-r^- //- ?a L /p. . NSWC/WOL TR 77-90 w \\ OOCUMLiMi CJLLiiCTlON FISH KILLING POTENTIAL OF A CYLINDRICAL CHARGE EXPLODED ABOVE THE WATER SURFACE BY JOHN F. GOERTNER RESEARCH AND TECHNOLOGY DEPARTMENT 12 DECEMBER 1978 Approved for public release, distribution unlimited. NAVAL SURFACE WEAPONS CENTER Dahlgren, Virginia 22448 • Silver Spring, Maryland 20910 T JO fD o H r+ • t o a ro p> o <; • ») h-* h- ' ^ W ^ c 00 f-i hn P o (D c o o o • t X M- T3 CD O t— ' a' M- o 3 < OP (t) rt o 3- tr 1-^ LO MBL/WH i 3- o D m □ ^^ LJ UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE fWTien Dalm Enltred) REPORT DOCUMENTATION PAGE READ INSTRUCTIONS BEFORE COMPLETING FORM 1 REPORT NUMBER NSWC/WOL TR 77-90 2 GOVT ACCESSION NO 3 RECIPIENT'S CATALOG NUMBER 4 TITLE (and Subtitle) Fish Killing Potential of a Cylindrical Charge Exploded Above the Water Surface 5, TYPE OF REPORT A PERIOD COVERED Final i. PERFORMING ORG. REPORT NUMBER 7. AUTHORfs; John F. Goertner B. CONTRACT OR GRANT NUMBERC»J 9 PERFORMING ORGANIZATION NAME AND ADDRESS Naval Surface Weapons Center White Oak, Silver Spring, Maryland 20910 10. PROGRAM ELEMENT. PROJECT, TASK AREA a WORK UNIT NUMBERS 63721N; S0400; S040001; CR14CA501 1- CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE 12 December 1978 13. NUMBER O"^ OAGES 39 14. MONITORING AGENCY NAME & ADDR ESSf// d/Z/erenl from Conlrolling Ollice) IS. SECURITY CLASS, (ol thia report) UNCLASSIFIED 1S«. DECLASSIFI CATION/ DOWN GRADING SCHEDULE 16 DISTRIBUTION STATEMENT (ot this Report) Approved for public release, distribution unlimited, 17. DISTRIBUTION STATEMENT (of the abslrmct entered Ir^ Block 20, II dlllerent Irom Report) 18- SUPPLEMENTARY NOTES 19 KEY WORDS (Continue on reverse aide If neceasmry mnd Identify by block nuiTyber) Explosions Airburst Underwater Explosions Swimbladder Fish Fish-kill Lethal Ranges 20 ABSTRACT (Continue on reverae aide If neceaamry mnd Identify by block nurr\ber) Two special air-burst test geometries are compared with two typical underwater explosion test geometries in order to determine the relative hazard to swimbladder fish. The method consists of approximate calculations for extreme values of compression and extension of the fishes' gas-filled swimbladder in response to the explosion pressure waves. The kill probability is then calculated from the ratio of maximum to minimum radius during the oscillatory response using an experimentall v dpterminpd fnnptinn. (Cont.) DD 1 JAN^S 1473 EDITION OF 1 NOV 65 IS OBSOLETE UNCLASSIFIED S/N 0 102-014- 660 1 SECURITY CLASSIFICATION OF THIS PAGE (When Date Snimrtd) UNCLASSIFIED -i-'_lJHlTY CLASSIFICATION OF THIS PAGECH'hen Dale Entered) Calculations are made for 1000-lb and 64,000-lb cylinders of H-6 explosive (L/D = 3.65) fired end-on, 1.3 diameters from the water surface. By assuming a uniform fish-density distribution throughout the water it is estimated that on the basis of fish-killed/ kg explosive a typical underwater explosion is some 1000 times more hazardous for killing fish than these air-burst tests. UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGEftf7l»n Dmim Enltrtd) NSWC/WOL TR 77-90 SUMMARY This report deals with the prediction of explosion injury to fish with swimbladders and is part of a continuing study of the effects of underwater explosions on marine life. Swimbladder fish are particularly 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 warheads at sea. The case considered here is an application of a general method developed at the Naval Surface Weapons Center to a special test configuration in which the explosive charge is above the water surface. This study is part of the ordnance pollution abatement program of the Naval Sea Systems Command and was supported by Task SEA 55001/19373. The author is indebted to George A. Young and Ermine A. Christian for valuable suggestions during the course of this work. O ^V,u. L^-Aj^-^ \jj, CJVLfin -d JULIUS W. ENIG By direction 1/2 NSWC/WOL TR 77-90 CONTENTS Page 1 . INTRODUCTION 5 2 . METHOD 6 3 . CALCULATIONS 7 3. 