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ROBERT FKANK HARVEY

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A COMPUTER WAR GAME FOR DETERMINING THE

COST-EFFECTIVENESS OF ACTIVE SONOBUOYS

by

Robert Frank Harvey-

Lieutenant, United States NavyB. A. , State University of Iowa, 1957

Submitted in partial fulfillment of the

requirements for the degree of

MASTER OF SCIENCE IN OPERATIONS RESEARCH

from the

NAVAL POSTGRADUATE SCHOOL

June 1967

I

ABSTRACT

In order to evaluate the relative effectiveness of different active

non-directional sonobuoys, a computer war game is developed. One

submarine, employing one evasion tactic, is opposed by one helicopter,

using five prosecution tactics. The tactic of the helicopter prior to the

initial detection of the submarine is seen to be critical, and this simu-

lation aids in determining an optimum tactic.

A cost-effectiveness model to use data from this simulation is

developed.

An example, using hypothetical but realistic data, is presented

to illustrate methods of determining the cost-effectiveness of each

sonobuoy type when used with its optimum tactic.

TABLE OF CONTENTS

CHAPTER PAGE

I. INTRODUCTION 7

The Problem 7

Review of the Literature 8

Organization of Remainder of Thesis 9

II. TACTICS SIMULATION 10

Purpose of the Model 10

Description of Simulation 11

Assumptions Made 12

III. INPUT INSTRUCTION 16

IV. OUTPUT DESCRIPTION 19

V. COST-EFFECTIVENESS EXAMPLE 22

The Assumed Problem 22

Result Desired 22

Use of Simulation Model 23

Cost-Effectiveness Model 28

Results of Example Problem 29

VI. SUMMARY AND CONCLUSIONS 34

Summary 34

Conclusions 34

BIBLIOGRAPHY 36

APPENDIX A. General Flow Charts 37

APPENDIX B. Dictionary of Program Names 48

CHAPTER PAGE

APPENDIX C. Computer Program in FORTRAN 63 53

APPENDIX D. Statistical Examination of Model 69

Random Numbers 69

Probability of Detection 71

APPENDIX E. Analysis of Model's Logic 74

LIST OF ILLUSTRATIONS

FIGURE PAGE

1. Input Data Descriptions 17

2. Main types of Output from Program 20

3. A Supplementary Output for Analysis of Random

Numbers 21

4. Probability of Detection by the SQS-AA 25

5. Probability of Detection by the SQS-XX 26

6. Probability of Detection by the SQS-YY 27

7. Costs of Three Sonobuoy Types 30

8. Data for the Cost-Effectiveness Model 32

9. Main Program Flow Chart 37

10. Helicopter-Sonobuoy Detection Subroutine Flow

Chart 38

11. Submarine Detection Subroutine Flow Chart 39

12. Helicopter Initial Tactic Subroutine Flow Chart 40

13. Helicopter Tactic-One-Ring Subroutine Flow Chart 41

14. Helicopter Tactic-Two-Ring Subroutine Flow Chart 42

15. Helicopter Tactic-Three-Ring Subroutine Flow

Chart 4 3

16. Helicopter Square Search Subroutine Flow Chart 44

17. Submarine First Tactic and Second Tactic Sub-

routine Flow Charts 45

18. Sonobuoy Economizing Subroutine Flow Chart 46

FIGURE PAGE

19. Random Number Test Subroutine Flow Chart 47

20. A Play which the Helicopter "Won" 75

CHAPTER I

INTRODUCTION

The United States Navy currently uses many types of devices in the

search for, and the localization and destruction of, enemy submarines.

The sonobuoy, which is an air-dropped, expendable, sonar capable

of relaying its findings to the aircraft, is one such device. A particular

type is the active non-directional sonobuoy, which sends a pulse of

sound into the water, and transmits the sound of that pulse and the

sound of an echo pulse from a possible submarine to the aircraft via

radio. From the difference in the two times, the range of the submarine

from the sonobuoy can be determined. The locus of the submarine's

possible positions is a hemisphere of that radius about the sonobuoy.

