Time corresponding to end of positive pressure phase (Figure 3.1.1) (At/T) The fraction portion of the number of oscillation cycles during the positive phase DTNEG Duration of the negative pressure phase (Figure 3.1.1) T neg Bubble period of oscillation during negative pressure phase (At/T) NP Parameter which locates the end of the negative phase in terms of bubble oscillation cycles (Equations B-13 thru B-16) a Coefficient used to estimate the bubble period of oscillation (Equation B-10) Fraction of oscillation energy removed each half- cycle to achieve damped oscillations (Equation B-23) a, 3 Exponents in the Shockwave similitude equations for PMAX and 0 (Equations C-2 and C-3) k,Z Coefficients in the Shockwave similitude equations for PMAX and 0 (Equations C-2 and C-3) NSWC/WOL TR 76-155 PMAX Shockwave peak overpressure referenced to initial ambient pressure, p., but generally referred to as "Shockwave peak pressure" 0 Shockwave decay constant (Figure 3.1.1) PCORR Coefficient used to adjust Shockwave peak overpressure for batch-to-batch variations in explosive charges (Equation 3.1.1) PNEG Pressure during negative phase (measured from hydrostatic) (Figure 3.1.1) R Slant range from charge R Radius of charge Rn Slant range from image of charge reflected in water surface Sound speed in water U Shock velocity in water Detonation velocity in charge PVAP Vapor pressure of water ABS Absolute pressure Acceleration of gravity PD(t) Free-field or direct-arrival Shockwave overpressure Pr(t) Surface-reflected overpressure wave 10 NSWC/WOL TR 7 6-155 p„ (t) Shockwave overpressure calculated by superposition of direct and surface-reflected waves, PSUM(t) = PD(t) + PR(t) PATM Atmospheric pressure y Depth of fish y. Depth of top of cavitation (on surface-reflected ray) y Depth of cavitation closure point (on surface-reflected ray) R Slant range from charge to cavitation closure point PMAX Shockwave peak overpressure at cavitation closure point 6 Shockwave decay constant at cavitation closure point R„ Slant range from charge to point of reflection at water surface DOB Depth of burst 11 NSWC/WOL TR 76-155 £■ _ ■a s E a> si iL .2 iS » 3 -a w »> O to a> V a - m a> TO w *" o w 0 «- C/) 0 LL 0 3 .2 2 tf £ w o o E o Z < a a at O "O a < f * 8 S to .2 2 < a s 0 3 ™ LU .c > 2 % I V 0) o -5 •H- O ♦^ 0) _ -a -g 3 (« ' "O fiJ t/> x -5 TO £ 3 5 i- ^ a 12 NSWC/WOL TR 76-155 DYNAMICAL MODEL FOR EXPLOSION INJURY TO FISH 1 INTRODUCTION AND SUMMARY This report describes a method for calculating the kill probability for bladder fish subjected to an underwater explosion. The method consists of an approximate calculation for the extreme values of com- pression and extension of the fishes' gas-filled swim bladder in response to the explosion pressure wave. The calculations are made for the damped radial oscillations of a spherical air bubble in water. The kill probability is then calculated as an experimentally determined function of the ratio of maximum to minimum radius during the oscilla- tory response. For each species of fish the effective swim bladder radius needed for the calculations is determined by trial and error thru correlating the observed injuries with the calculated ratio of maximum to minimum radius. The method is used to describe dissection results from 1500 Spot and White Perch caged at depths from 5 to 100 feet and subjected to pentolite explosions of from 1 to 70 lbs submerged at depths ranging from from 5 to 70 feet.1'2 These results are then used to calculate several examples of kill-probability and fish-kill distributions for a particular explosion geometry and several species and sizes of fish. Details of the computations are given in the appendices. Appendix C gives an approximate method for calculating the pressure signature from an underwater explosion subject to surface effects including cavitation. 1. Gaspin, Joel B., "Experimental Investigations of the Effects of Underwater Explosions on Swim Bladder Fish, I: 1973 Chesapeake Bay Tests", NSWC/WOL TR 75-58, 1975. 2. Gaspin, J. B., Wiley, M. L., and Peters, G. B., "Experimental Investigations of the Effects of Underwater Explosions on Swim Bladder Fish, II: 1975 Chesapeake Bay Tests", NSWC/WOL TR 76-61, 19 76. 13 NSWC/WOL TR 76-155 DYNAMICAL MODEL 2.1 THE SWIM BLADDER. Figure 2.1.1 shows a life-size tracing of a Spot (Leiostonms xanthurus Lacepede) which depicts the swim bladder and the surrounding internal organs. Figure 2.1.2 shows a swim bladder removed from a Spot. In our work we depicted the motion of this organ by that calculated for a spherical bubble of air. The size of this "equivalent spherical bubble" was first estimated by equating its volume to that of the fishes' swim bladder — then later we adjusted the size of the equivalent bubble to optimize the correlation between the calculated motion and the observed injuries. Figure 2.1.3 shows a life-size tracing of a White Perch (Mo rone americana Gmelin) , the other species of fish used in the work reported here. The inset shows the shape of the forward portion of the swim bladder in-place in the fish. 2.2 PRELIMINARY CALCULATIONS OF BLADDER OSCILLATION. We began this study by making order of magnitude calculations which approxi- mated the explosion pressure field with a step increase followed by a step decrease in pressure. The fishes' swim bladder was approximated by a spherical bubble of air in an infinite body of water — and, we calculated its undamped oscillatory response. These order of magnitude calculations showed that the oscillatory response of the swim bladder was a likely source of the fishes' injuries. They also pointed out a strong resonance which occurs when surface cut-off (the arrival of the rarefaction wave reflected from the water surface) happens at the instant of maximum bladder compression. This work was described in an internal Center report which is reproduced as Appendix A of this report. 2.3 CURRENT METHOD FOR CALCULATING BLADDER OSCILLATION. The method developed for calculation of the oscillatory response to the changing pressure field generated by an underwater explosion is described in detail in Appendix B. Here, we attempt to give the reader a feel for this computation and its approximate nature. Figure 2.3.1 shows the idealized pressure signature measured on an underwater explosion test together with the calculated pressure inside a fish's swim bladder 14 NSWC/WOL TR 76-155 (- < m X a. Ml > £ c ■o 1 Si c 0) 2 M 0) \- x: o £ CL o «/} !e u. g O £ 2 U »£ z C as o N < 0 oc >•- H re > "8 Q o> O c m "8 T-m *: T— >■ CM° 1 6 ja « U. N < DC cc ill a l- a < LU > _i >• P CO UJ cr> 2 Z ui Q CJ 00 2 5 15 NSWC/WOL TR 76-155 FIG. 2.1.2 SWIM BLADDER REMOVED FROM SPOT 16 NSWC/WOL TR 76-155 I o to O w UJ u. I o UJ a. UJ X u. O O 2 o < a. > a o a CO ei UJ 17 NSWC/WOL TR 76-155 Nt LU > < § LU CC D LU Ol CC a. z ^S o ^^ CO f o V o LU s H LL o cc Q- X r LU -^....^^^ o z o o z D LL LU Q Q < _i m z o < CO < LU N CO LU DC D CO CO LU CC 0. N LU /I CO o TIME 5SURE an: \_ / J ^~ y lu IS Q ^--^/ < — — " / _i / m o LU CC OL DC LU Q o xo _l CO CO 0 j O u. 3anss3dd 18 NSWC/WOL TR 76-155 as it responds to this applied pressure. Below the pressure traces are corresponding sizes calculated for the spherical air bubble used to represent the fish's swim bladder. This fluid motion can be likened to a mass attached between two springs, the end of one being fixed, the end of the other movable. 'ff^MSu '^-vJlQJL/-^^ The first spring is analogous to the internal gas pressure; the second to the changing external water pressure. Let us imagine the mass resting on a frictionless block of ice. It is at rest in a position of equilibrium. If at t=0 we quickly displace the movable spring to a new position, the mass will oscillate about a new position of equilibrium determined by the displacement of the end of the spring, The mass will oscillate about this new equilibrium position with an amplitude equal to the displacement of this equilibrium position from the initial at-rest position of the mass. This initial at-rest position now becomes an extremum of the oscillatory motion. Since, at each extremum of the motion the mass is instantaneously at rest, a subsequent jump displacement of the end of the spring occurring at an extremum simply shifts the motion to an oscillation about a new equilibrium position - and the new amplitude is just the distance of the mass at the time of the jump from this new equilibrium position. Likewise, for the bubble, step changes in the outside water pressure occurring at half-period intervals simply change the equili- brium pressure (equal to the outside pressure) of the oscillating 19 NSWC/WOL TR 76-155 bubble flow - and the new amplitude is just the instantaneous excursion of the bubble pressure from the changed outside pressure. We made use of this property of the motion to calculate the motion as the response to a series of pressure steps as shown in Figure 2.3.2. (Appendix B describes the way we estimated successive half-periods in order to construct the approximating step wave.) The transition from the positive to the negative pressure phase, i.e., surface cut-off, must be treated as a special case, since in general, this will not occur at an extremum of the motion. If cut-off occurs at a compression, this compression is then the compres- sion of the next half cycle also - and the subsequent expansion is the greatest possible. If cut-off occurs at an expansion and the new outside pressure is lower than that inside, this expansion becomes the compression of the next half cycle, there occurs a 180 degree phase shift, and the subsequent expansion is the smallest possible. In general, cut-off occurs somewhere in between and there is an intermediate phase shift and subsequent expansion or compression. In such cases we calculated this next half cycle at lowered pressure as starting at the time of the previous extremum but at a ficticious amplitude interpolated as a function of the time at which cut-off occurred. (The details of this procedure are described in Appendix B.) Finally, at the end of the negative phase, the return to ambient pressure can cut short or even prevent the final expansion. This was handled in an analogous manner to surface cut-off and is also described in Appendix B. To approximate the dissipation of energy which in nature must occur during the oscillation, we arbitrarily extracted a fraction — 30% — of the remaining oscillation energy at each half cycle of the motion. 20 NSWC/WOL TR 76-155 CO Z O Q. CO HI > cc o o CO o o D o _l < o cc o > < Ill H CO C3 < s X o cc a. a. < CM eo evi C3 3dnSS3bd 21/22 NSWC/WOL TR 76-155 3. CORRELATIONS WITH EXPERIMENTAL DATA 3.1 SUMMARY OF TEST DATA AND COMPUTATION RESULTS. Tables 3.1.1 thru 3.1.4 summarize the input and output parameters of the computa- tions of this report. These tables include all the test data for Spot and White Perch obtained on the 1973 and 1975 test series in the Chesapeake Bay. For the 1973 test data (the "500" Shot Numbers) the fishes' horizontal ranges and depth which are listed in the tables are the preset or intended values.1 On the 1975 tests, shots 783 thru 786, water currents caused significant deviations in horizontal range and depth. For these shots the preset values2 have been corrected as described in Appendix D. (Tables D-2 thru D-7 list corrected values for charge depth and fish and pressure gage locations for all shots of the 1975 test series.) The ambient pressure (Tables 3.1.1 and 3.1.2) is the total hydrostatic head at fish depth calculated for fresh water, density = 1000 kg/m3, and nominal atmospheric pressure, 1.013 x 10 5 pascals. The vapor pressure was calculated from the measured water temperature (1975 tests) or estimated water temperature (1973 tests) . The peak pressure PMAX in pascals and time constant 0 in milliseconds are calculated from the similitude relations for pentolite PMAX = PCORR x 5. 62 /T7l/3\ 1.14 x 107 ^L_ J (3.1.1) '1/3 fcfr) 0 = 0.084 Wx/J l-^\ °-23 (3.1.2) where W is the explosive mass in kilograms, R is the slant range from the charge in meters, and PCORR is an empirical constant that was used to adjust Equation 3.1.1 for batch-to-batch variations in the explo- sive charges. For the 1973 test series PCORR = 1.10 — for the 1975 tests PCORR = 0.95. (Text continued on naae 32) 23 NSWC/WOL TR 76-155 00 z o a. 00 UJ en H < _i -i o oo O rr — LU a Q Q o < «fr -i T— CO II Q Irt ? IS < c co s#ojin oh « n - ffl in -^ * co I i/i oh-o-»n o«r>r\j(\i ~« -.,$-. o — .c m o — • in i/i -• © © m -* ry ■# o-»tsj-^o i or m ry -* -^ «* ^ rvj — — — . •-n ^ — — m ~ — . — ■ ~i — — . — — m ** .* m -* ^ m .^ I UJ I ►- I UJ UJ I X •Si I < z i a ...»• O I < oo-*oo &• -# o — :r> o o j-, — « I Jify r (VI p- X CO ■* .0 r» N4SKM o. i a ■♦*■♦■•— n £ * ^ o i/ih Mrin * jj it * u". j"> -c a * ro — ■* r> (\j «ry n* * UJ t z a. ) O I — I- z • •- y -i_i IX i- I .. i — r~ in •* >o o»wn^ flNff njj 00 < i .- *n*b-« jj ■» (> j3 Ln *o *• co i0 ill ~. _j I o x «-< -* —— -• -« 0- j i ui O — i o ul V> ' in I i/> O I UJ I • _j c~ k ■♦ r\j ce in ^ * j: s * o « ul M9 © .- ^ u~i ■* — < lti ip x ruir mo a c * r k ^ o co in in in UJIUJV .•••• ...•• ....• •••• ..... ••••• ..... f~ in C\J IT ■* ff «*Oi- l/l tj (^^m^-— a- 0* >C *C <\J MoiD'-o o *o ~ m ~ r\j o o ul n-» J"> o>- ..... au — co — • cvj -o *-.«■—• — — cu in cu >o <\j nj — • * mw I I u z I > o I MM — IkhU i < * uj in m co ce ^ o .» ^ in — oj o* <\j o * a- o ■* co —• co .» .c < * h n * < * £ n * co h- © o ~. IUJ3I ..... ..... ..... ..... I2QW N4 r^oe-. Kf-ru-- ^-^ » oj r» ~ m m cm i — I I i • — UJ I W in a I • ■J CL P)NO«* m -» i*) ^ ♦ m ~ n x r- B lTi fu -c a n -J CO 0> « tt ffi .c - co o> m m co ~ i c uj < — cr o* co co — r^ — *- r\j ~ co co cij cr mtui r» r\j — . c\j c >r cy ■* * h- * cu *c ■» -. tvj m i uj or ff> .•••• ..... ••••• •••• .•••• ••••• ..••• W | X 0. — M | | M I P- ~ M I M — — I — I ,- | -« | _ _ _ | | _ , | | , ^ | — _-, ,- UJ I I I I I I I I I I II III I I I I I DC I UJ Z a. i > o I M M — Qlhl-U w i - « l ■♦ *- o * in co co >o ~ co fr-iAnm u-> ^ ^ x ir«co^t^ ccsor nrncvjo^ m i m a* i/l ru»ono * x — r\j ^* x u^ * ♦ x c>^i/»^- o'-'-'infy-* -- o IUJC/1UJ MCVJ>D^)r* Jl -» f\j J-. Jl Ul IT (\J(T IT aJOO^^S h- O * ■♦ * »H IXZU1 — . — — ^- ^- ivMnnn ojfynmm n**ui n * * ui tft n**^io in*©»O'0r- < C 0. I — o I LU I l-O- 5 ! •- CO | is\ i/i CO i jt i/) x (VJirr-f-m *»aojinin mofuifitxi enr-aitT f^r-cc>o^ ccoook o -«■ ■* ■* in UJ i-Km «NN*n ^ivo-f-m ir^^K* IQ.Q.— 0JM fNJfV (\jr\j f\; (\j (%J (\j — a iflw -J oi/itr *^^-»-* -*•*.».»-» -j 4- j ^ a— •••♦• ••••• U UJ tfl *; i—i/icr j: — ■ ^: — nC ^ — •o^-— ^) — ru^^- — ■ ^> ui «— «— j; it. — ^- ^-■•B^m^ _^.