1 Pressure-Time Inputs 7 3 . 2 Representative Fish Specimens , 7 3. 3 Kill Probability Calculations . , 12 3.4 Response to Exponential Waves of Short Duration 13 3.5 Patching of Solutions 16 4. RESULTS 18 4 . 1 General Observations 18 4 . 2 Kill Probability Contours 18 4. 3 Nominal Fish Kill 23 5. CONCLUSION 2 5 APPENDIX A. MEAN KILL VOLUME A-1 NSWC/WOL TR 77-90 ILLUSTRATIONS Figure Page 2.1 Underwater Pressure-Time Signatures Measured on 8-lb Tests (HOB = 0.28 m) 8 3.1.1 Sketch Showing Pressure-Time Signatures Used to Calculate Kill Probabilities (1000 lb H-6; Horizontal Range = 18.3 meters) 10 3.1.2 Sketch Showing Pressure-Time Signatures Used to Calculate Kill Probabilities (64,000 lb H-6; Horizontal Range = 73.2 meters) 11 4.2.1 Comparison of Predicted Kill Probability for 1000-lb Air Burst Test with Contours Calculated for 0.57 kg Pentolite at 9 m Depth - 21.5-cm White Perch 20 4.2.2 Comparison of Predicted Kill Probability for 64,000-lb Air Burst Test with Contours Calculated for 32 kg Pentolite at 9 m Depth - 21.5-cm White Perch 21 TABLES Table Page 1.1 Air Burst Test Parameters 6 3.2.1 Fish Input Parameters 12 3.5.1 Kill Probability Calculations 17 4.2.1 Variation of Kill Probability as a Function of Fishes' Depth 22 4.3.1 Water Volumes Enclosed by Kill Probability Contours 24 4.3.2 Estimated Nominal Fish Kill 24 NSWC/WOL TR 7 7-90 FISH KILLING POTENTIAL OF A CYLINDRICAL CHARGE EXPLODED ABOVE THE WATER SURFACE 1. INTRODUCTION The Naval Surface Weapons Center is currently carrying out a program of explosive tests designed to determine the underwater pressure field from a specially shaped charge exploded in air. This report presents a preliminary analysis of the potential of this special test configuration for inflicting unwanted fish-kill. This analysis is restricted to swimbladder fish and is based on the data and method developed in Reference 1. The method consists of an approximate calculation for the extreme values of compression and extension of the fishes' gas- filled swimbladder 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 oscillatory response. Test Configuration. The test configuration is equivalent, for the purposes of this report, to a cylinder of H-6 explosive (length /diameter ratio - 3.65, axis vertical) centrally initiated at a scaled height, h/W ' - 0.182 m/kg , above the water surface. Tests using three different explosive weights — 8, 1000, and 64,000 lb H-6 — are considered. Table 1.1 lists the pertinent test parameters. 1. Goertner, J, F., "Dynamical Model for Explosion Injury to Fish," NSWC/WOL TR 76-155, Mar 1978. NSWC/WOL TR 77-90 Table 1.1. Air Burst Test Parameters Explosive Weight* 8 lb 1000 lb 64,000 lb (3.63kg) (450 kg) (29,000 kg) Linear Scale Factor 1/20 1/4 1 Height of Burst** 0.28 m 1.40 m 5.60 m * H-6 explosive, RDX/TNT/AL/WAX (45/29/21/5) . ** Measured to point of initiation at center of charge. Section 2 outlines the method used for this analysis. Section 3 gives the method and some of the details of the calcula- tions. Sections 4 and 5 present the results and conclusion of this study. 