In the Summer of 1966, while working with the Systems Analysis

Staff of the Antisubmarine Warfare Systems Project Office, the author

encountered the problem of developing a method of comparing the costs

and effectiveness of several types of such active sonobuoys some of

which were currently in use in the fleet and others of which were under

consideration for future use.

The precursor of this model was originally developed and used to

solve the effectiveness part of the problem, and has been further devel-

oped since then.

I. THE PROBLEM

A new anti submarine warfare (ASW) helicopter was being designed

and to increase the effectiveness of the helicopter as an ASW fighting

unit, the vehicle, its sensing equipment, and its kill device were being

considered as a package. The kill device had been previously developed

and was suitable for this helicopter. One sensing device had been incor-

porated into the helicopter. It was a magnetic anomaly detection (MAD)

unit streamed behind the helicopter on a cable. When operated at a low

altitude it can detect an anomaly in the earth's magnetic field caused by

the presence of a steel submarine. MAD is a subsidiary sensing device,

and is not adequate for localization when used by itself.

The main device was to be an active sonobuoy system consisting of

sonobuoys and equipment in the helicopter to process the data radioed

from the sonobuoys. This system was under study and various compet-

ing systems of sonobuoys were to be evaluated. A system consists of

the sonobuoys and airborne receiving and processing equipment neces-

sary for the effective use of the sonobuoys.

II. REVIEW OF THE LITERATURE

In determining whether or not a satisfactory model had been devel-

oped by another agency the Defense Documentation Center was consulted

since it is the repository of technical publications for the Defense

Department. The Naval Postgraduate School library was searched

because student theses frequently deal with similar problems. The

Applied Physics Laboratory of Johns Hopkins University was consulted

since many ASW models have been developed there. Also checked was

Navy War Game Manual and its classified supplement.

All searches indicated that no model had been developed to handle

this problem.

8

IE. ORGANIZATION OF REMAINDER OF THESIS

A description of the model, its purpose and assumptions will be pre-

sented next, then input instructions for running the computer program

and a description of the output data will follow.

A cost-effectiveness example using hypothetical data will be followed

by a summary and conclusions.

The Bibliography is followed by an Appendix presenting flow charts,

definitions of program names, the computer program in FORTRAN 63, a

statistical examination of two critical aspects of the model, and the

results of an analysis of the model's logic.

CHAPTER II

TACTICS SIMULATION

Simulation was chosen because the problem was so complex that no

mathematical model known to the author could handle it.

One helicopter against one submarine was used, the assumption be-

ing that this was the most likely combination to occur.

From the analytic insight obtained by devising and playing a manual

war game based on the author's tactical experience in ASW, it quickly

became apparent that the helicopters tactics were so important as to

overwhelm all other parameters except the range of the sonobuoy.

It was decided to write a computer time- step simulation to evaluate

the optimum tactic of the helicopter for each model of sonobuoy. Then

the same program could be used to compare sonobuoy systems, using

the optimum tactic for each. Here, tactic is defined as the laying of a

pattern of sonobuoys on the water. The initial tactic is to lay a pattern

of sonobuoys which is prescribed by doctrine for such an occasion. The

pilot would continue it to completion unless a detection were obtained by

one or more sonobuoys in the pattern. Subsequent tactics would depend

upon the information received from the sonobuoys.

I. PURPOSE OF THE MODEL

The model has two functions. The first is to determine an optimum

initial tactic to be used with each model of sonobuoy. The second is to

determine the cost-effectiveness of each model of sonobuoy using the

optimum initial tactic for that model.

10

II. DESCRIPTION OF SIMULATION

The submarine's initial position is generated at random in a square

of size determined by the user. Its course is also generated randomly.

It pursues that course at its patrol speed until three conditions have been

met: (1) the light-off time of at least one sonobuoy has occurred, (2)

the present time, in seconds, is a multiple of thirty, and (3) the submar-

ine is within twice the input range of the sonobuoy from one or more

sonobuoys. At that time, it changes course to the reciprocal of the

average bearing to the sonobuoys which satisfy the above requirements.

