E.A. Lundstrom- Evaluation of Forest Fire Burn Model of Reaction Kinetics of Heterogeneous...

8/3/2019 E.A. Lundstrom- Evaluation of Forest Fire Burn Model of Reaction Kinetics of Heterogeneous Explosives

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Evaluation of ftrestfke Burr. Model ofReaction Kinetir,.!; of Hett8-oganecus Expiosives

byE.A. Lundstrom

Remarcn Department

0)MAY1983

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FORZWORD

This r~wrt GUMMram Oseertanmi~uts Obtned diting inveftivi~tton of high-,qp.dAhapact Ovito ciased munItIons. The Forest Fire burn model for energetic

ustaial~M~gitu , uod ifi tions 2r* devetopod, and the result is

"Ahwkwa Perfrmed,during flsaW year 1967 at the Na&'ai Weapons C~nter, China[WWe CaflC: UtWsr kauidn from the howseitive Munitions Adv~namd Deve1apasent Pmoratn,Proivam PLIment $36W Adwensed doev.opm~mt support of theoreticsl1 epeitusuntal, andan*17*km work n1*tftd to rccx.%~w,44 4;ý *apl~hale 4w~ pojwanw to wssintia' to

daveh!itw~t of* AtU-e technoloy sa -sor the design of ins~rouitive inunitcrns.

This report was reviewedl for tec.nica! accuracy by C.D.Lind.J

Under authority of

I. L.DKR, Read J. A. BURTRmwsmh DrposrmenL Capt.,U.S. Navy

Rekiseaed (o publication by0. ILSCHnRflR

Tehnea WCTehnc^thicprn 9

Pubisfti-d by h I' mat nmLrepartment

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UNCLASSIFIED

SECURITY CLASSIFICATION OF THIS PAGE IWhen Data Entered)I

19 . (Contd.)

high-pressure detonation regime where the conventional analysis fails.

UNCLASSIFIED

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CONTENTS

Introduction ..... ......... .. ,...................................... 3

Flow Field Analysis ............................................................... 3

Reaction K inetics ................................................................. 9

Numerical Calculations ........................................................... 10

Conclusions ...................................................................... 18

References ....................................................... 19

Figures:

1. Time-Space Diagram ofRunup of a Reactive Shock Wave to a Detonation ......... 42. Partially Reacting (Wt = Constant) Hugoniot Curves for PBX-9404 ............. 113. Solid Fraction as a Function of Shock Pressure for Reactive Hugoniot

Plotted in Figure 2 .......................................................... 124. Reaction Rate- W, Plotted as Function of Pressure Comparing Results

Obtained With Reactive Hugoniot and Nonreactive Shock Assumptions ......... 13

5. Reaction Rate- W&IW Showing EfTect of First-Order Kinetics Assumption ....... 146. Wedge Test Simulation Showing EfTect of Flyer Plate Impedance ................ 167. Effect of Reactive Hugoniot Assumption and Reaction Kinetics Model on

Wedge Test Simulated by a Plexiglas Flyer Plate .............................. 17

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INTRODUCTION

One of the central goals in explosives science is to extrapolate the results of simplesmall-scale testing to predict the outcome of complex problems of practical interest. Aremarkable procedure has been developed by C. Forest (Reference 1) that has enabled engi-neering calculations for a variety of problems involving shock-initiated reaction of hetero-geneous solid explosives. Forest assumed a global reaction rate model for the decomposition ofthe explosive and derived a method to calibrate the model using the results of wedge tests.

The result Is popularly known as the "Forest Fire" burn-rate model. The reaction model isthen used In one- and two-dimensional hydrodynamics computer codes where the details ofshock wave interactions with reacting explosive materials can be calculated. This procedurehas been successfully applied to a variety of very practical problems. (See References 2, 3, and4, for examples.)