2. METHOD The method followed in this study was to start from underwater pressure-time signatures measured on 8-lb tests. Figure 2.1 shows the complete set of pressure signatures measured on three identical tests . Selected pressure signatures were scaled up to the 1000-lb and 64,000-lb test configurations and were then used to calculate kill-probablilites for particular sizes and species of swimbladder fish. (Since the 8-lb tests were carried out in a small test pond, fish-kill was not calculated for this scale.) The pressure signatures selected for kill-probability calcula- tions were those at the greatest horizontal range from the charge (see Figure 2.1), since these are the most important for estimating the extent of the region of significant kill. We then compared the calculated kill probabilities for the 1000-lb and the 64,000-lb air burst tests with kill probabilities calculated for comparable underwater explosion tests. 2. Limited report by J. F. Pittman, Jan 1978; rej^arding DAWS POND Program II. A replicate set from the closest-in string of gages which vas obtained on the opposite side of the charge has been omitted from the figure. NSWC/WOL TR 77-90 3. CALCULATIONS 3.1 PRESSURE-TIME INPUTS. The first step in these calculations was to sketch-in average curves for the three sets of pressure-time signatures at the greatest horizontal range (3.66 m) shown in Figure 2.1. These average curves were then approximated either by two successive exponentials or by a square step followed by an exponential, since these simple wave forms could be calculated by the method presented in Reference 1. These approximating pressure-time signatures were then scaled up from 8 lb to 1000 lb and 64,000 lb -- the corresponding distances and times were increased in the ratio of the linear scale 1/3 factor (or W ' ) and pressures were held constant. The scaled approximating pressure-time signatures for the 1000-lb and 64,000-lb test configurations are shown in Figures 3.1.1 and 3.1.2, respec- tively. As in Reference 1 the exponential portions were calculated using two separate exponential segments joined at t = 1 . 8 9 p = PMAX e"^/® (t < 1.8 9) (3.1.1) p = 0.25 PMAXe-^/4-3 ^ ^^ > ^'^ ®) ^""^'^^^ The parameter 9 was taken as the time for the measured pressure to drop to 1/e of its peak value, PMAX. 3.2 REPRESENTATIVE FISH SPECIMENS. The fish selected for this study were Striped Bass (or Rockfish) and White Perch. These are the fish expected to be present during the 1000-lb tests in the Potomac River during April, May, and June, at the Dahlgren test site of the Naval Surface Weapons Center. For each species a single representative size was selected for this study -- 38-cm fork length for Striped Bass, 17-cm for White Perch. In addition, calculations were done for 21.5-cm White Perch in order to compare kill probabilities calculated for the air burst tests with kill probabilities previously calculated for charges detonated underwater (Reference 1). Table 3.2.1 summarizes the fish input data for these calculations . NSWC/WOLTR 77-90 R - 0 D - 0.61 150 10.0 t. 4.00 2.00-1 W'\^ R - 1.22 m D - 0.61 m iiLiZ*- 120 leo 240 TIME luSEC) 200 250 160 200 TIKI li,SEC) 60 90 TIMI (»SEC) MTo FIG. 2.1 UNDERWATER PRESSURE-TIME SIGNATURES MEASURED ON 8-LB TESTS (HOB = 0.28m) NSWC/WOL TR 77-90 2J0 36 0 480 TIME (i-SFCI R - 2 . 4« m D - 1 . 2 J " 200 500 «00 TIME (uSF.C) TIME USEC) "i — ' — ?5- R - 2 . 44 m D - 2.44 m R - 3.(( • D - 2.44m 120 ^l€0--^ TIME (uSEC) 240 3O0 FIG. 2.1 (CONTINUED) NSWC/WOL TR 77-90 1.46 M Pa 0= 0.095 msec 0.45 M Pa 0 = 1.115 msec 2.135 msec 1.61 MPa B= 0.150 msec DEPTH = 3.05 m 0.86 M Pa 9 = 0.590 msec UJ oc 3 M tn UJ oc 0. DEPTH = 6.1 1.680 msec 2.28 M Pa 6 = 0.200 msec DEPTH = 12.2 m 0.385 0.955 mesc TIME (NOT TO SCALE) FIG. 3.1.1 SKETCH SHOWING PRESSURE-TIME SIGNATURES USED TO CALCULATE KILL PROBABILITIES (1000 LB H-6 ; HORIZONTAL RANGE = 18.3 METERS) 10 NSWC/WOL TR 77-90 1.46 M Pa B= 0.380 msec 0.45 M Pa $ = 4.460 msec DEPTH = 12.2 m 8.540 msec 1.61 m 0 = 0.600 msec 0.86 M pa 9 = 2.360 msec DC D CO CO ut oc a. DEPTH = 24.4 m 6.720 msec 2.28 M Pa 0 = 0.800 msec DEPTH = 48.8 m 1.540 3.820 msec TIME (NOT TO SCALE) FIG. 3.1.2 SKETCH SHOWING PRESSURE-TIME SIGNATURES USED TO CALCULATE KILL PROBABILITIES (64,000 LB H-6 ; HORIZONTAL RANGE = 73.2 METERS) 11 NSWC/WOL TR 77-90 Table 3.2.1, Fish Input Parameters , / Effective Fork — Bladder Length Radius l" (Ai)o (Ai)nA (cm) (cm) 2/ Striped Bass 38 1.60 0.042- 3/ White Perch 17 0.94 0.055- White Perch- 21.5 1.18 0.055 A'The length measured from the most anterior part of the head to the deepest point of the notch in the tailfin. 