At the time of the first detection of a sonobuoy by the submarine, the

submarine doubles its speed and stays at that speed the remainder of the

play (replication).

The helicopter starts at its input position and flies at its input speed

toward the first input sonobuoy coordinates. When it reaches that posi-

tion it drops a sonobuoy and alters course toward the second input sono-

buoy coordinates. The light-off time of the sonobuoy is 180 seconds after

the time of the drop. The helicopter continues this sequence untiliit has

dropped the input number of sonobuoys in the initial tactic or until at

least one sonobuoy has achieved detection. In the first case, it then flies

a square search of side . 2 miles about the last sonobuoy coordinates.

It has been determined by analysis that this square is the helicopter's

optimum MAD entrapment tactic. In the second case it abandons the

tactic, not to return to it again, and commences TAC1, TAC2, or TAC3.

The detections occur as follows. Every thirty seconds a check is

made to see if the helicopter is within MAD range of the submarine.

11

If so, the replication ends in favor of the helicopter and a value of one

is assigned as the outcome of that replication. If no detection occurs

the game continues. Every thirty seconds all sonobuoys which have

lighted off are checked to see if the submarine is within sonobuoy detec-

tion range. The coordinates of the sonobuoys achieving detection and

their distances from the submarine, up to a total of three sonobuoys,

are recorded.

In the following description the term "ring" will refer to a circle

whose center is at a sonobuoy and whose radius is the detection range

of the sonobuoy.

If the helicopter gets information from only one sonobuoy, it checks

to see if it, the helicopter, is inside the ring. If so, it proceeds out-

ward from the sonobuoy to the ring, drops a sonobuoy, goes to the

opposite arc via the center and drops another sonobuoy. It then com-

mences a square search about the last sonobuoy.

The phrase "drops a sonobuoy" used anywhere except in TACA

means that subroutine ECON is called and, if no sonobuoy is within one-

half of its detection range from the helicopter at the position at which it

is ready to drop, a sonobuoy is dropped there. If none is dropped the

helicopter continues its current tactic.

If the helicopter receives information from two sonobuoys simultan-

eously, it flies to the nearest point of intersection of the two rings, drops

a sonobuoy, proceeds to the second intersection, drops another sonobuoy,

then flies a square search about the last.

12

If it receives information from three sonobuoys simultaneously it

proceeds to the point of mutual intersection of the three rings, drops a

sonobuoy, and flies a square seach about that position.

While the above is happening, every thirty seconds the sonobuoys

which have lighted off are being checked for information. If no sonobuoy

is acheiving detection, the current tactic continues. If one, two, or at

least three sonobuoys are achieving detection, the one, two, or three

ring tactic, respectively, is used. No information from any previous

tactic is used in this case.

If the submarine input escape time occurs the play ends in favor of

the submarine and a value of zero is assigned as the outcome of that

replication.

IK. ASSUMPTIONS MADE

Of the many assumptions made in adapting a computer model to

reality, the following major ones are listed.

A. Helicopter

1. The single helicopter starts from its initial position with

the crew knowing that there is a possible submarine within an

area about datum which is an input for each game.

2. The helicopter is crewed by reasoning persons whose goal

is to achieve MAD detection as quickly and using as few sono-

buoys as possible.

3. The helicopter, at the end of each tactic during which no

new information came in, flies a square search. When this is

13

done in the initial tactic and in the tactic which results from

only one sonobuoy achieving detection (one-ring tactic), it is

assumed to be waiting for information. This is equivalent to

random MAD in a "real" helicopter. In the two-ring and three-

ring tactics it is trying to entrap the submarine to achieve MAD

detection.

B. Submarine

1. At the start of play the submarine is proceeding on a straight

course toward an objective, submerged and at patrol speed,

unaware that the search phase detection has been made.