^^-. -- CD Lu < ^^^^^^^- — Xi — r-i ^ -iiC MP1 ^l PI « l/l PI Pl*->ljnP)P> PI c- « Ul n (r)D-#'f\JP) • xaco CO m^^iTiO"-" ifi^Ni— c— o irui o o i/i in c o © n j*. ip © ooc^mo H tflCl - •..• •■••• •— y i »-i^,^-^^- ^■sT'— 'PiiT — • * iv pi *r n — it r n — ip r pi m^-»-iir>pi p>pi-#(\jpi u. o — -> I • o tttcooa ocrvacx ocrv wet z - ••• • ..... ••••• ••••• mO < X ruiNj^sOh- in tP —• — f- « p->^,^.^.« inmminm 24 NSWC/WOL TR 76-155 O O < i 1/1 I I £r rs; I UJ I t- I I UJ Ui i I 5 l/l I I < f I I o I < Q. I a. [/) i >- IAJ I z a I o -J I U X coff r- i— < r- c-i f- omun in oo » m n * o f*> f*i *■* o s 9 in io ojn^nruoj oj ■* in -^ <*> (VJ r^m^rvom i\j m m <*> a* r- —t *h p* *— r^ e> ~h -o in ^o>miph (\jod o n ■* (*) «* cn i-h r- r- m in .» r*> r- -* oj cs* cd r«- lp cc x -£i -jd -o in •* oj rn ^ in ^ ** •» ro co r* m •* (N o r*- h- p«- (*i rn r-- h- f*- in l in O 1 UJ i • _j o>t£(\i9 o a 1 o o o r^ «c m * UI 1 UJ >- a 1 Z u ■H -. t\j ■* ■* fO ^HhC*(DN O IT ■* O *-• in <_> cc •* ft ^ f^ in -* o <\j ■* o > Q. i_> ■* — • ru ■* ^ ••* ~h co n n i— i <-* ■* in •* m ^h ph i I UJ z I > o Q i h- t- u CO — • •— 04 O O — i 0*- O O •& LP 3 1 Vi LL Vi I UJ 3 I CO UJ GO < i UJ I l/l l/> o. i »i/iq; a. u"i i\i •* oociaiiC nnn^^o o«t ^ffln o m m m co co co cr* 0* o 3 i ip uj < w in in m oj I?- • cc -» r- a) co tr r- s o oojr-cc* rr •#-#-» ct* cr> *c sc *o %c l/1 i uiq: CD ..♦•• ••••• •••«•• ••••■ • ••■ •••••• to i 2 a ~ ^i^-^H^H , „ | ( i I I I I I I i ■ — > i # t ^ ^*^~ | | t l | | UJ I 1 I I I I I I I I I a i uj z a i > o i _ _ _ o I i- p- (J UI I h I a o — -* -^ oj uji/tuj — ■ *>♦•* ^ m h- r- o a- in r- r»~ r~ o* c?> t\ nin a) h m cdcdcd ■* ■» m ■* *» ** X Z in it € C N ^. ^ —. ,1 .-t ^.-^^.^h^hph mr-imrorr in iTi i/i in .-« ph .-«.-( ~* .— ^- o X j_ cj — ■ ■* ■* *■ Ifl (VjiTiThh ■*-*■-» m ^* ~* iNuliTiOH -* (\Jf\J0j vO >© © t\J (\J (\J i^-i^f^^ cd •* -* rn rn i ■» * •» mm mtt^n c ^hh a- a* (\j cc cd cc CL ff) en O l/l rr a uj < < cc m > Q. ""* ►- z • «•. uj in i/i •-> w cr CO UJ < X a CD < a. *- >***>* ^* •» -»-*-*•*>*■ •*■-*-*•♦"*"* *•*>*--*■ ^* r*» CO CO CO (MMJi (M> ^ nnnc) Pi ft n n n n n n n n <*i ci ci ci ci o m ■— « <— i -h ^- — • — < — - ^-. — — ■ ooooo ooooo ©ooooo ooooo o o o o oooooo ~ i— lf\ i— ~* —* s0 •— *C —* ^H ^ ^) ^- ^) in .— r i— IH HH ci niri\jH oj —< o — o w^ ^ c* ^ o ocii^ on H HH(\J >-> (\J «■-! ^ - H f\j ^H _l _! I— I ^H pH l-l PH f-t ^^ m (\>(\J(\J HF«|T|(»|nn x x»— coirwo (MiT — irt^- ojirui^ir^- ooooo o ««^- mmnmnn i/> CL h>uj i rr nir(\ii*i fu ^- {J* ■— ■ C7* (vj h h j i«c (*imnr*in u. a — ^ — — X • 19 CC-*«*-*f^ iTiC7'^0>OK ifiOO^OOCT (Vj O (T iC np^r^p^c>o^ o*- in ji jo jo i-i r- un oj r- co o p*i ■£ -h a> h- in *> oj p- co un x> oj ro cr co p- o in oj n p"t o oo n £ s > .* o* oj r> p*> *r r«j oj —» pi * ■* pi ** «■* oj r» t> © s s- oj un oj in r- o jd — ■ ■* cr o* -« <>jiin<\i^ •»■ vo ^ cr r- ^* .» r- og o*J1^^ ■# ~* o © •* i/isoi^ ^ nj^-.^ m -^ ^ *h -. /> ,-* i>. co u*t n un ^* r* ■# pi oj -* oj »■* oj oj oj oj *-« 1/1 I >■ .H -T U I Z o "IS rr z i >- uj 2 : 5 o- »-i_i < -h j no o ^ ^ o < r-- o ■£ .# n o ^ rfi 4 ®-*r-o •£ i/i *- <-« in r\j in •-* -c ^^anj9 UJ H Z s cc o LL Ul «/} z o a. V) Ul cc 1 I i: fsi 1 UJ l t- 1 1 UJ 111 1 X 1/1 i < <^ 1 X O 1 < a i a. u-i 1 V -J I u *< O I z u & — * '_r i i t_> -_.' J,. ^ !-_■ 4. r~- «j «- r^ u 4.i p j jj ^— r- "u> vu ui r» »< ui im Ul ^ 4) « » l' ivj y •* oj ~* -c i inns* 4 u*i m s ^ mfxjN-^^ un oj r- i un cd r- >*> »-« ins « « un <-< pi ~* oj ^•-.(vocir .© r*. u- p-< r- i c ■* a ith^ s i" to in in ro r- un x ^coirui *c u^r- if ^ i i/iu jio-^o .— <* -* p"> jo J) m s « «c oj r~ oj ~* © ~* .* -* r- ** *o ph oj ^-< © — » m « oj o> •-• p* r- m <£ <\j oj I O > • i a o ~- oj ^ >— ^- ~« ^ oj -« oj oj m •-« ** H i > a -J -I i — — i O O •* ■* O lO X •* 4 o o o un rvj co cd o o un m x in -» in Oj CD •£.■ -C O O X — rg o o Q. i (i 1 Uj 1 Z 1 1 a o k © -* ^0 in ^ CT C s» (^ *— CC -* s£ ■4 «C *-H S- *C j ^ r- ^ PT l> O C -* -* X 0> o m o in «c x ^ a o ic m O CO O o in CVJ 4" r- r- oj ^h — i 0" — ^ Cf rs) (>- .-* ~ -+ OJ CI (\J (\i f< OJ (VJ <-■ ^ (T • *■• UJ Q Q n tz 1 • m a n p- o « ^ m x n cc r- X- un (Vi m m x X Oj X -* o (*i n x sO n n <£ id o «/> in in 1 (i 1 u li- ft a. — ■ ty cr f n ^ m x f\j (T IV if: if t- f\J ^* (V x ^ 0j -* h- 4 oj -c ■* LT 0J *jD ^ ifi ph n ^ n — i oj a « •* ^ _j i 0. 1 1 I/) 1 O i a D O in t\j b o m o X 'D ■* -* CO O r- J^ - O « Lfl M ^ -*■ o m o & pi un m oj un O OJ f*) sm i\j -h r> po * * n x II w m ^, ^ ^ OJ Oj p-4 j-i nj — CO ha a. i CC UJ CO i i i r- ^ i *- u UJ i 1 UJ in UJ t\J 0J ^D <£ f- ji ui oj j"t un CC (7- CJ* >D ff (? C» 4 S CO O 0*1 1*- o ^- j- j- —■ ^H ^ ^ F-. un h- r- u* O Ifl S N ff1 C* i ■> 7 in (\j (\i n n n t^i -t •* \ft J ifi 1/1 i i »-« O s < i i t- u w CC i < i i Q- I in u^ UJ 1 ¥ 1 Uj in er (V IT N S IT. in c rvj ji if n r- cc cr m o- x >c r^ x a x s- c ^- ^ ^ un r»- -* •* un a, ui in *- — « -* •♦ in « «— cc a tt, J1 Ci S N ^ MiT s ^ -J ^ S M^ >f »— r- •* r1 iCS S<*1 un f» (*- h- >tf m s s ^ x * ■» m n x ■# ■♦ PI PI ~> i 1 a. a *■* CNJ (V (\j f\j f\j f\j C\J Oj Oj CO CO CC amui Oi/ii: -*•**•»-* ■*-*>*** -*-»4--» -a-*^-*-* -*^-^»-* -#-»-*■** -*-*^-^ *-»■*■** ■*■*•*•*■* dujtf m o r^) (*i c+) mr*)p*)"OPi mpimm rnpinmpi n n n n pi rn p*, n pi m n fi m n n m (*i fi w n n n m Q <'I^ ooooc ooooo cz>ooo OOOOO OOOO OOOOO O O O O OOOOO OOOOO Uj > a - Cj- uj in in rf Hi/ii .£)—«>*!— .^j ^«oj^-^- ^-i^un^ ^-.^up^-^. ^^Jin*-" __cr«<-t ^0*1"-"^ _^«^)^, «^3^^)*-« x ui < «-'un^^ ojm^-uO'^ yj ma— •.... • • . • ••••• •• • •••• •«••• ••••• t-tujT ~* •& ~ ■£> *-i ■-■•iJOjPi^r- pn^^unpi ci «ui c, m rir-tp n ci ci <» (\j ci roinojpi mm v ^ ^ <\j — o- — o* ^U»Ow r^ f^ .-t ti £30 Ui I ■ tS xxoc-cr cc (\,tt i ^xxh- «axx-» — xa^# x-*-»-«p- x^-af*- urtccrcro* u^a-CfCTO1 i/iii 2 - ••••■ ••••• ••-• •■••• ••■• ••••• •••• •>••• ••••• fc-to-as m ry if) \0 k inin^ij*>un xowOj-xj xojoj>ori xojOjpi ■— iOjoumi*- — • oj oj f*- ms-r-o*o^ pir-r-c^o* u. I a - * ^H^*pipiun (\j i\i n — — • rn— •— *o m— «-^r--^ .-n — — . ^ unununjiPi j) ji ui n niji ifii> s n ui ui i*» s ^« ^^.(V, ^^,^r>j — —• oj ^™«t\j p-hOj *- Or^ 0> ■— • Oj P1^ un^ © X — > — 0.0. 0.0- 0.0. m mi/ ur iru- urun u"u". lT 26 NSWC/WOL TR 76-155 IDNHH^ ■£> JD £> J"i f\j inno-i^ ■* ■* m < I X *J ^r-t — — — — — i\*nj<\J-«.-«— ^.^^^.^h-, ^^^4^^« ^ ^ ^ ^ ^ I UJ I t- I UJ UJ I X S\ I < Z I t Oi< movcooa' vd « n ** m -^^co(\)t\ja» + -t rn-*ro^'>(n-^cO(*icx)(*i .\j ^> o x> d # vd o *n ' Mi> o £ ip 4 ^ h- in r*>^ eo < 1 •-• r-^oiAfs co cc 1/1 co n -»^-*0"coo)cocccd r-h-r-r-r-p-ininminm hmon n ^^1 ~ — -. — o 1 • -i *r *© rH m o UJIUJV •*••• ••••• ••••••••• ••••••»•••• ••••••• ••••• o 1 z u ,-1 ^« ,1 ,-, _ oj*-«^o(7'cd*c\j*-« f\,^H^^(\i(\j^^^H^^-t —1 (\j ■# * in * m . r^m-vcN^H 4 n n 4 c h-j)inonjmo^<\j Mni\j^oNi/icoiP(\j* ru o m at so x — ^ f\j 1 o >- • ••• ld(J (\J ~* 4) XI l/)CC C' N (\jr\)(\jMn(\JJ14-*-*(*t h ^ ^| cC CO 91 CO ~C uT> J"> f- «0 I « < UJ h- * CO ■— 1 d a in c in o o* I U_ D I ••• ••••••• • • • • • ** 1 Z o -* f\j -* .-« m m m m en r^r^r^*.*.*ininin -**^-»^>j-h — — 1-1 — . ■* 4 ■£>■£&<£> *o •£> ■£> •£ & jd 2 3 ! .- ™ or 1 • in or o 4 -c m !-■ ■*■»■* o o oooooocirjm f-f-h-r-mmooooo it in i\j ^ -< 4 4 r-r-r-cooo ^ D I o uj < a (\n". a o <-« *c \0 tn in r*-h-h-^-J5 or O UJ 1 O or i uj z 1 1 1 1 l 1 1 1 t 1 — t i 1 1 Q I t- t- U UJ I «-■ < UJ CN _J I O 3 I ■ aiQ.Q— ^^^ •***-* in in in *-«.-«--— tMojcimmfim — • ~h o o o -h —« 00000 «-. a 1 „„^~ „„^^~ CO < J UJ 1 «J 1 »- o Tj ixzi/i rommci^r ^ in j-. if ifi in minmininintnin i;inminininmmirmm ««^«^h_^^ _ — _ _ _ < 1-07 ••••• (— 1 H- u — 1 l 1 • — 1 m i/i l k in a cm ui in o <-i x -o <£ x x m m c, ^-a^ooo- nnmnr\jf\jooooo o o m in in r- r- ojouojoo 1 « uj < •■■ •••• ••• •••• ••«•• I Uj a ct Mn<—t^^>—i«^i— ••—<>-<■•— ■ ^_ ^, ^^ _-, _ ^_ „ _-._„„_ «* .1 x 00000 00000 000000000 00000000000 0000000 00000 > a - • *~ z • ~ UJ C/l (/) »-«uior «^^^-^h ^«£^>f^ »o>fisCr-r-f*-x,^x. -^-^^^rcroaocacci. 4 <£> o* 17 9 O1 17 <-oi'O'Oi ««-»ooeim « 4 4 in in 3 1 a" • «&*- ^- — ^, ^-« ^h ^- — — t\ r\ *- ••—•^^f>rr,cr)rrif^j(\j(\i c\j(\jr\ir^r^ ma— ••••• •••■ ••••• ••••••••••• ••••••• ••••• huj I nfimf n 1— > — •-* t^t m ^->^-»*-<-*^4oco ^ J" j" -i a a o cr ir o o h r-m ■» ^ 4 4 >* -4 ^ u~ u" U.O— ^-t— \ *-» — i-i •-* LJ I «o (V o a sj: x -1 -j 4 ,» -j r-r-r-inmiretaca. occc^-. — *■*■**< r-r^omn-#-« ^.«£*^-«-« mcrz- ■— o «j 1 ^^)u~i-*^-* ^-i ^-t ,— ^^ ^h ooojtX' o- Ji » a» — ^ ftj 27 o O NSWC/WOL TR 76-155 D Z ooooo ooooo ooooo r> © © o Oj — O O o in o o o o ooooo ooooo on«>onj o*> o wn o — « © o rvj m p* © © o o a in CC < 0- < a. « > u. _J UJ 0 _J b. 1 MO <-) < CE OOOOO a- o .— o o — o o — . f\j ® © m © o in f- «n ooiaos o UJ > a: 00 i z ooooo o n f\j cr o < oo oivin © m <\j © © o* o « © © — • o o •-* N-o<\JO O CT- fvj — O OOOOO — (V) -■ rvj -• — -. — « — r\j inj — — u _l < o Q z < I- 2 v> o LL (/) UJ cc D Q UJ > oc J jut D -JIN u — < juq; <(/*,< u o a in u o > a - i/i a ~ -•uii b. C — "N*** s (") ~ ^ in m r^- ^ -r o m m ^ CD r- -* o in <*> © s- * fn « ao m »-■ # aD os o-n o — n r\j r\j —. -* so ~ ct« -«^(*io — • in m — o © n -^ <\j ■♦ o ** nj »■* © tst ** ** ~ n M « ~ — • n r>j — — n — • »- — • m — ■ ~* -. ~. n —. -* r^ — —. ~ ~. nj in *» (\j *o ■»-*-* oj »© 04hn* a- •» n- o n ^ o © (\j k m r\j in * cr — • -c o — m ~ m -h -* cr> cl1- *c ^ fV) ru o it — * o © ^ "-< m o i/t o ^ in *c — r*- — r\j o ^ tnMifi ** * — — * — f\J in <\J «C ftj ♦ »h m (VMoff i^ o s w a r» nj o>n its (vj in 4 o — ■ ss^^-h. s * a: C- ao o ru © c\j in r- — .* c* f- * (*> ~ m o (»i r- r» © "wnnjn i\jftjnn(\j ru (\j ru r\j c\j <*> m (\i m mnnnm (*> r- n m n m ■♦ n n ♦ ■* f\j * — ^ f-ncooro m * •■■ in f- a r« x it ns * mi o nj m 0*- 0* o* © 0* © cc^oeo* ru r> © © ~ mnftjnn in — « in -* m in — •mo*— m -* -* o « © in in © © in m © © © in in in o oo^no -• «c — *o ~ - ^ - n >c — * t\j r> «c rn-^tnm m -* in n o m — -* in rn n pi -» f\i m CO r- co LU -I CO < en a z ~ —■ o « I u. x a. — «a a — T UJ 2 UG- crocooo- o o oj cc cc o orocc « c icn ->ai c cc ^ — c co ct ■» co ■*-#•» r-- r\j f\j -c «c r*- un in «c m in in in xi ltut cd cm ru *£> co r\i ry «o m cd r\j r\j r\j m --• f>j ru c\j r- --^nji (\j ru r«- r-« — • \i m n ^ « m ^- ^- © m ~ .-* p*- ~- <*>>^^,_,,-. mirmunrn < ►-• O X UJ * o rvj IT 28 NSWC/WOL TR 76-155 OOOO-h OOOOO O © © O O © © © © © © — • — t © O O © 2 m > x ~> -j i/i ♦— LU ►-* < > U- _J UJ D -J u. X MO Z> ►- u < or UJ o ox UJ 7 > Z> a: z uj ^ m o — < © © OM 0«OH IT^^hOJ© ^h ^hiPfho © (\j © •-« © •-* a it <\j m © r\j r— %c >c m © © IT CO if) © i/i r*i n o © © (•*• m ~£> ^ © co r»- m © co •* cc a uj X rsi < •-* _ ,-H ~H -H O © © O © © © © *G © © © r- m © cc «* co Q UJ D O O CO 1— ci u _i m < Z o o ♦ UJ — CL I- I- UJ < « h- _l _J UJ 3 _; X rsi U HH < _i u a: < tn «i u o o. CDff> OOh o O f) ^H © r*i n o h ^ ^i CO © »-• •£ N U1 vo r - «— < r- tN r- © f*> u"i ijn co co rn m -» inooo^D' ** r-*i— «© n © © o o o i-H ,-) rH .-H ^-t _4 _| ^* f\) (\J •-« 1-H 1/1 t— uj u")Pj(\JLf>cc sD in ^t- ct- ^* o> ~h m -h o m \£j a> ^d m *x> sO © -» »c u"i co <-« co ro —• «-• _j x -* ro r-- r- in ■*■ ff* W -4 it n a O1 iT c in t\ cc ^ m — • f\j *c o> o h >c a c oj 1/1U ••••• ••••• •••••• ••••• . ••• •••••• o>- ■* — (M -* -* — * «-h co m m ^h r-* ■* if) -» C"1 « « rn n it. •* a u -< ~- — -« '- a UJ l/l 0 3 f^(\jr-»C(\j m C1 *o ^ •* n >» ic it c* o m co ^ -* o cc rnr-co o o ui *c r-- « q m - ^.^.^Hr^m itocc^hcc ro -* •* rn cm (\j so rn -h >c o — • h-«cc moo o it- ■* t m n m •* n n m rn-*^ so r- in -* -* u"> co a — x I— •* f\j © r*- o> cc if i/i o ifi ^- C1 I co •* n ^ co ci c C" cc m©co n c oo n fni/i 1 o- ui 2 I .* .* ^- m m f\j(\jn(vm r\j oj © « ro «-* --< © ni --< <\j rvj •* *£ co ctojo^cc© l-H UJ U p|p|HHH ^,^-«^H.-ll-M ^H^H^H^HI— 1^-1 <— I •— I "—I •— • <— • ■— I HrH H ^nf\Jt— '<—•<— if\J U. _J ~ X ii- © © in <\i © ry in ^ in ^* rvj in in -* in ~h ©ooo© © ,-« ^h ,_, mmmnrnri irtH- • m uj i nniriivjn <\j -h cr « o oj^-^-o^o n wn^ o >* co co x — • -* © m m m U. O *- ,_,,_< -- (V^-^h^h C\J(VJtMf\J UJ X • o cc ** -* -» r*- in o o> o or1 if , ffO o ? a* rvj © cc %o »c in •—••—< ^— © © r- m m in i^a z- •• • • • • i—o >c >o in >*■ ^ •£) -*•»-* m m r- ?*- r*- r- u. i or - m in in it n~ (** a*, in f- f*- r*-. it tr it n n m? >-* w m oct-ct- <-* •-! -. -• « 0J — -H 0d O I < a ~ x UJ x o c — e x a c ~ < >-i ID X UJ It u * - (V IT 29 N CC NSWC/WOL TR 76-155 T 3 -> Z OOOOO OOOOO DOOO xoooo £000 00000 0000 00000 00000 '"*"> f*l O O O O C^ J". O O OO(S0 OOOOO OOOO O O — f\j O O J^ f\j — OOOOO OOOOO X !\l© *f*1000 OOOOO OOOO OOOOO OOl/tO OOfUCDO O h- ^ ~* OOOOO — ' o o o o < CC < a. I IOOO OOOOO OO — O O00OOO OOOO O O -* T "■ OOOOJ ^ O — O ^ 00 ~« O O O I- < o 00 o a -a »-< i/i to -* m .» r-, ir coooo oo-«o 00000 © o o rvir-xo* m «© ~- x r- o .* ry k- o it r m n o» go !*■ 0* un ^ * J1 (\j j-n"Tf\j<\j -h n * .* ro -* ~- ry jd x o r» r«- ry xi ry xi r»> £ £ ~* •* < X o CC LU a. ai I s o u. 00 UJ E UJ 0*1 Q ~ ~ « C I cr a. >~ 1 c — V. x 1 «- u_ u m a. ~ "— UJ X U- o — n ^ ^h a- ® t? n a- j d u t 7 x rr x cr o* cr- x o x o- j> cc re o-uff cc j a o" t t> mt 11 s >*«- a* x x x f O C X X j r^ 1 x x ,p — xt — in — o o 0x1X10 ooo-njo o x> <\i © rv x» — x> -^ im xi •— xi — « n^xifi m^xinm m^xin nn 4 mo n in c\j i*i ry « j> -^ it oj^o«^ > CC UJ CO ca O xcrooa oc'vxcc -a. a s — ac i f- S S' L X S' co UJ _l CO < I- <1 Q. — T UJ * o c — 3 C - 1/ «3 •-■ O -» r uj * • u -« — CVJ 30 NSWC/WOL TR 76-155 O O O O O O O O O O i/IOlTOOOOOO 00000030000 o o o o o o o o o o o o o ^ o o o i\i (\j o a) 4 hi mo^nj^rvj^HOOoo o •* o o o o o o m o o ^h t- UJ —I < > U_ -1 UJ => _l U. X (MO r> i- u < or UJ o m o -^ o o o f\j -* — • o r- — • ( (MT-tariifioo- « r~ m «i/i o> mt j ^ (t H l\J ff"- oLfi — oo *irnt>N <-" ( (?in-*o,(r)Lnoo^srn ^h Lfi 0s 0s CX- O O oic won O IT O O O O CT CT CT CO ^t ( ffir^UniTOOi-iNn ~h tf"l 0*1 © 0> O C CT CD f\j O ~h o UJ 3 < < t- _l _l UJ OJSN u <-. < JU I o —. ~ < o i: _t < 2 CD Or — I o — t/> z z t-< UJ a — u. o — n >-< rH cr ^ r- ~* it m >c (\jco>i3m'>o^-S'CO-* in^r-^HntTh-o-^r^-NO in *c <— • oj © r-- m cr o in o m {\jcor-r-o*1 x x in r— >* ^oiMMCMDfiM •4-tT^om-s-cTr^sC' — • in n .— i i-i .» ,o ru m m sc r^ o x in xcocococo s Cf-r,-x x o x r*- x f*- x » o -< n O1 cdcccctoj i in cc O" s m^-i-ccxf-«£io.— < r— cc-d-cr,x»-'irsO(Too f o o> o -* cc <-< c >c £• r*- -t sc t^ •*■ i ■*iriir>cco-*i1cao ■tinNH4vi>*'£iN(Ti(\j in cr x x cr f^ c cr •— < •* r»- ■— _ _ — _ _i _ ^ ^h _ _ ■-(■— | ,— . .-, ^- ^- .-I i-< .— I <— — .-H ^- _ r- r~ ,— — . ,— I f\j M r- r- H r- r- (V ^H PU (Vl "-" f\J ooooo ji in in r^ ^- Lnmmoooooo ^^^lOHrtnoonc) tn in -^ oj r\j oj f\j nj nj nj r«- f- mrnmmn ^^^mr*} <— i.-«^.4-.*.a-ooo *o»OnO«cxxooooo ^-. ^h m ^h — « -$■ .$■ *■ •* -* in in _i — . (\j m (\j n n n ^-._i_t_.^_rnfTirnfrif) .