In the selection of the reaction model and the derivation of its calibration procedure,Forest makes an assumption about the processes that occur in the explosive decompositiohthat is contrary to the widely held view of hot spot initiation of heterogeneous explosives. Healso makes several assumptions about the flow field obtained in the wedge test that affect thecalibration of the reaction model. These assumptions are inconsistent with calculations usingthe burn model. That is, when the Forest Fire burn model is used to calculate wedge testresults, one does not obtain the flow field assumed in the calibration of the model.

In tpite of inconsistencies in the theory, one is faced with a rather impressive history ofsuccess in correlating experiment with calculation for a wide variety of applications. There-fore, an attempt is made here to evaluate the effect of the various assumptions of the ForestFirn theory. The method used is to evaluate the reaction rates based on extreme cases of theassumptions and to evaluate their effect on results of numerical calculations of the wedgetest.

FLOW FIELD ANALYSIS

As a model of the shock-to-detonation transition observed in the wedge test, Forestproposed a hydrodynamic discontinuity within which some fraction of the solid reactants isconverted (burned) to gaseous products. In one extreme case, no solid is burned and thediscontinuity Is the familiar shock wave. In the other extreme, all of the solid is consumedand one has a detonation wave. In the following, the hydrodynamic discontinuity will also becalled a reacting shock wave. A wave diagram of an accelerating shock wave is shown inFigure 1. At a distance Xd the wave transitions to Chapman-Jouguet (CJ) detonation and thewave velocity is constant thereafter. The transition to detonation may be smooth or it may be

3



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DETONATION

I POINT

REACTIVE SHOCK

Xd

DISTANCE

FIGURE 1. Time-Space Diagram of Runup of a Reactive Shock Waveto a Detonation.

discontinuous. The fraction of solid burned within th" reacting shock wave increases with

wave propagation distance (or time) until it is all burned at Xd. In addition to combustion,

which occurs instantaneously within the discontinuity, the remaining solid continues to burn

behind the wave at some finite rate. The objective of the flow field analysis is to calculate the

burn rate behind the wave as a function of pressure and the velocity of the wave.

To calculate the burn rate, one starts with the Lagrangian equations for conservation ofmas, momentum, and energy (Reference 2)

Us = -PMo (la)

ý = U's (lb)

M-PV (ic)

and an arbitrary equation of state

P=P(VE,W) (Id)

where V, U, E, P, and W are the specific volume, velocity, energy per unit initial volume,

pressure, and solid mass fraction, respectively. The subscripts % nd m denote partial

derivatives with respect to time and the Lagrangian mass coordinate. In addition, one has the

4



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jump equations expressing conservation of mans, momentum, and energy across the reacting

shock wave (Reference 2)

PI a U , I/Vo (2a)

V1U, =Vo(U-UU) (2b)

El =U,2 (2c)

and the equation of state

PI = P(V1 E W ) (2d)

where the subscripts 0 and I denote conditions in the uniform initial state and the state justdownstream of the reactive shock wave. The velocity of the reactive shock is given by U,.

Equation 2 assumed that PO = 0, Eo = 0, and Uo = 0. Note that since the material is allowedto partially react within the discontinuity, there are six variables and four equations, leaving

two degrees of fredom instead of the usual one.

Forest calculated the burn rate W. as a function of thermodynamic parameters at state1, thi pressure gradient P.o, and what amounts to the wave acceleration. He found that a zero

pressure gradient P.6 gave good results. For simplicity, the presaure gradient is allowed to

vanish here early in the derivation.

The burn rate, Wg, can be obtained by differentiating the equation of state (Equation Id)

PS = PvV 1 + PSES + PwWW (3)

where the derivatives

v,wV av

EV'

are known functions of V, 5, and W and are computed numerically from Equation 2d. Thetime derivatives Vg and EZ are next eliminated from Equation 3 in favor of the velocity

gradient, U.,, using Equation I, yielding

5



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p•t (/PV- PPr)UM + PWWt 4

It is desired to express the derivatives Pg and U. in favor of the pressure gradient Pm and

derivatives in the direction of shock propagation, since these are known at the shock

boundary.