2. Upon first detecting an active sonobuoy, the submarine

skipper realizes he is being prosecuted by an aircraft dropping

active sonobuoys in his vicinity. He changes his short term

objective to eluding the aircraft, believing that if he manages

to escape detection for a short time he will be able to escape

the aircraft and resume his original objective. He therefore

doubles his speed and attempts to elude all sonobuoys by taking

as his course the reciprocal of the average bearing to all sono-

buoys which have commenced emitting sound (have "lighted off")

and which are within his detection range. Thereafter he com-

putes his course anew each time new data comes in, but keeps

his speed constant.

C. Sonobuoy

1. The sonobuoy has a "cooky cutter" probability distribution

function.

14

2. It has a three minute light -off time.

3. All survive impact with the water and achieve ranges which

are predictable.

D. MAD

1. The MAD gear has a "cooky cutter" probability distribution

function.

2. The gear is unaffected by helicopter maneuvering.

3. The gear achieves ranges which are predictable.

E. Other Assumptions

1. Both the helicopter and submarine make pinpoint and

instantaneous turns.

2. The water has constant and uniform properties.

3. Both the helicopter and the submarine have limitations upon

the speed with which they may receive, process, and act on

new data. The game was written so that new data can be acted

on every thirty seconds of play.

4. Ranges from the helicopter to the submarine and from the

sonobuoy transducer to the submarine are considered horizontal

ranges, not slant ranges. This simplifying assumption approxi-

mates the case of a helicopter at low altitude, and the sonobuoy

transducer and submarine at the same shallow depth.

15

CHAPTER III

INPUT INSTRUCTIONS

The input to this program is relatively simple. A maximum of 214

items is to be read in. One is the title of the data set, thirteen are

various performance parameters and miscellaneous items, and there

are up to 200 X and Y coordinates of sonobuoys. A maximum of 100

sonobuoys is allowed for the total used in all tactics of a single replica-

tion.

Figure 1 presents the card number, width of fields in terms of

columns, and a description of each field or group of fields.

16

Card Columns Format Description

1 1-12 2A6 Any alpha-numeric character may be usedto designate data set number.

2 1-5 F5. 1 VH = the speed of the helicopter in knots.

2 6-10 F5.1 VSS = the patrol speed of the submarine in

knots.

2 11-15 F5. 1 BRING = one-half of the side of a square,

centered on datum, in which the submarinemust start.

2 16-20 F5. 1 XHH = the helicopter's starting x coordinate

in nautical miles from datum, where(x,y) = (o, o) is datum.

2 21-25 F5. 1 YHH = the helicopter's starting y coordinate

in nautical miles from datum.

2 26-30 F5. 1 TMAX = the ex-e-a£e time of the submarinein hours.

2 31-35 F5. 1 RMAD = the radius of the MAD gear in

nautical miles.

2 36-40 F5. 1 RSB = the radius of the sonobuoy detecting

capability in nautical miles.

2 41-51 010 IIR = the starting argument for the randomnumber generator, in octal.

3 1-10 110 NSB = the number of sonobuoys in the initial

tactic.

3 11-20 110 NREP = the number of replications desiredin one game.

3 21-30 110 KTEST: If zero, no statistical testing of

random numbers will occur; K any posi-

tive integer is placed here, testing will

occur.

FIGURE 1

INPUT DATA DESCRIPTION

17

Card Columns Format Description

3 31-40 110 NRAN = the number of random numbers to

be tested.

4 1-5 F5. 1 A(2) = the x coordinate at which the first

sonobuoy in the initial tactic will be

dropped, in nautical miles from datum.

4 6-10 F5. 1 B(2) = the y coor dinate of the first sono-

buoy.

4 11-80 7F5. 1 x and y coordinates of sonobuoys two through

eight.

5-12 1-80 8F5. 1 As above for sonobuoys nine through sixteen

etc. , to a total of 100 sets of (x, y) coordin-

ates if desired. The number of (x,y)

coordinate sets must agree with NSB on

card 3.

FIGURE 1 (CONTINUED)

18

CHAPTER IV

OUTPUT DESCRIPTION

There are three main and one supplementary outputs from this

program.