-« <\j nj r\j oj ,-. ^h ,_, ^h ^* I • CD i/> a z ■ — O < : fVJOI r-.*on C'irininirinin — — <\j p- r- o m m •* ■* oj (M -h o o o o «£> >c >c >* -* x x x x x 31 NSWC/WOL TR 76-155 The positive duration TPOS (see sketch Figure 3.1.1) was calculated as described in Appendix C for the 1973 tests; for the 1975 tests measured values were used. The negative pressure PNEG and its duration DTNEG were measured from the pressure records. The last five columns, Tables 3.1.1 and 3.1.2, list calculated parameters for the oscillatory response of the swim bladder. The number of positive cycles is the positive duration measured in complete cycles of oscillation starting from the initial "at rest" expansion. The number of negative cycles locates the final return to ambient pressure (end of negative phase — see Figure 3.1.1) in terms of the bladder oscillation. "Zero" is taken as the last expansion occurring before surface cut-off. See, e.g., Figure 2.3.1. Thus, unless the number of negative cycles is greater than 0.5, no final expansion takes place during the negative phase. The number of negative cycles, (At/T) , is a measure of the contribution of the negative phase to the final bladder expansion. The relationship is roughly as follows: (At/T) < 0.5 No contribution 0.5 < (At/T)„_, < 1.0 Partial contribution NP 1.0 £ (At/T) Full contribution The reader is referred to Appendix B for a more complete description, The bladder oscillation parameters X, Y, Z are defined as follows : X = -100 In AMIN/A. (3.1.3) Y = 10 0 In AMAX/A. (3.1.4) Z = X + Y = 100 In AMAX/AMIN (3.1.5) 32 NSWC/WOL TR 76-155 oc 3 I- < Z o CO iii cc D co 00 111 o. Q D O -I < o z ! i 00 z o 00 CO 33 NSWC/WOL TR 76-155 where In is the natural logarithm, Aj^ is the initial at rest bladder radius, and AMIN and AMAX are the smallest and largest radii during the oscillatory response. In the cases studied so far, the first compression has always been AMIN, while AMAX generally occurs during or following the negative phase. We will use the bladder oscillation parameters X, Y, and Z in Sections 3.2 and 3.3 to discuss and correlate the observed injuries to fish specimens on our tests. The bladder radius, A. — Tables 3.1.3 and 3.1.4, column 7 — is the radius for a sphere of the same volume as the fishes' bladder at fish depth for a fish which has not acclimated, i.e., for a fish at equilibrium with one atmosphere pressure which is isothermally compressed to hydrostatic pressure at fish depth.* Bladder radius A. for non-acclimated fish is given by A. = (A.) A^Oy_x_loA V3 (3.1.6)** 1 ° V pi / where p. is the pressure at fish depth in pascals and (A.) , the radius at one atmosphere pressure, is given by (A±) /L - 0.033 (Spot) (3.1.7) (A.) /L = 0.055 (White Perch) (3.1.8) where L is the fork length of the fish. The constants 0.0 33 and 0.055 were selected for each species by trial and error so as to optimize the correlation between experimentally observed injuries to the test specimens and the calculated bladder oscillation parameter Z (e.g., Figure 3.2.1). *This is how it was done on the explosion tests. It would have been prohibitively expensive to have let the fish acclimate to testing depth, because of the time required. This problem is discussed by Gaspin, Wiley, Peters, 1976. ** For the calculations of this report the exponent, l/3y, where Y - 1.4 — for adiabatic compression — was inadvertently used. Since the computations reported here should be quite insensitive to this error, they were not redone. 34 NSWC/WOL TR 7 6-15 5 The number of fish of a given average size at each test specimen location and summaries of the injuries evaluated upon post-shot disection are listed in the last 5 columns of Tables 3.1.3 and 3.1.4. Thus, e.g., on Shot 531 (Table 3-1.3) at the 76.2 meter range position there were 10 Spot, all 10 of which received injuries of level 1 or greater, 7 of which received injuries of level 2 or greater, 5 of which received injuries of level 3, and none of which received level 4 injuries. (There were no injuries of level 5 observed on either the 1973 or 1975 tests.) Table 3.1.5 is a condensed version of the code used to evaluate the explosion damage to the fish upon post-shot dissection.3 Successive injury levels are of increasing severity and each fish is classified to fall into one and only one level of injury. Figure 3.1.2 depicts this fundamental design of the injury code. Thus, the fundamental physical problem of this report is to estimate test condi- tions for the transitions from one injury level to the next. We will do this by estimating the probability of events such as "occurrence of injury level 3 or greater" as a function of the calculated damage parameter Z (Equation 3.1.5). It is convenient — but not fundamental to the analysis -- that such "cumulative" injuries are also what is of practical interest in explosion testing. For example, the event "injury of level 3 or greater" has been found to correlate with the observed fish-kill* on underwater explosion tests. And, the event "injury of level 2 or greater" has been considered to give the fish "little chance to survive predation . " 3. The injury evaluation code is due to: Hubbs , C. L. , Schultz, E. P., and Wisner, R. , Unpublished preliminary report on "Investigation of Effects on Caged Fishes from Underwater Nitro-Carbo-Nitrate Explosions," U. of California, Scripps Institute of Oceanography, 1960. The complete code is also listed in reference 1. * The term "observed fish-kill" refers to the dead and dying fish found on the surface and bottom following an underwater explosion. 35 NSWC/WOL TR 76-155 Injury Level TABLE 3.1.5 CODE FOR EVALUATING VISIBLE FISH DAMAGE No damage Light hemorrhaging in tissues covering kidney Light hemorrhaging throughout body cavity, some kidney damage, but gas bladder intact Severe hemorrhaging throughout body cavity, gross kidney damage, and gas bladder burst Partial break-thru of body wall, bleeding about anus Ruptured body cavity, internal organs scrambled or lost 36 NSWC/WOL TR 76-155 < < Q I CO UJ -I CO to > < -J < > UJ o CO UJ E D ? UJ s § CO Z I- o Ul Q I > ui CO CM CO d UJ o< < -*- w T3A31 AtinrNi 37 NSWC/WOL TR 76-155 However, should the reader require for example the probability, P (level 2 injury), it is just the difference, P (level 2 or greater) - P (level 3 or greater). 3.2 OBSERVED INJURIES TO SPOT VS CALCULATED OSCILLATION PARAMETER Figure 3.2.1 shows the experimentally observed injuries (as shown in each row of Table 3.1.3) to Spot on the 1973 and 1975 tests plotted as a function of Z = 100 In AMAX/AMIN. There are three plots, one for each of the injury levels 1, 2, and 3. The plotted points represent the percent of fish of a given size at a given specimen location receiving injuries of the indicated level or greater. To investigate the functional dependence of the observed injury on the calculated oscillation parameter Z we constructed Table 3.2.1 and Figure 3.2.2. Table 3.2.1 was constructed from Table 3.1.3 by reordering (sorting) the entries in order of increas- ing value of Z and then separating the new table into groups repre- senting approximately 100 fish. The total observed injuries for each group was then summarized by the successive row entries in Table 3.2.1. Thus, for the first group with a mid-range value for Z=54; 41% of the fish received injuries of level 1 or greater; 11%, level 2 or greater; and 5%, level 3 or greater. Figure 3.2.2 shows plots of the averaged injury data tabulated in Table 3.2.1. The solid curves are drawn by eye through the data points. The experimental data for level 3 injuries to Spot exhibit less scatter than that for levels 1 or 2 ; and also less than for all levels of injury to White Perch (Section 3.3), Whether or not this has any physical significance is not known. Also shown, as a dashed line in Figure 3.2.2, is the equation (3.2.1) 1 + EXP [-0.055(Z-125) ] where p is the probability of observing injury of level 3 or greater, Equation 3.2.1 is the Cumulative Logistic Probability Function with 38 MSWC/WOL TR 76-155 100% 50 - 0 100% o -]0— o— a a a a o o a — po-oo — o ooooo o □ - o □ DO - D o o o° a INJURY LEVEL [T) o-o 1 — o o — bo— Q i i a in 3 I LL C3 < O cc 50 -ooooo o o □ CD O INJURY LEVEL [2] J 1 100% 50 □ 00 □ INJURY LEVEL [3] 50 100 150 200 250 FIG. 3.2.1 OBSERVED INJURIES TO SPOT AS A FUNCTION OF Z 39 NSWC/WOL TR 76-155 fa O O H En U D fa CO o fa en co fa fa O w fa Eh >h Eh M H fa <: PQ O fa fa < fa H D U a o a Q W Eh rfj D fa fa fa o Q W o g > u to i S-l 3 CD > ■H 4-) CCS rH e u CD > U CD CO XI O LD O LT) r-~ CM n IT) CM CO cd +j rrj "* m o\ CM r^ o m m IT) CTi cr\ o in o in m CO O o o o ■p c CD •H M o G a rd i cn T3 •H tin s O in co o CM CO <£> CFi CM in in H H CM CO W ►J fa < Eh CO in .H r» r- 4-1 •* CO o H CO r- >-{ 0 r^ O Q LU > CC LU 00 CQ o 0.50- 300 FIG. 3.2.2 OBSERVED CUMULATIVE INJURY TO SPOT AS A FUNCTION OF Z 41 NSWC/WOL TR 76-15 5 the parameter values, 0.055 and 125, fitted to the experimental data. The parameter value 0.055 was obtained by considering all of the Spot and White Perch data, levels 1, 2 and 3 from the two test series. The parameter value 125 -- the value of Z corresponding to 50% injury probability -- is the maximum likelihood fit value to the level 3 injury data for Spot. Equation 3.2.1 is considered to be a sufficiently precise representation of the data for most applications, such as those described in Section 4 of this report. 3.3 OBSERVED INJURIES TO WHITE PERCH VS CALCULATED OSCILLATION PARAMETER Figure 3.3.1 shows the experimentally observed injuries to White Perch on the 1973 and 1975 tests (as shown in each row of Table 3.1.4) plotted as a function of Z . To investigate the functional dependencies we constructed Table 3.3.1 and Figure 3.3.2 from the data presented in Table 3.1.4. The plot shown in Figure 3.3.2 for level 3 injuries exhibits excessive scatter. Perhaps these level 3 injuries to White Perch are more closely related to some other parameter of the bladder oscillation, but it did not appear worthwhile to investigate that possibility. Figure 3.3.3 shows the averaged injury data for both Spot and White Perch (Tables 3.2.1 and 3.3.1) plotted as a function of Z. The curves were drawn by eye through the combined data. These plots support the viewpoint of this report that the observed injuries to both species of fish -- Spot and White Perch -- are described by the same damage functions. (The coefficients — Equations 3.1.7 and 3.1.8 -- for the effective bladder radii used in the dynamical response calculations are different for the two species of fish, however. ) 42 NSWC/WOL TR 76-155 100% V) % o cc Q. 50 0 100% -CDtpXEDO- 50 0 100% 50 INJURY LEVEL (T) J I — i *ppi«»-rrTW»fWwTTT>-«-T-w-M-rTrwTr>on o JiiiiMiitn o — O □ O □ a INJURY LEVEL OO-i o j— oo oap — nm oo o a a a □ V a D a ao — a G □ o 0 a ° 8 o o a INJURY LEVEL @) a n-TTTHTJ ' 50 100 150 z 200 250 FIG. 3.3.1 OBSERVED INJURIES TO WHITE PERCH AS A FUNCTION OF Z 43 NSWC/WOL TR 76-155 52 O H H u 52 D Ph < CO < K U Ph W PhI w CO Eh H « K w S Eh W Ph S o Ph 3 < >H Ph Eh H 2 •J O H H P3 Eh < H O « D P fD a 2 Eh H < J P o w u > 1-1 Pi < Ph1 u CO CQ Cm O o Q W u g w > < W > >H H EH Eh H < hh hh H .3 03 S < £> pq o O Pi Q Ph W > >H « Pi W 1=3 CO 1-3 pq s o H o o CM o oo oo ^r C-- o LT\ m oo oo Ch w > W cm En o o oo on o D— o o o o oo co co CT\ o o Eh S H O Ph fe I O Q H s vo CM oo UD VO LPi CM O CM Lf> r\j H rH H CM W l>- CO C3 CM LO 53 Ph oc UJ o Q in > CC HI GO CO o 0.50 1.00 0.50 300 o SPOT d WHITE PERCH FIG. 3.3.3 OBSERVED CUMULATIVE INJURY AS A FUNCTION OF Z- SPOT AND WHITE PERCH COMBINED DATA 46 NSWC/WOL TR 76-155 3.4 COMPARISON OF SHOCKWAVE IMPULSE AND CALCULATED BLADDER OSCILLATION AS DAMAGE PARAMETERS Yelverton et al4 at the Lovelace Foundation working in a test pond with eight species of bladder fish at depths down to 10 feet obtained fish-kill results describable by an Impulse Damage Parameter, Z = 80 In [I/M1/3] (3.4.1) where In is the natural logarithm, I is the impulse of the positive portion of the pressure wave in psi-msec and M is the mass of the fish in grams. [The arbitrary constant, 80, was calculated by the author to correspond to the value, 100, in the Bladder Oscillation Parameter (Equation 3.1.5).] The results reported by Yelverton et al1* give a kill- probability 1 p = (3.4.2) 1 + EXP[-0.083(ZI-132) ] where Z is the Impulse Parameter. Equation 3.4.2 is derived from Figure 6 of Yelverton et al by fitting the cumulative logistic probability distribution to their results for observed mortality upon holding the fish for 24 hours after the explosion test. Figure 3.4.1a shows the level 3 injury results for Spot and White Perch (Tables 3.1.3 and 3.1.4) plotted as a function of the Impulse Damage Parameter. Note that the Impulse Damage Parameter does not describe these results . Figure 3.4.1b shows a subset of the level 3 injury results for Spot and White Perch plotted as a function of the Impulse Damage 4. Yelverton, J. T., et al, "The Relationship between Fish Size and their Response to Underwater Blast," DNA Report 3677T, Lovelace Foundation, 1975. 47 NSWC/WOL TR 76-155 100% (a) 50 ALL OF DATA O OD o o o o o o o o O O O DO DO O O o o IMPULSE DAMAGE PARAMETER (b) 100% 50 - IMPULSE DAMAGE PARAMETER 100% (c) 250 BLADDER OSCILLATION PARAMETER, Z FIG. 3.4.1 CORRELATIONS OF LEVEL 3 INJURIES FOR SPOT AND WHITE PERCH WITH IMPULSE DAMAGE PARAMETER AND WITH BLADDER OSCILLATION PARAMETER 48 NSWC/WOL TR 7 6-15 5 Parameter. In Figure 3.4.1b those data points where the bladder response calculation showed more than one oscillation during the posi- tive phase (Tables 3.1.3 and 3.1.4) have been removed. The curve is Equation 3.4.2, the kill-probability result from Yelverton et al (1975) . Thus, their 24-hr mortality is approximately equivalent to our level 3 dissection injuries;* and, perhaps more important, the Impulse Damage Parameter is shown to describe only those explosion geometries where the charge and/or the fish are at shallow enough depth that appro ximately one or less cycles of bladder oscillation occur before sur face reflection terminates the positive pressure phase. Figure 3.4.1c shows for comparison all of the level 3 injury results plotted as a function of the Bladder Oscillation Parameter. The curve is Equation 3.2.1 derived from the Spot level 3 injury data. 3.5 DISCUSSION OF INJURY CORRELATIONS It is not accidental that both the bladder oscillation parameter and the impulse damage parameter can be used to describe the fish-kill for shallow explosion geometries. To see how this comes about we examine the response of an air bubble to impulsive pressure loading. "Let the pressure be applied suddenly and let it disappear again before the bubble has had time to change appreciably in size. Then, the bubble will begin contracting inward at a certain radial velocity v. given by v. = — (3.5.1) pAi *In examining dead and disabled fish which have been collected from the water surface following underwater explosions Martin Wiley and Greig Peters (Chesapeake Biological Laboratory, Solomons, Md.) have found only fish having injuries of level 3 or greater. This indicates that fish having received lesser injuries do not show up in the visible fish kill although they may later fall victim to predation. 