To obtain directional derivatives, a simple exercise of the chain rule gives

j j* =P +P,,,i j

and

where the notation (Wl),denotes a time derivative in a direction on the space-time plane that

is parallel to the direction of the travel of the reactive shock. Using Equation Ib for Ur, while

noting that (am/as), = U/Vo, and evaluating the result at the shock boundary, Equations 5and 6 yield

dP U (7)

P At- PU /V

and

dU (8)

Here it is convenient to impose the simplifying assumption P. 0. Substituting Equations 7and 8 into 4, one obtains

Instead of derivatives with respect to I, the shock position, xI, is a more convenient variableand so Equation 9 becomes

at1 0re

Equation 10 isa preliminary result obtained by Forest in Reference 5.

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In order to relate the two derivatives, dU1Idxt and dPI/dxl, the reaction that takes place

within the discontinuity must be specified. Forest proposes a "reactive" Hugoniot in the form

of

Us MC=+3U (+Y)

This equation, together with Equation 2, determines W1 at the shock boundary. Combining

Equation 11 with Equation 2a to eliminate the shock velocity, Us, and differentiating the

result, one gets

f- C.+2,l)dU, (12)aO (Cr + U i

Substituting Equation 12 into Equation 10, one gets

u V2PV- PIPS I ~ (13)W, 1 -V~C+ S.lI P dz

r W I

relating the reaction rate W1 to the rate of pressure increase at the shock front.

An alternate and more self-consistent assumption is a nonreactive shock front with

W1 = 1. For some equations of state, the nonreactive Hugoniot reduces to the form of

Equation 11 with particular choices of Cr and S, This is true with the HOM equation of state

(Reference 2) used by Forest. In this case, Equation 13 can be applied to the nonreactive shockcase by proper choice of C, and S, For other equations of state, on e can derive a relation

equivalent to Equation 12 as follows. First diferentiate Equation 2d with W1 constant and

eliminate the derivative dE1 /dx1 with Equation 2c to obtain

dP dV dUt (14)- =P L-+ 2P U -dxl V dx T 1 dx

Then combine Equations 2a and 2b to eliminate U, and differentiate the result to get

-P dV dU1 (15)

lxd ri d zidU1

Eliminate dV,/dx1 between Equations 15 and 14 and solve for --- to obtain the resultdxl

dU1 Pi- (Vo - Vi)Pv dPl (16)

d 2U(PIP- P)dxl

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Substituting Equation 16 into Equation 10 to eliminate dU,/dxi and simplifying the resultwith Equation 2b gives

,[3Pz (Vo.2 - V 1P v I. •IV0P ()

W_____ dP 1 (17)

which is equivalent to Equation 13 fo r a nonreactive shock but is valid for any equation of

state.

Given the pressure rate of increase with distance, dPI/dzt, then Equation 13 or 17 maybe employed to calculate the required reaction rate (provided that P. = 0 is valid). When oneperforms an experiment where W1 and the thermodynamic state is known, then, in effect, onemeasures the reaction rate as a function of that thermodynamic state. Forest uses the wedgetest for this purpose.

In the wedge test, a shock wave is introduced into an explosive where it accelerates tobecome a detonation wave within a length called the run distance. A plot of the run distanceas a function of pressure is called a Pop plot after its originator, A. Popolato. When thelogarithm of the run distance is plotted against the logarithm of the initial shock pressure, astraight line is often obtained over a large range of pressure. These data have been obtainedfor a wide variety of explosives and detonabla propellants. For the wedge test- experimentswith initial shocks having different initial pressure - the "single-curve buildup principle" isobserved to be a good approximation. (See Reference 6 for a good discussion of this.) Thisprinciple postulates that the sbock that accelerates to detonation passes through a uniquespace-time trajectory regardlesa of the initial shock pressure. Accordingly, the Po p plot, takenfrom the results of several experiments, is also the pressure-distance history for any singletest. For a Pop plot correlation in the form of

enX :=A+BenP (18)

where A and B are constants, Xr is the run distance, and P is the initial pressure, the single-

curve buildup principle yields

dP dP (19)

dzI dX r BXr

Substituting Equation Ili into Equation 13 or Equation 17, one gets an explicit expression forthe reaction rate Wc as a function of the thermodynamic state of the material.