A read-out of the input parameters, as explained in Figure 1, is

illustrated in Figure 2(a). This is printed before the first replication

starts.

At the end of each replication four lines are printed. The first is

"outcome of this replication" and a 1.00 signifies a helicopter win,

while a . 00 signifies a submarine win. The other three are "number of

sonobuoys used," "game hours to completion," and "number of this

replication. " These are illustrated in Figure 2(b).

At the end of the entire game four more lines are printed; "average

probability of detection, " "average number of sonobuoys used, " "average

game hours to completion," and "number of replications in the game".

Figure 2(c) illustrates these lines.

If the random numbers generated are examined, a listing of signifi-

cant statistical information is made. The lists are "interval", "number

in this interval", "mean", "sample mean", and "sample variance".

These are shown in Figure 3 for the value IIR = 47532352.

19

TACTICS 10

120.0 6.0 4.0 0-20.0 1.0 .2 3.0 475323525 1 1 1355

-4. 4. 4. -4.

(a)

OUTCOME OF THIS REPLICATION = 1. 00

NUMBER OF SONOBUOYS USED = 3

GAME HOURS TO COMPLETION = . 27

NUMBER OF THIS REPLICATION = 1

(b)

AVERAGE PROBABILITY OF DETECTION = .18

AVERAGE NUMBER OF SONOBUOYS USED = 14.27

AVERAGE GAME HOURS TO COMPLETION = .75

NUMBER OF REPLICATIONS IN GAME = 271

(c)

FIGURE 2

MAIN TYPES OF OUTPUT FROM PROGRAM:(a) INPUT ;DATA; '(B)f DATA FROM ONEREPLICATION AND; (c) AVERAGE DATAFOR GAME

20

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21

CHAPTER V

COST -EFFECTIVENESS EXAMPLE

This simulation model can be used to determine an optimum initial

tactic for use with a given model sonobuoy system. Another use is to de-

termine the cost-effectiveness of different active non-directional sonobuoy

systems by first finding the optimum initial tactic for each, then compar-

ing the outputs "average probability of detection"and"average number of

sonobuoys used" together with cost information in a cost-effectiveness

model to aid in deciding among the competing sonobuoy systems.

All sonobuoys and their performance data, all output data, and all

costs are hypothetical but realistic.

I THE ASSUMED PROBLEM

One active sonobuoy, the SQS-AA, is in current use in the fleet. A

new helicopter is being developed and the main sensing device for it

could be one of two sonobuoys, the SQS-XX and the SQS-YY, currently

in the research phase. Only theoretical performance data is available

for thellatter two, while for the former both theoretical performance,

developed in the research phase, and observed performance data,

recorded in use, are available.

For the SQS-AA two cost studies are available: The initial study for

the proposed new sonobuoy SQS-AA, done in 1957; a follow up study on

the sonobuoy after it had been in the fleet one year, done in 1962.

Only one cost study is available for each of the SQS-XX and SQS-YY

sonobuoys; the initial studies, done in 1967.

II RESULT DESIRED

The solution to the problem will aid in determining which of the

proposed new sonobuoys, if either , should enter into the development phase.

22

Ill USE OF SIMULATION MODELi

i

The theoretical performance data for the SOS-AA has been used

because the methods used to determine it correspond to the methods

used to determine performance data for the SQS-XX and SQS-YY.

The following scenario was selected. An unidentified submarine is

detected by a shore unit and is determined to be within an area approxi-

mated by a square of certain input dimensions. That area is near a

convoy which has a destroyer based helicopter in the air to serve as a

"pouncer" aircraft. The helicopter is vectored to the area and starts a

localization process as described in chapter II, using tactics which are

systematically varied in a series of games.

First one sonobuoy, the SQS-AA, is evaluated. Its performance

data is put into the program together with a likely initial tactic which,

as previously, stated, is a set of sonobuoy coordinates. The other input

parameters are introduced now and will remain the same for all replica-

tions of all games of the series.

The first replication commences and the computer generates the

submarine starting position within the square, and its course at random.