49 NSWC/WOL TR 76-15 5 where p is the density of the water and I = Jp dt, the applied impulse."5 By the methods of Appendix A we can now calculate the radius ratio AMAX/AMIN for the oscillating bubble. See Figure 3.5.1. The solution -- by means of a tabulated function -- is of the form AMAX AMIN = FUNCTION A.^fpp- (3.5.2) where p. is the initial value of the ambient water pressure. Since ^1 p . does not vary greatly for shallow explosion geometries and since in most bladder fish the swim bladder comprises a roughly constant fraction of the total volume (about 6%) , Equation 3.5.2 can be written AMAX AMIN = FUNCTION 1/3 M ( approximately) (3.5.3) where we have substituted M, the mass of the fish, for the volume, since all fish are approximately neutrally buoyant. Eauation 3.5.3 shows that the Bladder Oscillation Parameter and the Impulse Damage Parameter are for practical purposes equivalent, for the special condition of shallow fish depth and impulsive pressure loading. Taken together, the results of the Lovelace Foundation for fish-kill as a function of the impulse and the present results described in terms of the bladder oscillation parameter (and, in part by the impulse damage parameter) give us confidence that we have achieved a correct approximate solution to the problem of 5. Kennard, E. H., "Radial Motion of Water Surrounding a Sphere of Gas in Relation to Pressure Waves," 1943, published in Vol. II of "Underwater Explosion Research," Office of Naval Research, 1950- 50 NSWC/WOLTR 76-155 APPLIED PRESSURE Pi IMPULSE, I =Jpdt Pi = INITIAL VALUE OF AMBIENT WATER PRESSURE BUBBLE PRESSURE Pi BUBBLE SIZE AMIN TIME AMAX FIGURE 3.5.1 SKETCH I LLUSTRATING BUBBLE RESPONSE TO A PRESSURE WAVE OF VERY SHORT DURATION 51 NSWC/WOL TR 76-155 predicting fish-kill.* The non-ideal appearance of the injury correlations shown in Figure 3.4.1b and c are no doubt due to the approximate nature of these two damage parameters. That the impulse damage parameter can be used to describe observed injuries for pressure waves of more than 1/2-cycle in duration (Figure 3.4.1b) is clear evidence of its approximate nature. Apparently, for shallow explosion geometries these two damage parameters approximate some unknown "true" damage parameter about equally well. Additional work could possibly yield a better damage parameter than either the Impulse Damage Parameter or the Bladder Oscillation Parameter. However such additional work does not seem justified because at present our ability to predict fish-kill is limited by other more critical factors, namely, knowledge of the pressure signature in the presence of surface and bottom effects and knowledge of the fish species/size/density distribution in the vicinity of the explosion. Finally, two observations are noted: (1) The bladder oscillation solution can be used to define the useful range of the impulse damage parameter. (2) For shallow explosion geometries fish-kill computations using the simpler impulse damage parameter can be used to check computations using the computed bladder oscillation parameter. *We are also confident (based on unpublished work to date) that the Lovelace Foundation results (Yelverton et al, 1975) can also be described in terms of the bladder oscillation parameter. To do so is not a routine matter, however, since the negative phase pressure and duration at each fish location must be calculated, and an effective bladder radius coefficient, (Ai)0/L (analogous to Equations 3.1.7 and 3.1.8), must be determined by trial-and-error calculations for each fish. 52 NSWC/WOL TR 76-155 4 APPLICATIONS 4 . 1 FISH-KILL CONTOURS Figure 4.1.1 shows the region of greater than 50% kill pre- dicted for 18-cm long Spot in the vicinity of a 32 kilogram pentolite explosion at 9 meter depth. The procedure for making Figure 4.1.1 is as follows. First, we calculate the bladder oscillation parameter Z for an array of horizontal ranges, x, and depths, y; i.e., Z = f(x,y). These values, Z = 100 In (AMAX/AMIN) , are tabulated in Table 4.1.1. Next, assuming that injury of level 3 constitutes kill, we read from Figure 3.2.2 the value, Z,-no = 120, for 50% kill probability. Finally, we plot in Figure 4.1.1 the regions of Table 4.1.1 having Z areater than Z50%. To calculate Z in Table 4.1.1 we first calculated an approxi- mate pressure-time signature by the method described in Appendix C. Then, we calculated the response to this signature as described in Section 2 and in Appendix B, except that these computations were for undamped oscillatory bladder response.* Figure 4.1.2 shows predicted regions of greater than 10%, 50% and 90% kill for 21.5-cm long White Perch for 32 KG pentolite at 9 meter depth. The procedure for making Figure 4.1.2 was the same as described for Figure 4.1.1. Values of Z,-.0 = 77 and Zorio = 190 read from Figure 3.2.2 were used to obtain the 10% and 90% kill contours in Figure 4.1.2. In Figure 4.1.2 contour details such as shown in Figure 4.1.1 have been smoothed out. Note two important features of our solution to the fish-kill problem which are evident in Figure 4.1.2: (1) The fish-kill is strongly dependent on the depth of the fish. *Due to "no damping" and because of discrepancies between the negative pressures and durations calculated by Appendix C and results from the 1975 test series these calculations are considered approximate — but quite adequate for the purposes of this report. 53 NSWC/WOL TR 76-155 z I- Q. Ill a m en I- < O f- Q- o CM M O a. oo o oo cc O o in < I cc o o UJ cc (saaiaiAi) Hidaa 54 (X w Eh K a. Eh a. w a C/3 M Ph NSWC/WOL TR 76-155 TABLE 4.1.1 BLADDER OSCILLATION PARAMETER Z AS A FUNCTION OF FISHES ' DEPTH AND HORIZONTAL RANGE* Charge: 32 KG Pentolite at 9 M Depth Fish: Spot, 18 cm Fork Length 61 HORIZONTAL RANGE (METERS) 91 122 152 183 0 - - - 1.5 29 9 333 131 3.0 302 291 139 4.6 310 288 111 6.1 228 217 194 7.6 244 185 193 9.1 174 207 150 10.7 228 151 135 12.2 156 140 149 13.7 205 159 140 15.2 149 116 95 16.8 188 131 102 18.3 142 138 132 19.8 175 107 91 21.3 136 140 86 22.9 163 95 106 24.4 133 91 92 25.9 110 114 80 27.4 128 96 95 29.0 125 119 82 30.5 118 92 74 213 244 94 52 44 39 153 111 112 72 96 131 143 98 139 102 98 122 158 - 124 128 171 131 104 119 147 137 103 98 115 136 111 89 94 109 111 90 110 92 112 99 123 75 90 100 98 90 66 87 74 103 62 67 78 90 76 55 104 68 87 60 82 59 76 65 67 71 58 75 76 85 50 66 91 57 53 50 60 54 73 42 *These values for Z were calculated using approximate predicted pressure-time inputs and no damping of the calculated bladder motion. 55 NSWC/WOL TR 76-155 CO cc LU I- 2 UJ O z < cc -I < ►- z o N CC O I I o cc LU a UJ I o in CM cc O o a. UJ Q o < < m -i 2 z a. CM CO < X cc u. O CO z g o LU CC CM "^ d (SH313IAI) Hidaa 56 NSWC/WOL TR 76-155 (2) Regions of less than 50% kill — since they encompass a tremendous volume of water — make a major contribution to the total number of fish killed by an underwater explosion. These two features are examined further in Sections 4.2 and 4.3. 4.2 KILL PROBABILITES AS A FUNCTION OF DEPTH FOR DIFFERENT SIZED FISH Figure 4.2.1 shows the variation of predicted kill-probability with fishes' depth at a fixed horizontal range for different fish corresponding to three different sized swim bladders. The predicted kill-probability is obtained from calculated Z-values, e.g., Table 4.1.1, using Equation 3.2.1 (dashed line in Figure 3.2.2). The approximate length of Striped Bass corresponding to the equivalent bladder radii of the bladder oscillation calculations was calculated from Bladder Radius = >Q42 (4.2.1)* Fish Length For the two larger sized fish in Figure 4.2.1 the maxima occurring at about 7 and 11 meters depth, respectively, are caused by surface cut-off occurring at the first half-cycle of bladder oscillation. At shallower depths the bladder does not have time to respond fully to the positive portion of the explosion wave; while coincidence of the first half-cycle and surface cut-off amounts to a resonance between the oscillatory response and the driving pressure field outside. Thus, at shallow depth the larger fish are in effect protected from harm by their swim bladders; while at the resonance depth their swim bladders "do them in." *The value .042 is 80% of that experimentally measured from a sample of 3 Stripped Bass. The value 80% represents a guess at the correction to go from measured radius to equivalent computation radius for this fish. 57 NSWC/WOL TR 76-155 (SU313IAI) Hld3Q : <" ' cc ^ "J 52 h- U. LLI uj 2 N «- 55 » n t ili 5 UJ ^ o 2 in to o ii o 52 ^ -■■^ < cc z o O "- N E E £? UJ ^ Q u. O Z o o o LL 5^ fr CM < o CO CO _ < Ifl _° CO <~ UJ ~ E i _l K- — 0- co uj < Q CO _ O 5 cc en °- i- -i < d UJ * o 1 UJ < o H X s2 o ^ CJ o 5 S CO " UJ * CM O CC CM -— _ 0. CO < r~ CM * d u. " co I CO y- < C3 CO 2 Q UJ £ £ £ C l_ U. CO 58 NSWC/WOL TR 76-155 4.3 TOTAL FISH-KILL AND ITS SPATIAL DISTRIBUTION In this section we calculate the total fish-kill from an underwater explosion and its distribution as a function of horizontal range and depth, assuming a uniform spatial distribution of a single size class of one species of fish. Table 4.3.1 (top) lists the bladder oscillation parameter Z for 21.5 cm White Perch calculated over a cylindrical grid surround- ing a 32 kilogram charge fired at 9 meter depth. Table 4.3.1 (bottom) lists the corresponding kill probabilities from Equation 3.2.1. To calculate the fish-kill we must know which fish are where; and, in general, this is impossible. Nevertheless, to gain insight as to the potential of a given explosion geometry for killing fish it is useful to assume a fictitious fish density distribution. For this purpose we will assume a nominal uniform density distribution of 1 fish per thousand cubic meters of water. To calculate the fish-kill we must integrate the product, fish density x kill probability, over the region surrounding the explosion. Thus, for this example we compute the products of "fish present" and "kill probability" (Tables 4.3.2 and 4.3.1) to get the "fish killed" in each mesh volume, Table 4.3.2 (bottom) — each mesh consisting of a cylindrical annulus 10 0 feet thick and 5 feet in depth. Summing the distribution of "fish killed" shown at the bottom of Table 4.3.2 results in a total kill of 1245 fish out of 6228 fish present. Note that we have neglected 200 fish present in the 150-ft radius cylinder of water containing the charge as well as all fish present beyond a horizontal range of 850 feet. Nevertheless, we have described the most significant portion of the distribution of fish killed by this underwater explosion. It is apparent, for example that if fish were present only at depths greater than 70 or 80 feet relatively few fish would be killed. Likewise, if fish (of this particular size) were present only within some 10 feet of the surface the kill would be relatively 59 NSWC/WOL TR 76-155 TABLE 4.3.1 BLADDER OSCILLATION PARAMETER AND KILL PROBABILITY AS A FUNCTION OF FISHES' DEPTH AND HORIZONTAL RANGE Charge: 32 KG Pentolite at 9 M Depth Fish: White Perch, 21.5 cm Fork Length Fish Depth (feet) Horizontal Range (feet) 200 300 400 500 600 700 800 5 - 251 208 41 41 35 10 7 10 - 220 211 119 73 32 30 28 15 - 206 215 156 100 62 31 26 20 - 287 197 131 129 86 79 58 25 - 206 180 147 114 109 74 69 30 - 168 175 130 146 94 93 64 35 - 172 187 117 120 113 88 81 40 - 211 163 120 97 102 97 96 45 - 168 125 135 89 94 99 84 50 - 144 110 139 94 76 8? 87 55 - 133 111 121 99 70 77 73 60 - 177 133 91 104 76 62 68 65 - 139 141 83 108 72 58 55 70 - 132 110 81 94 86 63 51 75 - 128 98 79 70 91 60 49 »0 - 154 86 98 67 87 66 54 85 - 107 110 105 63 76 70 52 90 - 120 119 81 61 56 75 57 95 - 125 76 66 69 54 65 61 100 - 122 88 71 84 51 56 65 i BLADDER OSCILLATION PARAMETER 200 300 400 500 600 700 800 Fish Depth (feet) 5 _ 1.00 .99 .01 .01 .01 .00 .00 10 - .99 .99 .42 .05 .01 .01 .00 15 - .99 .99 .85 .20 .03 .01 .00 20 - 1.00 .98 .58 .55 .10 .07 .02 25 - .99 .95 .77 .35 .29 .06 .04 30 - .91 .94 .57 .76 .15 .15 .03 35 - .93 .97 .39 .43 .34 .12 .08 40 - .99 .89 .43 .18 .22 .18 .17 45 - .91 .50 .63 .12 .15 .19 .09 50 - .74 .30 .68 .15 .06 .09 .11 55 - .61 .32 .45 .19 .05 .07 .05 60 - .95 .61 .13 .24 .06 .03 .04 65 - .68 .71 .09 .28 .05 .02 .02 70 - .60 .30 .08 .15 .10 .03 .02 75 - .54 .18 .07 .05 .13 .03 .02 80 - .83 .10 .18 .04 .11 .04 .02 85 - .27 .30 .25 .03 .06 .05 .02 90 - .43 .42 .06 .03 .02 .06 .02 95 - .50 .06 .04 .04 .02 .04 .03 100 - .46 .12 .05 .09 .02 .02 .04 KILL PROBABILITY 60 NSWC/WOL TR 76-155 TABLE 4.3.2 FISH PRESENT AND NUMBER KILLED AS A FUNCTION OF WATER DEPTH AND HORIZONTAL RANGE Charge: 32 KG Pentolite at 9 M Depth Fish: White Perch, 21.5 cm Fork Length Fish Density Distribution: _o 3 Uniform Density = 1 x 10 Fish/Meter Fish Depth (feet) Horizontal Range (feet) 200 300 400 500 600 700 800 5 - 18 27 36 44 53 62 71 10 - 18 27 36 44 53 62 71 15 - 18 27 36 44 53 62 71 20 - 18 27 36 44 53 62 71 25 - 18 27 36 44 53 62 71 30 - 18 27 36 44 53 62 71 35 - 18 27 36 44 53 62 71 40 - 18 27 36 44 53 62 71 45 - 18 27 36 44 53 62 71 50 - 18 27 36 44 53 62 71 55 - 18 27 36 44 53 62 71 60 - 18 27 36 44 53 62 71 6S - 18 ?7 36 44 53 62 71 70 - 18 27 36 44 53 62 71 75 - 18 27 36 44 53 62 71 80 - 18 27 36 44 53 62 71 85 - 18 27 36 44 53 62 71 90 - 18 27 36 44 53 62 71 95 - 18 27 36 44 53 62 71 100 - 18 27 36 44 53 62 71 FISH PRESENT 200 300 400 500 600 700 800 Fish Depth (feet) 5 - 18 26 0 0 0 0 0 10 - 18 26 15 2 0 0 0 15 - 18 27 30 9 2 0 0 20 - 18 26 21 25 6 5 2 25 - 18 25 27 16 16 4 3 30 - 16 25 20 34 8 9 2 35 - 17 26 14 19 18 7 6 40 - 18 24 15 8 12 11 12 45 - 16 13 23 5 8 12 7 50 - 13 8 24 7 3 5 8 55 - 11 8 16 9 2 4 4 60 - 17 16 5 11 3 2 3 65 - 12 19 3 13 3 2 70 - 11 8 3 7 6 2 75 - 10 5 3 2 7 2 80 - 15 3 7 2 6 2 85 - 5 8 9 1 3 3 90 - 8 11 3 1 1 4 2 95 - 9 2 1 2 1 2 2 100 - 8 3 2 4 1 1 3 FISH KILLED 61 NSWC/WOL TR 76-155 light. However, for fish of this size between depths of 20 and 60 feet the kill will be extensive out to a range of about 800 feet; and if a large school several hundred feet in diameter with a density say, of one fish per cubic meter were within this region, a disastrous fish-kill would result. (Such^ an- occurrence is unlikely, however, as it is Navy policy to delay operations if a school of fish is observed in the vicinity of the test site.) 62 NSWC/WOL TR 7 6-155 REFERENCES 1. Gaspin, Joel B., 1975, "Experimental Investigations of the Effects of Underwater Explosions on Swimbladder Fish, I: 1973 Chesapeake Bay Tests," NSWC/WOL/TR 75-58. 