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REACTION KINETICS

Forest assumes that the reaction of the explosive takes place according to a simple first-order decomposition reaction. Therefore, he fits the reaction rates calculated above to thefollowing expression for first-order kinetics:

W IW = A(P) (20)

where the reaction rate constant lIP) is independent of the solid mass fraction and is

expressed solely as a function of pressure. The choice of pressure as the independent variable

for the reaction rate constant is not unique; temperature, or internal energy, or any other

combination of state variables (such as in the HYDROX computer code in Reference 7) couldhave been just as easily chosen.

The first-order kinetics formula is based on the law of mass action and is useful as aglobal model of unimolecular decomposition reactions (Reference 8). It is not clear that this isthe dominating reaction mechanism in the shock-initiated combustion of heterogeneousexplosives. There is a problem with calibrating Equation 20 at high pressures, where W% sfinite and well-behaved while W1 can become small or vanish, depending upon the choice of

the reacting shock Hugoniot. In some of the numerical hydrodynamics codes that utilizeForest Fire, the rate is set to infinity whenever the pressure becomes greater than the CJvalue. This is accomplished numerically simply by convertinG all remaining solid explosive togaseous products when the CJ pressure is 'exceeded. This feature makes application of ForestFire difficult for prob:ems where the reaction zone of the detonation wave must be resolved.

An alternate hypothesis to the first-order kinetics assumption used by Forest is theignition and growth zoncept used to describe explosive decomposition by Lee and Tarver

(Reference 9), and Tarver and Hallquist (Reference 10). The shock initiation of the

heterogeneous solid explosive is modeled by ignition at localized hot spots, followed by grainburning at the growing boundaries. This model has had some success in correlating thedetailed mass velocity profiles in the flow field behind the shock during shock-to-detonationexperiments, lending credibility to the basic concept. According to the ignition and growth

model, the global reaction rate is a minimum at the shock boundary where W1 - 1 because of

the amall burn-surface area of the hot spots. This is in direct opposition to the a.1sumption of

first-order kinetics, where the reaction is maximum at the shock.

For comparison with the first-order kinetics assumption, an alternate global model for.the explosive decomposition is

wig f(p) (21)

which ignores all dependence of the reaction rate on the solid mass fraction. In the followingcalculations, Equation 21 will be referred to as the constant rate model. This model should liesomewhere between the extremes of the ignition and growth burn model and the first-order

kinetics employed by Forest. It can be noted that Equation 21 does no t have the singuiarity

when W1 = 0, as Equation 20 does.

9



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NUMERICAL CALCULATIONS

The effect of the various assumptions employed in the Forest Fire burn model derivationare best tested numerically. The calculations will employ the explosive PBX-9404 because ofthe large amount of experimental data available fo r it. The equations and constants for theHOM equation of state for PBX-9404 are given in Reference 2. These are used except for theHugoniot of the unreacted explosive and the wedge test run distance correlation (Pop plot),

which are obtained from Reference 11.

Partially reacting Hugoniot curves with constant W, are calculated for 9404 and areplottid on the P-V plane in Figuro 2. The unreacting shock Hugoniot is the curve labeled

W1 = 1 in the figure, and the CJ point for steady detonation is labeled on the combustionproducts (Wj = 0) curve. Reacting Hugoniot curves corresponding to different choices of theconstants Crand Sr in Equation 11 can also be represented on the P-V plane. For on e choice ofthe constants, the reacting Hugoniot passes through both the initial state and the CJ point.

This Hugoniot is shown on Figure 2 and willbe

usedfo r the reacting shock example in thefollowing calculations. The explosive solid fraction W, is not constant on this curve. The

,'ariationofsolid fraction with pressure along the reacting shock Hugoniot is shown in Figure

3. The unrbacting shock Hugoniot that will be used for comparison in the calculations is the

Wy = I curve ! Fieure 2.