2^/Reference 1, Equation 4.2.1 J^/Reference 1, Equation 3.1.8 4/For comparison with underwater burst calculations 3.3 KILL PROBABILITY CALCULATIONS. These were done by the method presented in Reference 1. Basically, this consists of calculating the damped oscillatory response (radial oscillations) of a spherical air bubble corresponding to the fishes' swimbladder. This oscillatory response supplies the calculated damage parameter Z = X + Y (3.3.1) where X = -100 In AMIN/A. (3.3.2) Y = 10 0 In AMAX/A. (3.3.3) Where In is the natural logarithm, A. is the initial at-rest bubble radius, and AMIN and AMAX are the smallest and largest radii during the oscillatory response.* Note, that we choose not to combine Equations 3.3.1,2,3 into Z = 100 In AMAX/AMIN in order to emphasize the fundamental independence of the damage parameter components, X and Y. *ln this study AMAX occasionally occurred prior to AMIN, and this was permitted even though this has not happened under the testing conditions studied to date, (However, had we not used the occasional AMAX values occurring prior to AMIN the results of this study would still he, for practical purposes, identical , ) 12 NSWC/WOL TR 77-90 The kill probability, p, is then calculated as 1 p = (3.3.4)* 1 + EXP [-0.055(Z-125) ] This equation represents underwater explosion test data from some 1500 caged Spot and White Perch over a wide range of explosive test conditions. Equation 3.3.4 was used for predicting the Striped Bass kill as well as for White Perch, since unpublished preliminary results with 16 species of fish indicate that Equation 3.3.4 applies to the majority of swimbladder fish.** 3.4 RESPONSE TO EXPONENTIAL WAVES OF SHORT DURATION. The method used in Reference 1 to calculate the oscillatory response to exponential waves was to patch together solutions to successive square steps of half-period duration. This solution breaks down, however, as the time constant 9 becomes less than the duration of the calculated first half-period of the motion, and the calculated size of the first compression gets too small. This comes about because, in the limit as 9 becomes smaller and smaller, the first approximating step takes on the value one-half PMAX, the average of the initial and final pressures--and consequently, the damage para- meter, X = -100 In AMIN/A. , does not go to zero as 9 approaches zero. Impulsive Loading Approximation. This approximation is for the limiting case of pulses of infinitely short duration. Under impulsive loading the initial radial velocity v. of the bubble is given by v. = 1- ~" - (3.4.1) 1 pA. *Reference 1, Equation 3.2.1 **Equation 3.3.^ describes explosion test result_s for 10 of the l6 species tested. The other 6 species required larger values for Z (= 125 in Equation 3.3.^). 