2. Gaspin, J.B., M. L. Wiley, and G. B. Peters, 1976, "Experimental Investigation of the Effects of Underwater Explosions on Swimbladder Fish, II: 1975 Chesapeake Bay Tests," NSWC/WOL/TR 76-61. 3. Hubbs, C. L., E. P. Schultz, and R. Wisner, 1960, Unpublished preliminary report on investigation of effects on caged fishes from underwater Nitro-Carbo-Nitrate explosions, U. of Calif. Scripps Institute of Oceanography. 4. Yelverton, J. T., et al, 1975, "The Relationship between Fish Size and their Response to Underwater Blast", Lovelace Foundation, DNA Report 3677T. 5. Kennard, E. H., 1943, "Radial Motion of Water Surrounding a Sphere of Gas in Relation to Pressure Waves", published in Vol. II of "Underwater Explosion Research", Office of Naval Research, 1950. 6. Goertner, J. F., 1974, "Response of Air Bubbles to Underwater Explosion Pressures: Square Step Approximation with Application to Fish-bladder-cavity response", Unpublished internal technical note NOLTN 10205. 7. Cole, R. H., 1948, "Underwater Explosions", Princeton University Press. 63 NSWC/WOL TR 7 6-155 8. Snay, H. G. , and E. A. Christian, 1952, "Underwater Explosion Phenomena: The Parameters of a Non-Migrating Bubble Oscillating in an Incompressible Medium", NAVORD Report 2437 9. Weston, D. E. , 1966 "Sound Propagation in the Presence of Bladder Fish", published in Vol. II of "Underwater Acoustics", edited by V. M. Albers, 1967, Plenum Press 10. Lippson, A. J., 1973, "The Chesapeake Bay in Maryland— an Atlas of Natural Resources", John Hopkins University Press 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 12. Sternberg, H. M., and W. A. Walker, 1971, "Calculated Flow and Energy Distribution Following Underwater Detonation of a Pentolite Sphere", Physics of Fluids, September 1971 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 1974 64 NSWC/WOL TR 76-155 APPENDIX A RESPONSE OF GAS BLADDER TO UNDERWATER EXPLOSION PRESSURES: SQUARE STEP APPROXIMATION6 ABSTRACT This appendix presents the theory of the radial motion of a gas-filled spherical bubble responding to step changes in the water pressure. The theory is used to estimate the motion of a fish-bladder sized bubble subjected to the pressure signature from an underwater explosion. Some important qualitative results as well as some crude quantitative results are readily obtained. For example: (1) For a simple positive step which returns to ambient pressure, the maximum bladder extension depends on both the magnitude and duration of the pressure pulse. If cut-off occurs when the bladder (undamped oscillation) is at maximum size, no extension beyond its initial at-rest size occurs. If cut-off occurs at any other time, some over-extension of the bladder occurs. (2) A sudden decrease in the ambient pressure will always result in some over-extension of the bladder. If this neqative pressure (below ambient) follows a positive step with cut-off occurring at maximum size, the over-extension is due solely to the negative portion of the pressure signature; if not, the over-extension is due to both the positive step and the negative pressure following cut-off. The effects are additive in a non-linear manner described in this appendix. 6. Appendix A was formerly given internal distribution as NOLTN 10205 , Goertner , 1974, "Response of Air Bubbles to Underwater Explosion Pressures: Square Step Approximation with Application to Fish-bladder -cavity Response". A-l NSWC/WOL TR 76-155 I. ON THE MOTION OF AN AIR BUBBLE SUBJECTED TO A SERIES OF STEP CHANGES IN THE OUTSIDE WATER PRESSURE 1. Consider a spherical bubble at rest in water at the initial value p. of the ambient pressure. Let A± be its initial radius when at rest. Its internal air pressure is the initial ambient pressure p^ . At t = o, the ambient pressure jumps to a new value p ; and the bubble is then oscillating. The situation for the air pressure inside the bubble, trying to adjust to the new outside pressure, is sketched in Figure A-l. 2. In this Appendix we concern ourselves with the motion of a bubble subjected to a succession of jumps to new ambient pressures pn. At each ambient pressure the bubble motion is described by the following differential equation J | (^A3) A2 +^P0A3 + E(A) = Y (Al) Kinetic Energy Potential of Energy of Surrounding Water Pushed-back Water t Total Energy Internal Energy of Air Inside Bubble 7. Cole, R. H. , 19U8, "Underwater Explosions", Princeton University Press. A- 2 NSWC/WOL TR 76-155 m M Pi = Pl = PM = P = Initial outside water pressure New value of outside water pressure Bubble air pressure at maximum size Bubble air pressure at "Equilibrium" Pn P = Bubble air pressure at minimum size m FIG. A-1 BUBBLE AIR PRESSURE AND OUTSIDE WATER PRESSURE AS A FUNCTION OF TIME (SKETCH) A-3 NSWC/WOL TR 76-155 _,_. P'(A) "X V(A) ,,„> where E (A) =— —+ — 1 (A2) A = Bubble Radius dA A = -g^r , the radial velocity P (A) = Air Pressure Inside the Bubble V(A) = Bubble Volume = -j^ A Y = Exponent in Adiabatic P-V Relationship = 1.4 (for air) p = Water Density = constant P0 = Ambient Water Pressure = constant Y = Total Energy of Bubble Oscillation = constant 3. The oscillatory motion described by Equation Al has much in common with the oscillation of a simple mass-spring system — the difference is that for the bubble oscillation the "mass" changes with time and the "spring" is non-linear. The overall behavior of oscillating gas bubbles was worked out in considerable detail by Snay and Christian. They rewrote Equation Al in the non-dimensional form a3 a2 + a3 + k a"3^"1^! (A3) where a is the non-dimensional radius a= A/L and a is the derivative of "a" with respect to the non-dimensional time t1 = t/C . The parameters k and y characterize the bubble motion. "k" can be expressed by k = PMm Po(Y-D i + p^M y lm "I -i) J where P„ is the internal pressure at either extremum of the bubble Mm r oscillation — M refers to the maximum bubble volume (P = minimum pressure) , m refers to the minimum bubble volume (P„ = maximum c m pressure) — and P0 is the ambient hydrostatic pressure. 8 Snay, H. G. , and E. A. Christian, 1952, "Underwater Explosion Phenomena: The Parameters of a Non-Migrating Bubble Oscillating in an Incompressible Medium", NAVORD Report 21*37 A- 4 NSWC/WOL TR 76-155 The length scale factor L and the time scale factor C are defined by 1/2 (A5) (A6) where Y is the total energy (Equation Al) and p is the density of the water. 5. Snay and Christian in their report have determined the overall behavior of the oscillatory solutions to Equation A3 for y in the range, 1.0 < y <1.5. Table Al (below) list some of their results for Y = 1.4. The dimensionless quantities — a., a and T' ^ Mm — are the maximum radius, the minimum radius and the period of oscillation of the bubble, respectively. TABLE A-l Bubble Parameters for y = 1.4 k M a /a,, nr M T' T ' Calculated From Equation A32 0.0 1.000 0.0 1.492 1.476 0.05 0.982 0.085 1.505 1.496 0.10 0.963 0.152 1.522 1.516 0.15 0.942 0.220 1.538 1.536 0.20 0.920 0.288 1.557 1.556 0.25 0.893 0.364 1.577 1.576 0.30 0.863 0.447 1.596 1.596 0.35 0.823 0.548 1.616 1.616 0.40 0.768 0.699 1.636 1.636 0.432 0.659 1.000 1.650 1.649 A-5 NSWC/WOL TR 76-155 6. In what follows, we will use both Equations Al and A3. Transitions from one outside pressure level, p , to another, p ,., ^n ^n+1 are simply described using Equation Al. And, Snay and Christian's results, e.g., those listed in Table I, which were computed from Equation A3, are convenient for computing the bubble behavior within a given state. 7. Boundary Conditions at Pressure Jumps. We now consider a step change in outside pressure from p to p , . . Let V be the c 3 c ^n ^n+1 c n bubble volume at the instant of change, and y and y , . be the old ., n Jn+1 and new total energies. For the n state we rewrite Equation Al as /4tt p A3 \a2 + 4iTp A3 + Vs" ) ^n 3 / 4tt p A \a + 4iTp A + E(A) =Y (A7) 2 I ^J- — sr n n Now, since the oscillating system described by (A7) has finite mass, neither A nor A can change impulsively, i.e., AA = 0 (A8) AA = 0 (A9) at each pressure jump. Thus, the first and third terms of (A7) do not change at the jump, and the change in the total enerqy is given by Yn+1 = Yn + (Pn+l " Pn) Vc (A10) n where V is the bubble volume at the time of the jump, n 8. Equations (A7) , (A8), (A10) completely specify the motion in the n state given suitable initial conditions. In the present case the initial or zeroth state is specified by A = constant = A. (All) P(A.) = constant = p. (A12) l *i A- 6 NSWC/WOL TR 7 6-155 In particular, the total energy Y and the outside pressure p are sufficient to specify the amplitude of the oscillation. And, if the radius function A(t) is known, the phase will then be determined by the jump conditions, AA = 0 and AA = 0 . +■ v> 9. Some General Equations for the n State. We now list some further equations that can be used to calculate the parameters +* v» of the bubble oscillation in the n state. kn = 7T 7r (A13) — (pf-r) /3Y X1/3 Ln = (^wV) (A14) - I ' (A15) :n " Ln(%) (AMAXJ a (kn) x Ln (A16) AMIX AMAX = Tabulated Function (k ) (A17) n 'A- \ 3Y P(A) = p.lp- J (A18) ]/3Y (A19) T = t(k ) x C (A20) n n n A-7 NSWC/WOL TR 76-15 5 Equation A19 gives the equilibrium radius A (radius after the oscillation has damped out) for the bubble in the n state. A19 is derived from (A18) by setting P (A) equal to p n 10. Bubble Motion in State 1. Consider the step change in outside pressure from p, to p.. In accordance with the jump conditions (A8) and (A9) and the initial conditions (All) and (A12) we set A = 0 and A = A. in (A7) to obtain the total energy Yl = (Pl + Y=T> Vi (A21) where we have also used Equation A2 to evaluate the internal energy E(A.) 11. Since A = 0, the oscillation in state 1 starts at an extremum. Whether this extremum is a maximum volume V„ or minimum M V"m is determined by p being "greater than" or "less than" p.. If p, > p . , then AMX = Ai (A22) PMi = Pi (A23) IF p. < p. , then \ = Ai Pn - Pi (A25) A- 8 NSWC/WOL TR 76-155 12. Since the oscillation in state 1 starts at an extremum, the bubble parameter k can easily be computed from Equation A4 . From (A4) together with (A23) and A25 we get kl = xi(1+xi) Y (A26) where xi ■ Tr^lbr (A27) 13. Calculation of the Subsequent Extremum. The bubble radius at the next extremum (]/2 period later in time) is calculated from the initial value A = A. by either dividing or multiplying by the ratio ( — J obtained from Table I (by linear interpolation \am/l for the calculations done here) . The corresponding air pressure P inside the bubble is then calculated using Equation A18, i.e., (A28) 14. Calculation of the Bubble Period. The bubble period of oscillation T is the product of the dimensionless period, t = F(y,k) , given in Table I and the time scale factor C (Equations A15 and A14) Tx = T' x C (A29) Combining (A14, (A21) and (A27) , we write for the length scale factor Lx = Ai (1 + X1)]/3 (A30) A-9 NSWC/WOL TR 76-155 And, combining (A15) , (A27) and (A30) , we write the time scale factor as 1/2 Ci = (9^±JL ^ j (1 + Xi) A_ (A31) where p is the water density. 15. For our purposes the dimensionless period T1, is conveniently approximated by the linear function T ' - 1.476 + 0.4 k (A32> Values of T ' calculated by Equation A32 are listed in Table 1 alongside the tabulated function. The approximation, Equation A3 2, is good to better than 0.5% for values of k } 0.1. 16. Finally, combining (A26), (A27) , (A29), (A31) and (A32) we write for the period of oscillation * " (t *) 1/2 , /. (1 + X]_) ' (1.476 + 0.4kT) Ai (A33) The physical quantities in Equation A33 may be expressed in any consistent set of units. For English Engineering Units we have T, = Bubble Period (SECONDS) 3 p = Density of the Water (SLUGS/FT ) 2 Initial Value of Ambient Water Pressure (LBS/FT ) ^i ' [pressure in LBS/FT2 = (pressure in PSI) x 144] A. = Initial Radius of Bubble (FT) l A-10 NSWC/WOL TR 76-155 17. Simplifying Assumption. To proceed further with the general case we would now need the bubble radius as a function of time in order to apply the jump equations (A8) , (A9) and (A10) at the instant the outside pressure changes to its new value, p- • Although not particularly difficult, such computations are beyond the limited scope of this study. Consequently, at this point we introduce the simplifying assumption that all pressure changes occur at an instant when A = 0, i.e., either at an extremum or at equilibrium bubble radius after the oscillation has completely damped out. Pressure jumps, p to p , , which happen to occur at bubble extrema give the greatest and also the least amplitudes of ■f- V» oscillation in the n+1 state (V = V.. in Equation A10) . Thus, c Mm even when the pressure jumps occur at other times than the extrema, we can place exact upper and lower limits on the amplitude of oscillation in each state. 18. Bubble Motion in State 2. In accordance with our simplifying assumption we will assume the pressure jump, p, to p_ , occurs at a time t such that cl t = N X ^ T. (A34) C, 2 1 where N is any positive integer. Alternatively, t may be taken cl large enough that the bubble oscillation has damped out, i.e., — 1/3y A = A, = A. (p,/p.) ' ', the equilibrium radius. 19. Let V , A , P be the volume, radius and air Cl Cl °1 pressure, respectively, of the bubble at time, t . If the new out- Cl side pressure p„ is higher than P , the air pressure inside the l cl bubble, the new oscillation begins at maximum volume; and if p„ is lower than P , the oscillation begins at minimum volume. Or, c 1 restated we have A-ll where NSWC/WOL TR 76-155 If p > P , then A = A (A35) l C1 M2 C1 PM = P„ (A36) M2 C]_ If pn < P , then A = A (A37) 2 cl m2 °1 P = P (A38) m2 Cl 20. Next, for the bubble parameter k we have k2 = X2 (1 + X2) Y (A39) P X. = -, 4 (A40) L2 (Y-D P2 With this value for k_ the bubble radius at the subsequent extremum can now be calculated by either dividing or multiplying the starting value A by the ratio (a AO » obtained from Table I. The corre- c, m M z sponding air pressure P inside the bubble can then be calculated by Equation A18. And finally the period of oscillation can be calculated from T„ = (§f*2) V2 (1 +X0)]/3 (1.476 + 0.4 k,) A^ (A41) 2 ^~ ' 2 | vx "2' li,"u ' 2' c1 A-12 NSWC/WOL TR 76-155 21. Bubble Motion in State n. The corresponding equations for the n state can easily be obtained from those for state 2 by substituting "n's" for '^'s" and "n-l's" for "l's". The only apparent exception is that the equivalent equation for (A34) should read T = T +N XtT (A42) c c . 