The reiactiin rote, Wt, was calculated using Equation 13 for both reacting andSureacting shock n'ypothese, and the result plotted in Figure 4. At low pressures, the resultsare rmarly identical. It it only at pressus near the CJ point that the reactive shock casegive* slightly higher reaction -ates. The difference between the two curves is negligiblecompered to differs.wes induced by the choice of the reaction model.

In Figure 3. the quot.ent Wv/W 1 i- plotted as a fun,.tion of pressure for both the reacting

shock cww and the nonreacting case, where for the latter W1=

1. The difference between thetwo results is suostaztial, parti,.arlý', at high pressures where, according to Figure 3, W,"", to eam us the CJ pressure is approtched. Physically, very little reaction takes place

within the shock, and the ztmrical codes where the Forest Fire burn model is employed donot include such a pbenomaenon. Thekvf•re. the assumption o a reacting shock wave used byFomet to calculal, the rnzction rates is not srtisfied in the resulting numerical calculations.

The further -sump!Joa of irst-order kinet4cs exaggerates the consequences of the reactive

shock assumption.

To compare the effect of the various assumptions and models, calculations are made ofthe run dionce obtAned in the wedge teot. A one-dimensional Lagrangian hydrodynamics

computer code was used for the cAlculations. It uses the SIN code algorithm described inReference 2.

There is some arlitraziness in a general simulation of the wedge test because of the

different types of shock attenuators and explos& e drivers actually used in the tests. These are

necessary in order to introduce shock waves of different intensities into the explosive

10



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Material. Calculations show that the run distac in the explosive depends on the shock

impedance of the attenuators. To evaluate the magnitude of this effect, Figure 6 shows run

distance calculated as a function of initial shock pressure for two extreme coves. In the first

case, the shock was produced by the impact of a plexigles flyer plate. In the second, the shockwas generated by imposing a constant velocity (a piston) upon the boundary of the explosive

material, thus simulating an infinite shock impedance. The HOM equation of state for

plexiglass (Reference 2) was used. Fo r this calculation, constant rate kinetics (Equation 21)

was used for the burn model and was fitted using the nonreacting shock Hugoniot. The run

distance for the plexiglass flyer plate in Figure 6 Is approximately 20% longer than the

corresponding distance calculated for the constant velocity piston. In the following

calculations, the plexiglass flyer is used.

The influence of the reaction model on run distafce is shown in Figure 7. The run

distance normalized by the experimental value obtained from the Pop plot is plotted against

the input shock pressure. Each of the two kinetics models is fitted to the extreme choices of

nonreacting shock Hugoniots and the reacting Hugoniot which passes throughthe CJ point.

The curves are labeled in the figure for first-order kinetics:

FF1-reacting HugoniotFF2-nonreacting shock

and for constant rate kinetics:

FF3-reacting HugoniotFF4-nonreacting shock

For the first-order kinetics model, a wide range of response can be obtained by the choice of

the reacting Hugoniot. The calculated results at low initial shock pressure, however, are not

very sensitive to the kinetic model or its calibration. This is because the solid mass fraction isnearly unity at low pressures on the reacting Hugoniot used for the calibration, and this

condition is obtained for most of the run distance.

The difference in behavior of thei different models is most extreme at the high-pressure

end. This pressure region im f importance in physical problems where the detonation reaction

zone must be resolved. These problems include, for example, critical diameter, response to

thin, high-speed flyer plates, an d minimum priming charge tests. Any calculation of these

types of problems using a variation of the Forest Fire burn model should be viewed

skeptically until thorough experimental verification is obtained.

One consequence of the constant rate kinetics model is that its implementation is more

automatic than the first-order kinetics model. The range of calculated run distance shown in

Figure ? is much lIe between the reacting and nonreacting choices of Hugoniot. This meansthat one can get a good correlation with the wedge test experiment with a minimum of

guessing at reacting Hugoniots. In this regard, however, it can be noted from FIgure 7 that

the constant rate curves, FF3 and FF4, are reasonably straight lines, so some improvement

could be obtained by artificially modifying the input Pop plot.