13 NSWC/WOL TR 77-90 where p is the density of the water and I - /p dt, the applied 3 impulse. In order to extend the range of usefulness of this approximation we compute the applied impulse at t = 0 as e I = /p(t) dt = PMAX X e X [1 - e ] = 0,6 32 X PMAX X e (3.4.2 The total energy Y following impulsive loading is given by* T 9 p . V. Y = - p V vl^ + p.v. + -*• ^ 2 '^ i i ^i i Y-1 (3.4.3) where p. and V. are the initial pressure and volume of the bubble, and Y is the adiabatic exponent (= 1.4 for air). In Equation 3.4.3 the first term is the kinetic energy imparted to the surrounding water by the impulsive loading, the second the potential energy of the surrounding water, and the third the internal energy of the air inside the bubble. From the total energy Y we calculate the dimensionless bubble oscillation parameter k used to describe the motion ' ' ^-1 (pk ) (3.3.3)** CJombining 3.4.1, 3.4.3, and 3.4.4 we can express k in terms of the impulse and initial bubble radius * Reference 1, Equation Al ** Reference 1, Equation A13 3. 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. 14 NSWC/WOL TR 77-90 k = Y-1 Y-1 2 \a_.Yp i.pp. -Y (3.4.5) Damage Parameters X and Y. The problem is to calculate the damage parameters X and Y, Equations 3.3.2 and 3.3.3, respectively. Thus we must calculate AMIN/A. and AMAX/A.. We proceed as follows. First, using k (Equation 3.4.5) we look up AMIN/AMAX in Table A-1 of Reference 1. Next, we calculate the pressure ratio (Y-1) PMIN P. K AMIN AMAX (3.4.6) "^ /amin \ "^ I AMAXy 1 - AMIN 3 (Y-1) AMAX / where PMIN is the air pressure at the first compression. Finally, using the adiabatic pressure-volume relationship we get AMIN ^ / PMIN Y _1_ 3y (3.4.7) and AMAX _ / AMIN ] / ( AMIN AMAX (3.4.8) With increasing 0 both the first compression and the subse- quent expansion calculated by this approximation become too large. Thus both damage parameters, X = -100 In AMIN/A. and Y = lOO In AMAX/A. become progressively too large with increasing values of 9. 4. Snay, H. G. and Christian, E. A., 1952, "Underwater Explosion Phenomena: The Parameters of a Non-Migrating Bubble Oscillating in an Incompressible Medium," NAVORD Report 2437, Equation 14a. 15 NSWC/WOL TR 77-90 Which Approximation to Use. For those cases where the calculation by half-period square steps showed 0 to be the order of a half-period or less, we calculated the fish damage parameter, Z = X + Y, by both approximations. Since the systematic errors in both of these approximations result in values of Z which are too high--square steps for 0 values too small, impulse for 9 values too large--we calculated these cases by both approximations and selected the one giving the smallest value of the damage parameter Z. It turned out that the crossover for the Z values calculated by the two approximations occurred for e values equal to approximately six-tenths of the first half-period calculated by square steps. 3.5 PATCHING OF SOLUTIONS. The response of the equivalent bubble to the pressure-time signature was determined separately for each of the two pulses shown in Figures 3.1.1 and 3.1.2. To facilitate the calculations the response to the second pulse was calculated as starting from rest at the initial ambient radius and pressure, A^ and p.. Results of the separate calculations were then scanned to obtain the extreme values of the radius, AMIN and AMAX. Table 3.5.1 summarizes the results of these calculations. The values of X and Y selected to calculate the damage parameter, Z = X + Y, are indicated with a check mark. Note that the value of X or Y selected is the maximum of the value calculated for the first pulse and that second pulse value corresponding to the method of calculation--square or impulsive loading--selected according to the criterion given in Section 3.4. For example, for the first entry (first row) in Table 3.5.1, the "Impulsive Loading" calculation was used for the second pulse, since this value of Z = X + Y (48 + 38) is less than the value calculated by "Square Steps" (102 + 40). Thus, the value for Z representing the combined response to the first and second pulse is the sum of 64_, the greatest X value (taken from first pulse having discarded the value 102) , and 3_8' the greatest Y value (taken from second pulse having discarded the value 4_0) . Additional Details. Response to the first pulse for the two shallowest depths (Figures 3.1.1 and 3.1.2) was calculated by the method of Reference 1 by setting TPOS (Reference 1, Figure 3.1.1) equal to the time of arrival of the second pulse. Response to the first pulse (square step) for the deepest depth was calculated setting PMAX equal to the step pressure and 9 equal to approximately 10^ times the duration of the step. Other parameters were =et as follows: TFOS = step duration, PNEG = plateau pressure following step, and DTNEG = duration of plateau pressure. 16 NSWC/WOL TR 77-90 z o D u _l < 00 < CO o oc a. in < i-H C 0V3 Csl IT) a> rH ro -^ ro 00 CM fN ro 00 O O u: KD \£) ■H 1-1 fsi ^ i^ uo ro in in UD fN fN CN .H i—i X ft >< fN m fN ro r~~ ro r- rH T <-{ fN ro <-H in in l£> KD •^ X o c^ CO ro fN nH CM PO ro O O O OD CO 00 r- r- r- II ■—1 r-\ i—\ l—i rH rH ,—\ <—t ,—1 .—{ S3 (D > cn -H C W -H ^ "^ ^ ^ ^ < X 0) ■H X) CO nH ro r- r- r- VD ■^ ^ -^ ^ ^ ^ ^ rH o ro r- rH ^ CO VD CM o CT^ ro r^ i-H vi> 00 o o ,—\ 3 -P •^ ■<3- •^ ro ro ro rH fN ro ,-i .-t o o CTK) II >< 0) >. ^ -P fH ro K£> 1— 1 \D f-i K£> o in o O O o O o o fH nj o in 3 1— 1 rH rH ^ ft 0) > cr -H C tn -H -H < ^ TD 00 r^ r- ro in r- ■^ CO r- 0) 3 10 ■^ ro fN 00 VJD -^T "^r ,—\ 00 w & 0 rH f-i —i 6 J M < a ft M c c 0) Ul fN GO r- ^ ^ ^ -^ -^ -,^ ^ ^^ •^ ■^ --^ ^^ rH (N U 0. (N (N o i—{ o^ ■^ fN < k • • • • • n \D fN CN »* 03 1-4 ,—{ IN CM - - - ■<1' m • X ;§ . ro 00 r~ r-i 0) 03 > J ■H CQ in J-i J O 0 01 o ^ (1) o o aE- o ^ X o •r w t-i VD >1 ■H XI (0 o M •H M (U JJ 3 a e o o o +1 T3 dl m 3 17 NSWC/WOL TR 7 7-9 0 Response to the second pulse at all depths was calculated both by the method of Reference 1 (square steps) and by the impulsive loading approximation described in Section 3.4. As described in Section 3.4, the method giving the smallest value for Z = X + Y was then selected to represent the response to the second pulse, 4. RESULTS 4.1 GENERAL OBSERVATIONS. The final column of Table 3,5.1 lists the kill probabilities corresponding to the calculated fish damage parameter Z for the representative 1000-lb and 64,000-lb test conditions selected for this study. Relative to the uncertainties inherent to this study, the variation of kill probability with fish size is not great. This factor of two variation at the two shallowest locations for the 1000-lb test geometry is largely due to the variable response of the different sized swimbladders to impulsive loading by the second pressure pulse. One would expect the longer duration pressure pulses of the 64,000-lb test geometry to cause larger kill probabilities at corresponding scaled locations. Except for the marginal case of the shallowest gage location this does not occur, since the effect of 4 times greater depth at corresponding scaled locations on the 64,000-lb test more than offsets the effect of longer pulse durations. This generally lesser kill probability at corresponding locations of the 64,000-lb test geometry is a direct result of increased hydrostatic pressure suppressing the amplitude of swimbladder oscillation. 4.2 KILL PROBABILITY CONTOURS. To give meaning to these kill probability results we compare them to similar calculations for underwater explosions. Figures 4.2.1 and 4.2.2 show contours of constant kill probability calculated for charge weights of 0.57 and 32 kg pentolite respectively, exploded at a depth of 9 meters.