2 n n n-1 A-13 NSWC/WOL TR 76-15 5 II. ON THE MOTION OF A SWIM-BLADDER-SIZE AIR BUBBLE SUBJECTED TO AN EXPLOSION GENERATED PRESSURE WAVE 22. At the present time we ask such questions as: "Can a nearby explosion kill or seriously damage fish by extending their swim bladders?" Prodded by this, let us calculate the behavior of a bladder-sized air bubble subjected to an explosion pressure signature — one which kills many, but not all, of the fish present. The pressure signature shown in Figure A-2 is derived from a experi- mental test condition (Shot 525, Chesapeake Bay Tests, July-Aug 73) and appears to meet this criterion. It corresponds to a fish cage location where, upon subsequent dissection, all ten of ten 5.4" long Spot and six of ten 7.2" long White Perch were judged to have received lethal damage. For this calculation we will further approximate the outside pressure signature with the square-stepped one which is also shown in Figure A-2. 23. To get a better feel for physical phenomena, we will do the calculation in three stages. First, we will calculate the response to the positive portion, a square-step which returns to the initial ambient pressure level; then, the response to a simple step decrease in outside pressure to the level of the explosion induced underpressure; and finally, the combined response to the square- stepped signature sketched in Figure A-2. 24. We will take our bladder-sized air bubble from a 5.4" long Spot, and start the calculation with an initial (at rest) bubble radius given by* Aj_ = 0.0395 L (A43) it Footnote on page A-16 A-14 NSWC/WOL TR 76-155 -|K in C o o [x, 0) 6 •H EH ISd UT 3«mssaad: SQ-niosqv c 0> -p c (]) -p is H CJ H *H oi a; Uh 0) P •p o •H CD ^ - - J- CM • * IA t— -p -p 0) OJ 0> 01 Hh bfl a al K .C • -P fc Ph (1 01 w P cc D < Z o io UI 2 UJ C£ D < S ui cc < o o H Z UI Z o a. X UI CM < O) C3 -P •P •H 0) u. rH O) o «M a; -p M c o h 0) t- cri Ph £ II I > to fi A H •P ft CO 01 VD o A-15 NSWC/WOL TR 76-155 where L is the fork length of the fish. For our 5.4" Spot this gives an initial bubble radius A. = 0.0178 ft (A44) The initial ambient pressure p^^ = 32 psi, which corresponds to a depth of 40 feet in fresh water. The magnitude of the pressure step, Pl " Pi' is 50 Psi; and its time duration TPOS = 2.3 milliseconds. The period ^ at p = 82 psi turns out to be 0.569 milliseconds, so that the oscillation in State 1, which starts at maximum bubble size A the time cut off occurs M = Ai, goes through 2.3/0.569 =4.04 periods of oscillation by (Footnote from page A-14) *This gives a rough approximation to the bladder volume of a 5.4" lone fish at 40ft-depth and 500 feet distant from a 68-lb pentolite charge (Shot 525) . Equation A43 was conjured up by the author for a "nominal fish". It represents the radius of a sphere of 1/20 of g the estimated volume of the fish (after Weston) . The volume of the fish is taken as an ellipsoid whose semi-major axes (A,B,C) bear the relation, A = 0.38 L, B = 0.30 A, C = 0.25 B, where L is the overall length of the fish. The above coefficients are average values taken from crude measurements of sketches of fish shown by Lippson. 9. Weston, D. E. , 1966, "Sound Propagation in the Presence of Bladder Fish", published in Vol. II of "Underwater Acoustics", edited by V. M. Alters, 1967, Plenum Press 10. Lippson, A. J., 1973, "The Chesapeake Bay in Maryland — an Atlas of Natural Resources", John Hopkins University Press A-l( NSWC/WOL TR 76-15 5 25. At cut-off time, TPOS, the measured outside water pressure drops to about 13 psi (Figure A2). Table A2 lists limiting case results for the final maximum radius (in State 2) which were calculated from the above parameter values by assuming cut-off times TPOS occurina at A.,, A , and also sufficiently late that the Mm ■* _ oscillation has damped-out (so that A = constant = A) . 26. Two sets of values for A /A. are given in Table A2 , M2 1 one for a final outside pressure p_ = p. =32 psi, the other for the measured value of p„ = 13 psi. The results listed in the top row of Table A2 (cut-off at bubble maximum) are the same as if the positive outside overpressure, p. - p., had never occurred. In other words, the upper right hand value of A /A. also applies to a simple step decrease in the ambient pressure p. to a new value, p_ = 13 psi. 27. It is apparent from these crude results that both positive and negative excursions of the outside pressure significantly influence the final overshoot; and that time-of-occurrence of cut-off relative to the phase of the bubble oscillation cycle is of critical importance for positive excursions. It also looks like a good bet that underwater explosions do kill or cause serious damage to nearby fish by extending their swim bladders. 28. Figures A3 and A4 sketch the qualitative behavior of the inside air pressure and the bubble radius as functions of time for the six cases listed in Table A2 . A-17 NSWC/WOL TR 76-155 u. LL O h- D O z o <" s < 0) $ to to £> ft U O o1 o W ft 1) > •H P 0) bo t\J «* OO -3- o OJ Lf\ o O CO EC LU > o CO 5 < cc u. O LU u z LU a z LU a. LU a I 3 CO CO ^ o o H CM CM CO to 0) ft p a3 to Ch O 1 -H P c 2 -H o S ft i o I p P 3 o I 0) to £h ft O a < s 111 cc < o < o LU CO Z o Q. co HI cc 00 CQ D 03 A-19 NSWC/WOL TR 76-155 LU cc D co CO LU CC a. CC Z < 03 Q LU I > < QC < a CO < O I- LU CO z O a. CO CD CO D CO < (3 A-20 NSWC/WOL TR 76-155 III. DISCUSSION 29. After the above analysis was completed, George Young brought to my attention a similar analysis done in 1943 by E. H. Kennard (in connection with the proposed use of screens of bubbles as a protective device against explosion shock waves) . His development and presentation of the incompressible bubble theory (pp. 190-191, Ref. 5) is verv convenient for calculating bubble motions such as the example used in this note, i.e., response to jumps in constant outside pressure states restricted to those instants when the radial velocity, A = 0. I redid the calculations summarized in Table A2 using Kennard1 s "bubble theory" and the bubble radii and periods of oscillation were in all cases within 1% of my previous values calculated using the equations presented in this Appendix. A-21 NSWC/WOL TR 76-155 IV. CONCLUSIONS 30. I hope that the analysis presented here (or some further development of it) will prove useful in correlating observed fish injury and kill with incident explosion pressure signatures. The present analysis is but a crude first cut, however; and if this approach to understanding fish damage should appear fruitful, considerable further development will probably be desirable and perhaps essential to achieving a useful correlation. Nevertheless, some things are already clear. For example: (1) By itself, a step increase in the ambient pressure cannot extend the bubble/bladder beyond its original size, since the bubble oscillates between its original volume and some minimum volume which depends on the magnitude of the incident shock pressure. Extensions beyond the initial at-rest volume can only occur after return to ambient pressure or below. (2) For a simple positive step pressure which returns to the ambient level, the maximum bubble/bladder extension depends on both the magnitude and duration of the pressure pulse. If cut-off occurs at the instant of maximum bubble volume, the bubble is returned to its initial at-rest state, having undergone no extension beyond this initial at-rest state. If cut-off occurs at any other time, some extension beyond the initial at-rest volume occurs. For a given incident pressure level, the greatest bubble/bladder extensions occur when cut-off is at the instant of minimum bubble volume. * * Footnote next page A-22 NSWC/WOL TR 76-155 (3) A step decrease in the ambient pressure always results in an extension of the bubble/bladder. If such a drop follows a positive step where cut-off occurs at maximum bubble volume, the extension beyond initial at-rest volume is due solely to the negative portion of the pressure signature; if not, the over-extension is due to both the positive step and the underpressure following cut-off. The effects are additive in the non-linear manner described in this appendix. (Footnote from preceding page) *For a simple step pressure pulse of level p , the energy of the residual bubble oscillation is given by Y'2 = X2-Y. = (Pl - p.) x (V. - 7Ci) where V is the bubble volume at the instant of cut-off. Thus, the energy of the Cl residual oscillation and, consequently, extension of the bubble/bladder beyond initial at-rest volume take on greatest values for V = V and tend to zero as c m V approaches V . c rr M A-23/24 NSWC/WOL TR 76-155 APPENDIX B METHOD FOR CALCULATING GAS BLADDER RESPONSE TO EXPLOSION PRESSURE WAVE Figure 2.3.2 sketched the way we approximated the explosion pressure signature by a sequence of pressure steps in order to calculate the bladder response by means of the equations developed in Appendix A. Appendix B gives the details of the procedure. Boundary Condition at Pressure Jumps. Step changes in the outside water pressure from p to p , , occurring at half-period c ^n ^n+1 ^ c intervals change the equilibrium pressure P0 of the oscillating bubble flow (equal to the outside pressure p ) . Since the oscillatory system described by Equation Al has finite mass, neither A nor A can change impulsively, i.e., A A = 0 (Bl) and A A = 0 (B2) for all pressure jumps. And, thus for pressure jumps occurring at extrema where A=0 , only the equilibrium pressure P„ can change. Let A be the maximum or minimum bubble radius at the c n time of the pressure jump p to p , , . If A is greater than the t- j f t-n ^n+1 c 3 n new equilibrium radius* A , , , the new oscillation begins at maximum n+1 * _ The equilibrium radius A is the at-rest radius which corresponds to the equilibrium pressure E, (= p , the outside pressure). A is calculated ^ n n from p using Equation B6, below. B-l NSWC/WOL TR 76-155 size; and if A is smaller than A ,. the new oscillation begins at c n+1 n minimum size. Or, restated we have If A > A .. , then AMAX .- = A (B3) c n+1 » n+1 c n n If A < A .. . then AMIN ,. . (B4) c n+1 > n+1 = A n c n Equilibrium Bubble Radius. At any time during the motion the internal gas pressure p is related to the bubble radius by P(A) = pi^l) (B5) Setting P(A) equal to p in (B5) yields the equilibrium bubble radius , -/3Y /Pi\ X A = A. I — (B6) where y is the adiabatic exponent for air (= 1.40) and the subscript "i" refers to the initial ambient "at rest" state. Equilibrium Bubble Period. The equilibrium bubble period T (for vanishingly small oscillations about the equilibrium radius) n . 5 was given by Kennard. T = 2ttA /p/3Vp (B7) n n ' rn 3 where p is the water density = 1.940 slugs/ft . B-2 NSWC/WOL TR 76-155 Inserting the values for the water density and adiabatic exponent, equation B7 becomes _ A T = 29.7— =S— milliseconds (B7a) n /^ where A is in inches and p is pounds per square inch. Maximum and Minimum Radius, and Period of Oscillation. With increasing amplitude the period increases; the ratio of the periods, T/T, is plotted as a function of the maximum radius AMAX in Figure Bl. The same figure also shows the minimum radius AMIN plotted as a function AMAX. Both curves were calculated by the method given in Appendix A. Some Details of the Computation. Consider the computation shown in Figure 2.3.2. We will assume that the pressure signature begins with a shock front followed by an approximately exponential decay. To get the average outside pressure for the first half-period of the motion we estimate the period of oscillation by T =cxx T* (B8) where T* is the equilibrium period calculated using the pressure value at the start of the motion (i.e., the Shockwave peak pressure + initial ambient) and oc is an arbitrary constant. (For the present computations an ©(-value of 1.25 was used for the first half-cycle of oscillation.) The parameter T* is calculated from Equation B7 using a corresponding A* calculated from Equation B6 . The starting point is the initial bubble or bladder radius A. which was estimated from experimentally measured values. For the present calculations the ratio (A. ) 0/L B-3 NSWC/WOL TR 76-155 o to , 1 i ■■ \ h 2 i < w V \ \ CO c\i to csi C\i CM Csi o c\i l< >< < CO cc D CO 5 CO X UJ cc n < 5 O < 1- < u. o H UJ co D O -J cc < Q > > CO z ill CO z O > < 1- (J D < a O _i ?■ UJ _i -> HI U CO < X D O to z GO UJ _i < o cc 1- 0. k < rr CO CO CO _l => 3 •>- -1 < n n cc o z UJ < rr < cc UJ > CO O X u. LL S ? O O CO D n n D 2 o o Q < Z cc rr < UJ UJ CC k ^> Q. 0. II II II II II l< X Z 0 1- < «; 1- 00 6 CO © © CM o" < z UJ _l CO 03 m cc O CO z o o CO o o. < Q Z 3 O U z E cc UJ cc CO UJ > cc => o 03 d z; s'< 0.90, the maximum bubble size is taken equal to AMAX. In any event, if (At/T) < 0.90, we also calculate the final oscillation that would occur if surface cut-off had returned the outside pressure directly to ambient. If this results in a greater maximum expansion, we take this value as the maximum size achieved during final expansion. Damping. Equation Al describes undamped radial pulsation of an ideal frictionless fluid. While it seems unnecessary to make a detailed study of energy dissipation in the fishes' oscillating swim bladder, it does seem prudent to at least approximately account B-8 NSWC/WOL TR 76-155 for the fact that such dissipation must occur. In this study we did so by withdrawing a fraction 3 of the energy of the oscillatory motion at each extremum. The total energy at an extremum can be calculated from Equation Al by dropping the first term and substituting from (A2) and (B5) to get n Hn y-1 \ V. -Y *VMm*n (B15) 4 3 where (VM ) is the bubble volume, *n (A.. ) Rewriting (B5) as p(V) = pi (V/V±) -Y (B16) and noting that p = p(v )= P- (V„/V. ) ' and substituting n n ci n' i into (B15) we get Y = -JL- Pn V n y-1 n n (B17) for the energy of the non-oscillating equilibrium bubble. Subtracting y from y we get the bubble energy of oscillation , Yn Yn Yn (B18) B-9 NSWC/WOL TR 76-155 Finally combining (B15) , (B17) and (B18) and again noting that p = p. (V/V.) ^ we get the dimensionless equation, Y Y-l , 1 Y Y V, Mm V -Y V, Mm V -1 (B19) for the bubble energy of oscillation. At each extremum the bubble volume (or radius) was changed to yield a new energy of oscillation, Y" = (1 -3) Y1 (B20) For this study we took 3 = 0.30 (B21) Considering the precision of our present experimental data, the precise value chosen for 6 does not appear to be critical. B-10 NSWC/WOL TR 76-155 APPENDIX C APPROXIMATE METHOD FOR CALCULATING THE PRESSURE-TIME SIGNATURE Figure 3.1.1 shows the idealized form of pressure-time signature used for the bladder response computations of this report. For planning the 1975 series of explosion tests and for the examples presented in Section 4 of this report we needed to predict for arbitrary explosion geometries the variables, PMAX, 9, TPOS , PNEG, DTNEG, shown in Figure 3.1.1. This Appendix tells how this was done. PRESSURE SIGNATURE BEFORE SURFACE CUT-OFF. The initial positive portion of the signature is the direct wave from the under- water explosion. The sudden negative excursion is caused by the arrival of the reflected rarefaction wave from the water surface. This phenomenon is known as "surface cut-off". We calculate the time, TPOS, of this arrival relative to the direct arrival by R..