15



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10

S 0 PLEXIGLASS FLYER

6+ PISTON

4-

3 0

2-

1.0-

0.8-

0.6 "

LU0.4-

0.3-

0.2 ml+

0.100.08-

0.06- +

0.04- +

0.03-- +

0.02-0

0.01,10 100 1000

PRESSURE, kber

FIGURE 6 Wedge Tes't Simulation Showing Effect of Flyer Plate Impedance.



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4.0

3.0-

2.0F

FF4

m.0MM Go Mýv m o M mm-mm

0.7- FF 1

10 20 30 40 60 80 100 200 300 400

PRESSURE, kbar

FIGURE 7. Effovt ifu Rea~ctive fHugoniot Assumption and Reaction KineticsModel on Wedge Test Simulated by a Plexiglas F'lyer Plate.



ZNWC TP 6898

In the course of making the calculations, plots of pressure profiles of the reactive flowwere made. Initially the pressure gradient was quite small and P : 0 appeared to be a valid

assumption. However, at later times, after a period of shock acceleration, a very strong

gradient developed. This being the case,it

is not clearwhy

the Forest Fire burnmodel

gives

such good overall agreement for the wedge test run distance. If on e examines individual

ezperimental wave trajectories corresponding to different initial shock pressure to verify thesingle-curve buildup principle, one finds curves of wave velocity, Us, plotted against waveposition, X1, which all lie in a narrow band. However, individual shock-wave accelerations

within this band can deviate substantially from the mean and from one another. One canspeculate that input of an average shock trajectory will yield a good prediction of global

results like run distance, even though details of the process may be erroneous.

CONCLUSIONS

The reaction rate, Wg, expressed as a function of pressure, is not sensitive to the choice ofreactive or nonreactive Hugoniot used in its calibration. The choice becomes important whenthe formula for first-order kinetics is assumed to express the rate. With the first-order

kinetics formula calibrated first using the extreme reactive and then the nonreactiveHugoniot, the calculated wedge test results bracket the experimental results. One cantherefore fine-tune the agreement with experiment by adjusting the choice of reactive

Hugoniot. The drawback to this approach is that neither the first-order kinetics nor thereactive Hugoniot has any physical relation to shock-initiated burning in heterogeneousexplosive. A simpler constant reaction rate approach is suggested that avoids the difficultiesofchoosing an unphysical reactive Hugoniot while giving a satisfactory correlation with thewedge test results.

Calculations of wedge teat results at low initial shock pressure were basicallyinsensitive to the kinetic model and the Hugoniot used in its calibration. The differences werequite large, however, for wedge test calculations starting with high initial shock pressures.

The reason is that at low pressure, the solid mass fraction is nearly one for most of the rundistance. Under this circumstance, there is no essential difference between the variousreaction models and their calibration.

The Forest Fire burn law as formulated by Forest is not applicable to high-pressurephenomena where the pressure may exceed the CJ value. This situation is obtained, for

example, whenever the reaction zone in a detonation must be resolved. The constant rateapproach discussed here may be a reasonable way to extrapolate moderate pressure reactionrates to pressures greater than the CJ value. The validity of this approach needs to be tested.

18



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REFERENCES

1. Los Alamos Scientific Laboratory. "Two-Dimensional Homogeneous and Heterogeneous

Detonation Wave Propagation,* by C. L. Mader and C. A. Forest. Los Alamos, N. Mex.,

LASL, June 1976. (LA-6259, publication UNCLASSIFIED.)

2. Charles L. Mader. Numerical Modeling of Detonations.Berkeley and Los Angeles,

University of California Pres, 1979.

3. A. L. Bowman, C. A. Forest, J. D. Kershner, C. L. Mader, and G.H. Pimbley. "Numerical

Modeling of Shock Sensitivity Experiments," Proceedingsof the Seventh Symposium

(International) on Detonation, June 1981. (NSWC MP-82-334, publicationUNCLASSIFIED.)