* *H-6 is more energetic than pentolite. It probably takes about 1.1 to 1,2 times as much pentolite on a weight basis to produce roughly equivalent underwater pressure fields in the air-burst and underwater-burst configurations considered oRr.o^J^§r-^ffi?J'-^«S2»-l'^^"i'^3lsrit weight" corrections were made in doing the compari- ouiio lUL L.nis rcpo L L • 18 NSWC/WOL TR 77-90 The three kill probabilities calculated at each air burst test geometry-- 1000-lb and 64,000-lb --are also shown (enclosed by solid circles) on Figures 4.2.1 and 4.2.2. In the following paragraphs we will use these plots to make order-of-magnitude estimates of the fish-killing potential of these four explosion test geometries. The computed kill probability data for the underwater explosions is more complete than that for the air bursts. For the purposes of this report the author has sketched in (dashed curves, Figures 4.2.1 and 4.2.2) possible extrapolations to the 50% and 10% kill contours. These extrapolations are made in lieu of further computations because they do not affect the order-of-magnitude conclusions of this report. (Were it required, the author does not foresee any difficulty in extending these contours by further computations to shallower depths and also to the region directly beneath the charge.) For the air burst tests our data is meager. About the best we can do is a crude estimate for a single kill probability contour for each test configuration. For the 1000-lb air burst test (Figure 4.2.1) we take as an estimate for the region of greater than 50% kill the shaded area--a cylinder of water 20 meters in radius and 25 meters deep. In order to estimate the lower boundary for 50% kill on the 1000-lb air burst test we needed more than the three kill probabili- ties listed inside the solid circles (Figure 4.2.1). Thus, in order to estimate the falloff of the kill probability with increasing depth we calculated what is probably an upper bound by using the pressure- time signature measured at the deepest gage (Figure 3.1.1) and calculating the kill probability corresponding to this signature as a function of hydrostatic pressure (different fish depths) . The kill probabilities listed inside the dashed circles of Figure 4.2.1 were obtained this way. (Table 4.2.1 gives the complete results of these calculations where only the fishes' depth was varied.) For the 64,000-lb air burst test we take as an estimate for the region of greater than 10% kill a cylinder of water 70 meters in radius and 50 meters deep (shaded area, Figure 4.2.2). 19 NSWC/WOL TR 77-90 K UJ I- (3 Z < QC Z o N E o X CO OC 3 O O u 00 I o UJ Q. UJ I fY- Lrt < CO < CQ O CC a. 6^ is O 2 -I UJ _j Q- Q UJ l- o Q UJ CC 0. u. O Z o CC < a. O u CM d D O < (SdBiaiAl) HldBQ 20 NSWC/WOL TR 77-90 HORIZONTAL RANGE (METERS) 200 300 C/5 cc UJ H UJ S a. Ill Q FIG. 4.2.2 COMPARISON OF PREDICTED KILL PROBABILITY FOR 64,000-LB AIR BURST TEST WITH CONTOURS CALCULATED FOR 32 KG PENTOLITE AT 9 M DEPTH - 21.5-CM WHITE PERCH 21 NSWC/WOL TR 77-90 Table 4.2.1. Variation of Kill Probability as a Function of Fishes' Depth 21.5-cin White Perch p(t) = PMAX e"^'^^ : PMAX - 2.28 MPa, 0 = 0.200 msec Fish Damage Parameters Depth X Y Z = X + Y Kill Probability (meters) (%) 10 113 23 137 65 20 93 18 111 32 30 80 16 96 17 40 71 14 84 10 50 63 13 76 6 22 NSWC/WOL TR 77-90 4.3 NOMINAL FISH KILL. In order to assess the fish-killing potential of an explosion we define a "Nominal Fish Kill" based on an assumed uniform fish density distribution of 10 fish of specific species and size per cubic meter of water. Thus, to calculate the Nominal Fish Kill we compute the /p dv where p is the calculated kill probability and multiply by the assumed uniform fish density, i.e.. Nominal Fish Kill = lO""^ /p dv (4.3.1) where v is the water volume in meters. We now wish to calculate the Nominal Fish Kill for the four explosion test geometries described by Figures 4.2.1 and 4.2.2. To do this we approximate /p dv (Equation 4,3.1) by the volume of water enclosed by the 50%-kill contour.