-R TPOS = — (CI) where R is the slant range from the charge, R, is the slant range from the image of the charge mirrored in the water surface, and c0 is the sound speed in the water. See Figure CI. We calculate the free-field portion of the signature using a modification of the empirical Shockwave Similitude Equations. The peak pressure PMAX and the decay constant 8 are calculated by the usual similitude relations C-l NSWC/WOL TR 76-155 V) D O LU o < LL. oc GO LL o > 5 o LU o z S o X V) I o t- LU V) O LL C-2 NSWC/WOL TR 76-155 l/3\a PMAX = k (L- (C2) (^7 a. w V3 /_R \P (C3) O3) where W is the explosive weight of the charge, R is the slant range from the charge, and k, a , £, and 8 are empirical constants (see, e.g., Reference 7). Values for the constants, k, and I and $ used for the calculations of this report can be obtained from Equations 3.1.1 and 3.1.3. The instantaneous free-field (or direct arrival) pressure, p_, was calculated using two separate exponential segments joined at t = 1.8 0 PMAX e"t/G (t < 1.8 0) (C4a) PD(t)=j 0.25 PMAX e"t/4'3 6 (t > 1.8 0) (C4b) which were fitted to the pressure signatures recorded on the 1973 explosion test series. CALCULATION OF PNEG, NEGATIVE PRESSURE FOLLOWING SURFACE CUT-OFF. PNEG was determined by a calculation along the surface reflected ray from the charge to the fish. If the surface reflected ray went thru the region of bulk cavitation, PNEG was computed from the depths at which the ray intersected the top and bottom of the cavitation. Otherwise, PNEG was computed from the linear super- position of the direct and surface-reflected pressure waves. C-3 NSWC/WOL TR 76-15 5 Calculation of PNEG Above/Inside/Under Region of Cavitation Let the depths, y and y , locate the top and bottom of the region of cavitation. Let p =p.+PNEG be the absolute pressure under the Ado 1 influence of cavitation, i.e., following arrival of the surface reflected wave. For fish located above/inside/under the region of cavitation, p, DC. is determined as follows: Ado Above: pAT3C, changes linearly with depth from PATM at Add the surface to PVAP at the top of the cavitation. Inside: p,DC. = PVAP Ado Under: pABg = PVAP + pg(y-yc) where PVAP and p are the vapor pressure and density of water, and g is the acceleration of gravity. Since PNEG = Pabs - Pi y (C6c) C-4 NSWC/WOL TR 76-155 FIG. C-2 VARIATION OF PNEG ABOVE/INSIDE/UNDER REGION OF BULK CAVITATION C-5 NSWC/WOL ¥R 76-155 Calculation of Depth, y , of Bottom of Cavitation. Given Equations C6a, b, c the problem of determining PNEG reduces to determination of the depths y and y of the top and bottom of the cavitation. To determine y we plotted, as a function of the charge weight W, values of y calculated from PNEG-values measured on the c 1 1973 Chesapeake Bay Test Program using Equation C6c. The equation.* y = 4.4 W0,3 (C7) c where W is the explosive weight in pounds pentolite and y is in feet was used to approximate these measurements. Calculation of Depth, y , of Top of Cavitation. The top (beginning) of the cavitation region was taken as the point on the reflected ray where the reflected shock first lowered the absolute pressure to the vapor pressure of the water. To calculate y we use the linear superposition of the direct and surface-reflected pressure waves , PSUM(t) = PD(t) + PR(t) (C8) The direct wave, p (t) , is given by equations C2 , 3, 4. The reflected wave, p (t) , can also be calcuated using Equations C2, 3, 4 provided one makes the substitutions "-k" for "k" and "R, " (slant range from image) for "R". To determine y we then solve for the point on the reflected ray path where *Equation CT gives a crude empirical fit to the PNEG-values measured on the 1973 test program. It was used out of necessity to make kill probability calculations used to design the 1975 test program hut has not been re-evauluated using those and other available PNEG-measurements. C-6 NSWC/WOL TR 76-155 p. + pn(TPOS) + p_(TPOS) = PVAP (C9) 1 D i\ Calculation of PNEG when Reflected Ray is Beyond Region of Cavitation. If the total pressure, p. + p (TPOS) + p (TPOS) , ID R 0 3 upon arrival of the surface refection at depth, y = 4.4 W (Equation C7) , was greater than or equal to PVAP, the reflected ray was considered to lie beyond the region of cavitation. When this happened PNEG was approximated by PNEG = |[pD(TPOS) + pR(TPOS)] (CIO) calculated at the location of the fish. CALCULATION OF DTNEG, DURATION OF NEGATIVE PRESSURE, PNEG. DTNEG was also determined by a calculation along the surface" reflected ray from the charge to the fish. If the surface-reflected ray went thru the region of cavitation and the condition, R/W1/3 < 80 (Cll) where R = slant range from charge to fish in feet W = explosive weight (pentolite) in pounds was true, then DTNEG was calculated from the time-of-f light of the water layer on top of the cavitated region. Otherwise, DTNEG was computed from the linear superposition of the direct and surface- reflected pressure waves. C-7 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. _LCnAmM (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 c0 = 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 NSWC/WOL TR 76-155 CO Z o D O -I < u z o > < u LL o > ce o 111 o C3 z g o I (A z o CO 6 d LU U CC < x u C-9 NSWC/WOL TR 76-155 To determine DTNEG, we plotted the ratio of TFLIGHT (calculated by C12) to DTNEG-values measured on the 1973 Chesapeake Bay Program , as a function of R /AMAX, where R is the slant range from charae to c c cavitation closure point and AMAX is the maximum radius of the explosion bubble. This plot is represented by the empirical equation* TFLIGHT DTNEG = 4.04 - 1.13 ln(R /AMAX) (C13) where AMAX = 12 .7 W DOB + (33.9/14.7) -PATM. V3 (C14) and, AMAX and DOB are in feet, PATM is in pounds per square inch, and W is the explosive weight in pounds pentolite. Thus, in summary, when the reflected ray intersected the region of cavitation and Equation Cll was true, Equations C12, 13, 14 were used to calculate DTNEG. Calculation of DTNEG from Superposition of Direct and Surface-Refelcted Waves. If the reflected ray did not intersect the region of cavitation or Equation Cll was false, DTNEG was calculated from the linear superposition of the direct and reflected pressure waves by means of an empirical equation adjusted to the 1973 Chesapeake Bay Test data. This empirical equation was *This empirical fit was used to make the kill probability calculations for design- ing the 1975 test program. It has not been re-evaluated using the 1975 test program and other available DTNEG-measurements . C-10 NSWC/WOL TR 76-155 DTNEG = p~yM(PNEG/10) - TPOS (C15) where PqnM is the inverse of Equation C8, TPOS is the positive duration, and PNEG is calculated by the appropriate equation, C6 or CIO. Thus, the end of the negative phase was taken as the point where the negative pressure calculated by Equation C8 returned to 10% of the value, PNEG. C-ll/12 NSWC/WOL TR 76-155 APPENDIX D LOCATION OF FISH CAGES BY SOUND RANGING On four of the six shots of the 1975 tests, water currents caused significant deviation of the charge and the fish cages from their intended positions. The charge was suspended on one line and the cages — with a pressure gage attached to each — where suspended on another. In this appendix, we consider the problem of determining the deviations of the charge and the string of fish cages from their intended locations. The separation, x0 , of the two lines at the surface was assumed known. Figure Dl shows the geometry of the problem. The length of the charge support line and the lengths of line between gages were also assumed known. We further assumed that the charge and gages lie in the the same vertical plane. We solved this problem using the measured arrival times of the direct Shockwave and its reflected tension wave from the water surface at the respective gage locations. Step 1 was to use the relative arrivals of the direct shock to determine an orientation for the gage line giving a set of constant differences between the calculated arrivals and the measured ones. Step 2 was to use these gage positions to calculate the surface cut-off time — the time interval between arrival of the direct shock and its reflection-- and to compare these values with the corresponding measured values. If there existed a systematic discrepancy in surface cut-off times not accountable to variations in the sound speed over the two ray paths, we then adjusted the angle, 8 , of the charge support line and redid steps 1 and 2. The calculations were redone until there D-l NSWC/WOL TR 76-155 ^x X<^£1 J ' CO < -I U _l < o CD z < cc a z D O CO CC o > CC I- 2 o C3 D-2 NSWC/WOL TR 76-155 was no systematic discrepancy in surface sut-off time not accountable to variation in sound speed over the two ray paths. The computations of steps 1 and 2 assumed that the sound speed did not vary with depth. R. S. Price of this center has developed a high-speed computer program which takes into account the sound speed variation with depth--but assumes that the gages are in a straight line. For the computations done here, these two effects-- curvature of the gage line and sound speed variation--are the same order of magnitude. In these computations, errors of about 0.4 milliseconds are caused by variations in sound speed. These correspond to gage position errors of about 2 feet. For our purposes errors of this magnitude were acceptable, however, significantly improved precision could be obtained by accounting for both gage line curvature and sound speed variation in the calculations . As a final check on the computations we compared the absolute time of arrival of the direct Shockwave measured on the pressure gage records to that calculated for the Shockwave travelling between our computed charge and gage locations. To do this we calculated the time, At , between the electrical firing pulse meas ^ ^ and direct Shockwave arrival as follows At = At , + VEL. CORR. + FIRING DELAY (Dl) meas sound where At , = transit time for a sound wave sound VEL. CORR. = correction to At , to account for detonation sound wave velocity inside the charge and Shockwave velocity in the water FIRING DELAY = dwell time between firing pulse and initiation of charge D-3 NSWC/WOL TR 76-155 The firing delay depends on the firing circuit, length and type of firing line, and the detonator. For the 1975 tests we estimated from a comparable test setup that FIRING DELAY = +0.31 + 0.05 milliseconds (D2) The correction, VEL. CORR. , to At , must be calculated. sound It is given by the following equation VEL. CORR. = - --2- c0 r R/Ro u L l ,R Co / K, _ c°\ (D3) where R0 = radius of the charge c0 = sound velocity in the water U = shock velocity in the water R = radial distance to gage D = detonation velocity in the charge The first term inside the brackets represents the contribution due to the water shock while the second, that due to the detonation wave Equation D3 was derived from the sketch shown in Figure D-2 . The integrand in Equation D3 was obtained by fitting results from a hydrodynamic code calculation for pentolite by 12 Sternberg and Walker with the following equations 12/ Sternberg, H. M. , and W. A. Walker, 1971, "Calculated Flow and Energy Distribution Following Underwater Detonation of a Pentolite Sphere", Physics of Fluids, September 1971 D-4 NSWC/WOL TR 76-155 < > E cc < O (- CO z O cc cc o o > o o > HI > < o o I CO Q Z < z o t- < z o CM Q d D-5 NSWC/WOL TR 76-155 ^- -1 = EXP | 8.84-160.9 + ^ 0%^° > for R/R0 < 25 (D4a) — -1 = EXP < -3.264 - 1.098 In 5Z|a. \ for 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/R0 = 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 NSWC/WOL TR 76-155 i Q W ft ft < Eh CD z o H Eh < Eh P ft s o u >H U ■tc < CD 2 ,»-» * ft in 00 w ft o w 1 cr> \D CM ro in Q S CD -P -U CD g 1 1 I 1 1 I I O < < " — 1 ft ft u M CD < w ^r o ■^ CO CO ** ft IS Eh CD >£> >£> o o 1X1 o O g c3 H Eh * — I 1 1 I Eh >h U Eh W U ^-* H ft S >H u cj ft H < w ■H H iH H ■H iH c o ft J CD m m CO ro ro ro ft u H W g w ft Q — > ft >H u Eh ^~. o H • u in rH IT) ro ro in ft U ft ft in * — » • • ft Eh o O o 0~i a> o o ft CO 00 00 CN CN H Q in < ft * -x * D-7 NSV7C/T-70L TR 76-155 TABLE D-2 CORRECTED CAGE AND GAGE LOCATIONS SHOT 782 Charge: 70.4 lbs pentolite Charge wire length: 30 feet Charge wire angle: 0 degrees Charge depth: 30 feet Charge-to-gage line distance: 300 feet Sound speed: 48 50 ft/sec Water depth*: 156 feet WIRE DISTANCE WIRE ANGLE CAGE AND GAGE COORDINATE S HOR. RANGE DEPTH HOR. RANGE DEPTH (FEET) (DEG.) (FEET) (FEET) (METERS) (METERS) 0 300 0.0 91.4 0.0 5 0 300 5.0 91.4 1.5 10 0 300 10.0 91.4 3.0 15 0 300 15.0 91.4 4.6 40 0 300 40.0 91.4 12.2 45 0 300 45.0 91.4 13.7 50 0 300 50.0 91.4 15.2 55 0 300 55.0 91.4 16.8 57.5 0 300 57.5 91.4 17.5 77.5 87.5 0 0 300 300 77.5 87.5 91.4 91.4 23.6 26.7 97.5 0 300 97.5 91.4 29.7 ♦Calculated from times of arrival of bottom reflection D-8 NSWCAfOL TR 76-155 TABLE D -3 CORRECTED CAGE AND GAGE LOCATIONS SHOT 783 Charge: 70.2 lbs pentolite Charge wire length: 30 feet Charge wire angle: 0 degrees Charge depth: 30 feet Charge-to-gage line distance: 200 feet Sound speed: 4857 ft/sec Water depth*: 152 feet WIRE DISTANCE WIRE ANGLE CAGE ANE ) GAGE COORDINATES HOR. HOR. RANGE DEPTH RANGE DEPTH (FEET) (DEG.) (FEET) (FEET) (METERS) (METERS) 0 200.0 0.0 61.0 0.0 5 -10.5 199.1 4.9 60.7 1.5 10 -10.5 198.2 9.8 60.4 3.0 15 -10.5 197.3 14.7 60.1 4.5 40 -10.5 192.7 39.3 58.7 12.0 45 -10.5 191.8 44.2 58.5 13.5 50 -10.5 190.9 49.2 58.2 15.0 55 -10.5 190.0 54.1 57.9 16.5 60 -10.5 189.1 59.0 57.6 18.0 80 -10.5 185.4 78.7 56.5 24.0 90 - 8 184.0 88.6 56.1 27.0 100 - 5 183.2 98.5 55.8 30.0 *Calculated from times of arrival of bottom reflection. D-9 NSVTC/WOL TR 76-155 TABLE D-4 CORRECTED CAGE AND GAGE LOCATIONS SHOT 78 4 Charge: 71.6 lbs pentolite Charge wire length: 30 feet Charge wire angle: 0 degrees Charge depth: 30 feet Charge-to-gage line distance: 300 feet Sound speed: 4866 ft/sec Water depth*: 135 feet WIRE DISTANCE WIRE ANGLE CAGE ANC GAGE COORDINATES HOR. HOR. RANGE DEPTH RANGE DEPTH (FEET) 0 (DEG.) (FEET) 300.0 (FEET) 0.0 (METERS) 91.4 (METERS) 0.0 5 11 301.0 4.9 91.7 1.5 10 11 301.9 9.8 92.0 3.0 20 10 303.6 19.7 92.5 6.0 30 10 305.4 29.5 93.1 9.0 40 9 306.9 39.4 93.5 12.0 45 8 307.6 44.3 93.8 13.5 50 6 308.2 49.3 93.9 15.0 55 4 308.5 54.3 94.0 16.6 60 3 308.8 59.3 94.1 18.1 80 90 2 1 309.5 309.6 79.3 89.3 94.3 94.4 24.2 27.2 100 1 309.8 99.3 94.4 30.3 ♦Calculated from times of arrival of bottom reflection. D-10 NSVTC/T-70L TR 76-155 TABLE D-5 CORRECTED CAGE AND GAGE LOCATIONS SHOT 785 Charge: 1.25 lbs pentolite Charge wire length: 30 feet Charge wire angle: -5 degrees Charge depth: 29.9 feet Charge-to-gage line distance: 40 feet Sound speed: 4864 ft/sec Water depth*: 160 feet WIRE DISTANCE WIRE ANGLE CAGE ANE ) GAGE COORDINATES HOR. HOR. RANGE DEPTH RANGE DEPTH (FEET) (DEG.) (FEET) (FEET) (METERS) (METERS) 0 42.6 0.0 13.0 0.0 5 -11 41.7 4.9 12.7 1.5 10 -11 40.7 9.8 12.4 3.0 20 -11 39.3 19.7 12.0 6.0 30 - 7 38.1 29.6 11.6 9.0 40 - 7 37.1 39.6 11.3 12.1 50 - 5 36.0 49.5 11.0 15.1 60 - 4 35.0 59.5 10.7 18.1 70 - 2 33.9 69.4 10.3 21.2 80 + 2 34.1 79.4 10.4 24.2 90 + 5 34.4 89.4 10.5 27.2 100 + 5 35.1 99.4 10.7 30.3 *Calculated from times of arrival of bottom reflection, D-ll NSVC/5TOL TR 76-155 TABLE D-6 CORRECTED CAGE AND GAGE LOCATIONS SHOT 786 Charge: 1.26 lbs pentolite Charge wire length: 30 feet Charge wire angle: -10 degrees Charge depth: 29. 