4. U.S. Army Ballistic Research Laboratories. "Numerical Modeling of Projectile Impact

Shock Initiation of Bare and Covered Composition B," by J. Starkenberg, Y. Huang, an dA. Arbuckle. Aberdeen Proving Ground, Md., BRL, August 1984. (ARBRL-TR-02576,publication UNCLASSIFIED.)

5. C. A. Forest. "Burning and Detonation," Proceedings of the Seventh Symposium(Jnternational) on Detonation, June 1981. (NSWC MP-82-334, publication

UNCLASSIFIED.)

6. J. J. Dick. "B'4ldup to Detonation in Solid High Explosives During Plane Shock

Initiation: Some Comparisons," Proceedings of the Eighteenth Symposium(International) on Combustion,1981.

7. Los Alamos Scientific Laboratory. "HYDROX, A One-Dimensional Lagrangian

Hydrodynamics Code,' by M. S. Shaw an d G. K. Straub. Los Alamos, N. Mex., LASL,March 1981. (LA-8642-M, publication UNCLASSIFIED.)

8. V. N. Kondrat'ev. Chemical Kinetics of Gas Reactions. New York, Pergamon Press,

1964.

9. E. L. Lee and C. M. Tarver. "Phenomenological Model of Shock Initiation inHeterogeneous Explosives," Phys.Fluids,Vol. 23 (1980), p. 2382.

10. C. M.Tarver and J. 0. Hallquist. "Modeling Two-Dimensional Shock Initiation andDetonation Wave Phenomena in PBX 9404 and LX-17," Proceedings of the Seuenth

Symposium (International) n Detonation,June 1981. (NSWC MP-82-334, publicationUNCLASSIFIED.)

11 . T. R.Gibbs and A. Popolato. LASL Explosive PropertyData.Berkeley and Los Angeles,

University of California Press, 1980.

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9 NavalI AM SYstim ComandAZ-S0 (2)AU-50O (2)

A (2)AM.-920 (1)AM-932J, D. Warren (1)Am-,32X (1)

6 9%l4 of Naval Operatins.

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1 Cora nieri Q/lat, U. S. Pacific Fleet (Code 325)SAirest nd Imaluati Squadron 53, hdm Lawe

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1 Davi~d ?awo Naval Si ckCeter, metheeda2 NAMMl Acaemys, !Vaq118(Direcotr of Research)I Naval Air F e•eet

2 Naval Air Fons, Pasific FloetI Naval Air Stati.m, North Il.md2 Naval Ai Zest a t River (Caotral Library)1 Rsafl Avionics Center, Induianpolis (Technical Librery)I Naval IXplosive Orbmce Dsoa Technology Center, Indian Heed1 Naval 0cmf systems Center, Sai Dieg (Code1 Naval *rdamuem Station, Infian noew (T brezcy)1 Naval Postgraduate School, Monterey (Tiechnical, Library, G. Kinney)1 Naval Rese•arc Laboratory (A. Villi•-)4 Naval Surface warfare Center, DaligrSM

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10 a ýSa•ae, White Oak Laboratory, Silver SpringRiO

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Odded Missile Waread Section (1)Technica Library (1)

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1 yawl WC1olle1e, NeWPOtI Offfte of *Ma 3*sserch Detacmt (Pasadena) Pasadenat Office of W l Tecmalop, Arlington (01-2051 Operatioml Test mad Ivaluati.n Force, Atlantic2 Pacific Nissile Test Center, Point NuW

Code 1245, Nofrey (1)Techai"a Library (1)

I or~ime Coa" Air Staticn, Beaufort1 AW Armmzt meition and ammica Coamad, Rock island (DJSAR-LZP-L, Technical

Library)3A= Nissile C0e0ad, Resnwe Arsenal

DAZD-B-SST, J. utland (1)I Aberdee Proving Groa• (DeOWSvPInt and Proof Ser-csm)

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