* Table 4.3.1 lists the calculated water volumes enclosed by the 50% and 10% kill contours for the four explosion geometries. The calculated volumes for the underwater explosions were used to estimate an average value of the volume ratio, 50%-to-10% kill, (= 33|%) which we then used to esti- mate the 50% kill volume for the full scale air burst test (Figure 4.2.2) . The Nominal Fish Kill values calculated from these 50% kill volumes (Table 4.3.1, first column) are listed in Table 4.3.2.** The final column of Table 4.3.2 lists the Nominal Fish Kill per kilogram of explosive used. Thus, on a fish/kg basis the underwater shots are some 1000 times more effective in killing fish than the air burst test configurations. *This approximation underestimates Jp dv. For the example worked out in Table 4.3.1 of Reference 1 (same set of calculations as used here for the 32 kg under- water explosion) this approximation results in a value for Nomina] Fish Kill which is 89% of the value obtained thru the approximate integration described by the Table. For the underwater explosions, volumes enclosed by the contours were calculated by summing cone frustrum elements which approximated successive slices of the figure of revolution. **Alternatively, x^?e could describe the fish killing potential in terms of a Mean Kill Volume = Jp dv. (See Appendix A.) Thus, the Nominal Fish Kill is simply the Mean Kill Volume expressed in thousands of cubic meters of water. 23 NSWC/WOL TR 7 7-90 Table 4.3.1. Water Volumes Enclosed by Kill Probability Contours (Thousands of Cubic Meters) Ratio Kill Probability Contour 50% Vol, 10% Vol, 50% 10% 0.57 kg Underwater 34 110 0.31 32 kg Underwater 1430 3960 0.36 450 kg Air Burst 31 29,000 kg Air Burst 258* 770 *Estiinated value = 33^% of 10% Kill Volume Table 4.3.2. Estimated Nominal Fish Kill -3 3 Assumption: Uniform Fish Density = 10 Fish/ (Meter) 0.57 kg Underwater 32 kg Underwater 450 kg Air Burst 29 ,000 kg Air Burst Nominal Nominal Fish Kill Kill/kg 34 60 1430 45 31 69x10"^ 260 9x10"^ 24 NSWC/WOL TR 77-90 5. CONCLUSION On a fish-killed/kg explosive basis a typical underwater explosion is some 1000 times more hazardous for killing fish than the two air burst test geometries considered. 25/26 NSWC/WOL TR 77-90 APPENDIX A MEAN KILL VOLUME An alternative measure of the fish-killing potential of an explosion geometry is the Mean Kill Volume (or MKV) defined on the basis of an assumed uniform spatial distribution of fish. Let D be the assumed uniform spatial density for fish of a given species and size. Assuming D, let N be the number of fish killed by a given explosion geometry. We then define the mean kill volume by MKV = N/D (Al) Thus, the mean kill volume is the volume of water which multiplied by the assumed uniform fish density results in the number of fish killed by the explosion. Since N is generally computed by N = /p X D dV (A2) where p is the kill probability, we can also express the mean kill volume directly in terms of the kill probability MKV = /p dV (A3) In this way we can avoid referencing the fish density distribution which is generally unknown. Given an approximately random distribution of fish the MKV is an appropriate parameter for comparing the fish-killing potential of explosion test configurations.* *If one has specific knowledge of the fish density distribution, such as the presence of only bottom-feeding or surface -feeding fish then this additional knowledge should, of course, be used. A-1/2 NSWC/WOL TR 77-90 DISTRIBUTION Naval Biosciences Laboratory Naval Supply Center Oak Oakland, CA 94625 Attn: Louis H. DiSalvo LT JG John F . Wyman Commanding Officer Naval Underwater System,s Center Newport, RI C2 840 Attn: Roy R. 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