5 feet Charge-to-gage line distance: 40 feet Sound speed: 4886 ft/sec Water depth*: 115 feet WIRE DISTANCE WIRE ANGLE CAGE ANC GAGE COORDINATES HOR. HOR. RANGE DEPTH RANGE DEPTH (FEET) 0 (DEG.) (FEET) 45.2 (FEET) 0.0 (METERS) 13.8 (METERS) 0.0 5 -30 42.7 4.3 13.0 1.3 10 -30 40.2 8.7 12.3 2.7 20 -24 36.1 17.8 11.0 5.4 30 -19 32.9 27.3 10.0 8.3 40 -15 30.3 36.9 9.2 11.2 50 -12 28.2 46.7 8.6 14.2 55 -10 27.4 51.6 8.4 15.7 60 -10 26.5 56.5 8.1 17.2 65 - 8 25.8 61.5 7.9 18.7 70 - 6 25.3 66.5 7.7 20.3 75 - 4 24.9 71.5 7.6 21.8 80 - 2 24.7 76.4 7.5 23.3 ♦Calculated from times of arrival of bottom reflection. D-12 NSTC/tyOL TR 76-155 TABLE D -7 CORRECTED CAGE AND GAGE LOCATIONS SHOT 787 Charge: 72.2 lbs pentolite Charge wire length: 10 feet Charge wire angle: 0 degrees Charge depth: 10 feet Charge-to-gage line distance: 30 0 feet Sound speed: 4922 ft/sec Water depth*: 14 8 feet WIRE DISTANCE WIRE ANGLE CAGE ANE i GAGE COORDINATES HOR. HOR. RANGE DEPTH RANGE DEPTH (FEET) (DEG.) (FEET) (FEET) (METERS) (METERS) 0 300 0 91.4 0.0 5 0 300 5 91.4 1.5 10 0 300 10 91.4 3.0 40 0 300 40 91.4 12.2 50 0 300 50 91.4 15.2 55 0 300 55 91.4 16.8 60 0 300 60 91.4 18.3 70 0 300 70 91.4 21.3 80 0 300 80 91.4 24.4 90 0 300 90 91.4 27.4 100 0 300 100 91.4 30.5 *Calculated from times of arrival of bottom reflection D-13/14 NSWC/WOL TR 76-155 APPENDIX E NOTE ON FISH CLOSE TO THE WATER SURFACE According to the bladder oscillation model for explosion injury, as the fishes' depth tends to zero near the water surface the kill probability should also tend to zero reqardless of how high the incident pressure. Eventually, however, for fish at the water surface and sufficiently close to the charge, the bladder oscillation model must break down and a different mechanism for injury must take over. Apparently, this happens so close to the charge, and to the water surface, to be of little practical importance, since results reported by the Lovelace Foundation show no evidence of such a transition for 149 gm Carp (length = 21 cm) at a depth of 5 cm subjected to 5.58 megapascals (810 psi) incident pressure. A possible close-in non-bladder injurv mechanism is tissue damage due directly to compression by the incident Shockwave. If this is the case, tissue damage probably also occurs due to the pressure wave (generally an order of magnitude areater) emitted by the oscillating swim bladder. Assuming that this is the meaning of the ratio, AMIN/A., in the damage parameter Z, we rewrite Equation 3.1.3 in terms of the adiabatic compression ratio, PMIN/p0 , as __1 /pmtn\ X = _100 m (^_N) 3Y (ei) where PMIN is the maximum value of the oscillating bladder pressure (corresponding to radius AMIN at the first compression) , p^ is the initial ambient pressure, and y, the adiabatic exponent for air. Using El we then rewrite 3.1.5 as E-l NSWC/WOL TR 76-155 Z = i°-° In PMIN/^ + 100 In AMAX/A± (E2) Note that Equation E2 is equivalent to 3.1.5. It is just our point of view that has changed. Now let us suppose, for fish very close* to the water surface, that the Shockwave peak overpressure PMAX is the only- tissue damaging pressure. The damage parameter by this mechanism equivalent to Equation E2 is then given by 100 , PMAX ' 3y ^+1 (E3) . Pi J where PMIN is replaced by PMAX + p. and the second term drops out. Note that Z _,..,.., must always be smaller than Z calculated by PMAX J Equation 3.1.5 except for those cases — the ones of interest here-- where the pressure wave is of such short duration that the transient response of the swimbladder is suppressed*. Thus, when in doubt which damage parameter to use — zPMAv (Equation E3) or Z (Equation 3 . 1 . 5) --calculate both parameters, and use the greater value. Finally, we estimate the overpressure level, PMAX, associated with the assumption that all the damage corresponding to the damage parameter Z is due directly to tissue compression by the incident Shockwave. Solving E3 for PMAX we get "* Since Z is equivalent to the damage parameter X (Equation 3.1.3) calculated from the non-oscillatory steady-state response of an infinitely small bubble to an overpressure PMAX of finite rise time. E-2 NSWC/WOL TR 76-155 PMAX - Pi EXP[ (3yZpMAX/100) - 1] (E4) Setting p. = 1 atmosphere (1.014 x 10 pascals) and Z™,,^, = 125 (50% kill value—Equation 3.2.1) we get PMAX PMAX =19.2 MPa (=2790 psi) (E5) (approximately 24 charge diameters) for the overpressure level PMAX corresponding to 50% kill by this mechanism to fish which are very close to the water surface . E-3/E-4 NSWC/WOL TR 7 6-15 5 DISTRIBUTION Naval Biosciences Laboratory Naval Supply Center Oak Oakland, CA 94625 Attn: Louis H. DiSalvo LTJG John F. Wyman Commanding Officer Naval Underwater Systems Center Newport, RI C2840 Attn: Roy R. Mans tan, Code EA 11 Naval Ship Research and Development Center Underwater Explosions Research Division Portsmouth, VA 2 3709 Attn: LCDR R. H. Burt Richard Oliver Commander Naval Ocean Systems Center San Diego, CA 92152 Attn: G. B. Anderson S. Yamamoto, Code 40 6 D. A. Wilson F. G. Wood, Code 40 Code 6565 Michael H. Salazar Jack W. Hoyt J. D. Warner, Code 2531 William C. Cummings , Cede 4013 Naval Ocean Systems Center Hawaii Laboratory P.O. Box 997, Kailua, Oahu Hawaii, 96734 Attn: Evan C. Evans, III Head Marine Environmental Management Office Officer in Charge New London Laboratory Naval Underwater Systems Center New London, CT 06 320 Attn: Albert B. Brooks Charles L. Brown, Jr., Code TA13 Commanding Officer Naval Explosive Ordnance Disposal Facility Indian Head, MD 20 6 40 Attn: Library Division Lionel A. Dickinson, Code 5D Richard Burdette Lyle Malotky 1 NSWC/WOL TR 7 6-15 5 Commanding Officer Naval Explosive Ordnance Disposal School Indian Head, MD 20 6 40 Attn: LCDR E. W. McConnell Commander David W. Taylor Naval Ship Research and Development Center Bethesda, MD 20034 Attn: Library, Code 5641 Commanding Officer Naval Coastal Systems Laboratory Panama City, FL 32401 Attn: Code 350 John A. Brasewell, Code 773 Everett L. Richards, Code 721 Officer in Charge Civil Engineering Laboratory Naval Construction Battalion Center Port Hueneme, CA 9 3043 Attn: Code L70 Code L71 Code L4 3 Code L65 Commanding Officer Naval Air Station Patuxent River, MD 206 70 Attn: A. L. Clark, Environmental Protection Coordinator Public Works Department Commander Naval Sea Systems Command Washington, D. C. 20362 Attn: SEA-0 3 3 SEA-0 332 SEA-332B SEA-09G32 SEA-03B U. S. Army Engineer District 100 McAllister Street San Francisco, CA 94102 Attn: Tom Crews, III, Environmental Branch Edgewood Arsenal Edgewood, MD 21010 Attn: David Kramer Harold Sommer Allen E. Hilsmeier NSWC/WOL TR 7 6-15 5 U. S. Army Engineer Division, Pacific Ocean Environmental Section Bldg. 230, Ft. Shafter APO San Francisco 96558 Attn: Michael T. Lee, Biologist Director Waterways Experiment Station P. 0. Box 631 Vicksburg, MS 39180 Attn: Technical Library J. N. Strange Kim Davis WESNE ADTC/DLV Eglin AFB, FL 32542 Attn: J. C. Cornette National Marine Fisheries Service Auke Bay Biological Laboratory P. 0. Box 155 Auke Bay, AK 99821 Attn: Theodore Merrell National Marine Fisheries Service Water Resources Division P. 0. Box 1668 Juneau, AK 99 801 Attn: Dale R. Evans, Chief National Marine Fisheries Service Southwest Fisheries Center P. 0. Box 271 La Jolla, CA 92037 Department of Commerce National Oceanic and Atmospheric Administration Washington Science Center, Bldg. 5 6010 Executive Blvd. Rockville, MD 20852 Attn: Donald P. Martineau, Deputy Associate Administrator for Marine Resources CAPT Scott E. Drummond, Room 918 CDR John G. McMillan, USN LTJG Richard A. Zachariason, Room 805 Sidney T. Smith, Room 100 Milton S. Arnostam Emmet t S. Hill, Jr. Fletcher F. Echard, AD 1X3 NSWC/WOL TR 76-155 Department of Commerce Biological Laboratory Milford, CT 06460 Department of the Interior 1107 NE 45th Street Suite 110 Seattle, WA 98105 Attn: Karen Bachman Mark L. Holmes Department of the Interior Bureau of Sports Fisheries and Wildlife Interior Building Washington, D. C. 20240 Attn: John S. Gottschalk, Director Bureau of Commercial Fisheries Interior Building Washington, D. C. 20 240 Attn: Philip M. Roedel, Director State of Maryland Fish and Wildlife Administration Annapolis, MD 21404 Attn: Charles Frisbie Barbara Holden State of North Carolina Department of Natural and Economic Resources Division of Marine Fisheries Box 769 Morehead City, NC 28557 Attn: Willard Lane, Artificial Feef Program Jim Tyler, Artificial Reef Program South Carolina Marine Resources Division 2024 Maybank Highway Charleston, SC 29412 Attn: Michael D. McKenzie Trust Territory Environmental Protection Eoard P. 0. Box 215 Yap, W.C.I. 96943 Attn: M. Falanruw, Staff Ecologist Howard J. King, B-2 580 Taylcr Avenue Annapolis, MD 21401 NSWC/WOL TR 7 6-15 5 State of Alaska Department cf Fish and Game 333 Raspberry Road Anchorage, AK 99 50 2 Attn: Lance L. Trasky, Fisheries Research Biologist Deputy Commissioner Alaska Department of Fish and Game Support Building Juneau, AK 99801 Attn: Joseph R. Blum State of Alaska Department of Fish and Game Habitat Section 333 Raspberry Road Anchorage, AK 9 9 501 Department of Fish and Game Wildlife Protection Branch 1416 Ninth Street Sacramento, CA 9 5 814 State of California Marine Resources Division 350 Golden Shore Long Eeach, CA 9 0 802 Attn: Doyle Gates, Regional Manager State of Florida Department of Natural Resources Larson Building Tallahassee, FL 32304 State of Louisiana Wildlife and Fisheries Commission P. 0. Box 44095, Capital Station Baton Rough, LA 70 80 4 Attn: Fred Dunham Virginia Institute cf Marine Science Gloucester Point, VA 23062 Attn: William J. Hargis, Director University of Washington College of Fisheries Fisheries Research Institute Seattle, WA 9 819 5 Attn: Dave R. Gibbons Charles Simenstad, Biologist NSWC/WOL TR 76-155 Director Woods Hole Oceanographic Institution Woods Hole, MA 02543 Attn: Bostwick Ketchum Gifford C. Ewing Earl E. Hays Library Director Scripps Institution of Oceanography La Jolla, CA 92037 Attn: Fred Spiess School of Oceanography Oregon State University Corvallis, OR 97331 Attn: A. G. Carey, Jr. Librarian Chesapeake Bay Institute The Johns Hopkins University Baltimore, MD 21218 Chesapeake Eiological Laboratory P. 0. Box 3 8 Solomons, MD 206 88 Attn: T. S. Y. Koo Joseph A. Mihursky Martin L. Wiley John S. Wilson Marine Physical Laboratory, S10/UCSD Bldg. 106, Naval Undersea Center San Diego, CA 92106 Attn: Charles B. Bishop University of Hawaii at Manoa Hawaii Institute of Marine Biology P. 0. Box 1346, Coconut Island Kaneohe, HI 96744 Attn: George H. Balazs, Jr., Marine Biologist Department of Eiology Juniata College Huntingdon, PA 166 52 Attn: Robert L. Fisher Marine Resources Division California State Fisheries Lab 350 South Magnolia Long Eeach, CA 30802 Attn: Robert Kanlen NSWC/WOL TR 7 6-155 Argus Pressure Grouting Services, Inc. 22000 Ryan Road Warren, MI 4 8091 Attn: Albin Gronowicz, President Hydronautics 7210 Pindell School Road Laurel, MD 20910 Attn: Norman Shapira Robert E. Eckels & Associates Consulting Engineers 2101 Youngfield Golden, CO 80401 Woodward Clyde Consultant Box 1149 Orange, CA 9 2668 Attn: Jack Kiker B.C.C. Sub Ocean Services 1022 Wirt Road Houston, TX 77055 Attn: Thomas L. Kirchberg Lovelace Biomedical & Environmental Research Institute, Inc. P. 0. Box 5890 Albuquerque, NM 87115 Attn: Donald R. Richmond E. Royce Fletcher Robert K. Jones John T. Yelverton Meteorology Research, Inc. 464 West Woodbury Road Altadena, CA 91001 Attn: George Wof finder Mount Auburn Research Associates, Inc. 385 Elliot Street Newton, MA 0 216 4 Attn: Sheldon L. Kahalas Tetra Tech, Inc. 6 30 N. Rosemead Blvd. Pasadena, CA 91107 Attn: Li-San Hwang Explo Precision Engineering Corporation Manager of Technical Services Gretna, LA 70053 Attn: John J. Ridgeway NSWC/WOL TR 76-155 Crisfield Laboratory Box 351 Crisfield, MD 21817 Attn: M. W. Paparella Defense Documentation Center Cameron Station Alexandria, VA 22314 12 Office of Naval Research Washington, D.C. 20350 Code 1+82 NDW.NSWC(W).5605/1 (Rev. 5.78) TO AID IN UPDATING THE DISTRIBUTION LIST FOR NAVAL SURFACE WEAPONS CENTER, WHITE OAK TECHNICAL REPORTS PLEASE COMPLETE THE FORM BELOW: TO ALL HOLDERS OF NSWC/WOL/TR 76- 155 by John F. Goertner, Code R-14 DO NOT RETURN THIS FORM IF ALL INFORMATION IS CURRENT A. FACILITY NAME AND ADDRESS (OLD) (Show Zip Code) NEW ADDRESS (Show Zip Code) B. ATTENTION LINE ADDRESSES: □ REMOVE THIS FACILITY FROM THE DISTRIBUTION LiST FOR TECHNICAL REPORTS ON THIS SUBJECT. D. NUMBER OF COPIES DESIRED GPO B30-764 Y[-X 3003 :N0liN311V 0L60Z 0NVHAHVW 'ONIddS H3A1IS ')IVO 31IHM d31N3D SN0dV3M SDVddnS "IVAVN d3QNVWW0D 91C 000 AAVN 3H1 dO XN3WXdVd30 QIYd S33d ONV 30VlS0d ooe$'3sn 3ivAiad aod AiiVNBd ss3Nisna nviDiddo 01603 ON 'ONIddS 2f3A~1IS 'XVO 31IHM H31N3D SN0dV3M SDVddflS "IVAVN AAVN 3H1 30 iN3VNlH Vd3d