Then the computer "moves" the helicopter and submarine until either

"wins" a play. That terminates one replication of one game. For the

next replication only the submarine's starting coordinates and course

are different. After a preset, input, number of replications, various

important data is averaged and presented on the output sheet. Then the

next set of input data is introduced to start a new game. This might

23

differ from the first set, for example, only in the radius of the pattern

of sonobuoys in the initial tactic.

This process is continued until all sonobuoys, used with all tactics

likely to bring success to the helicopter, have been investigated. The

best tactic for each is determined by graphing (average) probability of

detection against any other significant parameter desired. For example,

in figure 4 the radius of the sonobuoy pattern about datum was chosen.

Figure 4(a) shows those two tactics plotted for all tactics which utilized

the SOS-AA against conventional submarines of six knots patrol speed

and twelve knot "escape" speed. Figure 4(b) shows the same for nuclear

submarines of fifteen knot patrol speed and thirty knot escape speed.

Figures 5 and 6 show the same type of graphs for the SQS-XX and

SQS-YY respectively. The circular pattern of sonobuoys yields the

highest probability of detection of the three types of tactics considered.

Since the maximum ordinate on the graph falls at significantly different

radii for conventional and nuclear submarines, the study would indicate

different tactics against the two types of submarines. Both would

employ the circular pattern but at different radii. Consequently, in the

cost-effectiveness model to follow, the probability of detection for con-

i

ventional and nuclear submarines will be dealth with separately. Note:

These graphs are hypothetical but are similar to classified production

runs made with this model.

This ends the effectiveness portion of the model and could be a

separate tactics study of itself. However the optimum tactic,

24

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Radius of pattern in nautical miles

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Radius of pattern in nautical miles

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FIGURE k

PROBABILITY OF DETECTION OF (a) CONVENTIONALAND (b) MJCLEAH SUBMARINES BY THE SQS-AA

25

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circular pattern

circular pluscenter sonobuoy

Radius of pattern in nautical miles(b)

FIGURE 5

PROBABILITY OF DETECTION OF (a) CONVENTIONALAND (b) NUCLSAR SUBMARINES BY THE SQS-XX

26

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Radius of pattern in nautical miles(b)

FIGURE 6

PROBABILITY Of DETECTION OF (a) CONVENTIONALAND (b) NUCL \R SUBMARINES BY THE SQS-YY

27

probability of detection, and average number of sonobuoys used provide

data for a cost-effectiveness study.

IV COST -EFFECTIVENESS MODEL

The initial cost studies on all three sonobuoys were selected for

comparison purposes. Each study employs the ten year system cost

technique. Build-up costs are negligible, since the forces which are

to operate the equipment are already operating other sensing equip-

ment which would be supplanted by the new sonobuoy systems.

The ten year figure is arrived at by estimating that the sensor

would be replaced entirely by another within ten years.

The cost of the aircraft to carry the sonobuoy is ignored since the

aircraft cost is added in at a higher level of analysis. Note that the

original aircraft which carried the SQS-AA was fixed wing while the

type envisioned for the SQS-XX or SQS-YY is rotary winged. However

this model works equally well for fixed wing and rotary wing aircraft,

the only difference being in the input speeds of the two types.

The cost-effectiveness model and the terms used in it are as

follows.

P . = Probability of detection of a conventional submarine by i

—

sonobuoy type.

P_. = Probability of detection of a nuclear submarine by the i

—

sonobuoy type.

i = 1 refers to the SQS-AA

i = 2 refers to the SQS-XX

i = 3 refers to the SQS-YY

28

A = That fraction of the enemy's subsurface fleet devoted to conven-

tional submarines in the 1970 decade.

A = That fraction of the enemy's subsurface fleet devoted to nuclear

submarines in the 1970 decade.i

(Al+ A

2= 1)

S . = The number of sonobuoys of the i— type used by the helicopterli

in its optimum tactic against conventional submarines.

S_. = The number of sonobuoys of the i— type used by the helicopter

in its optimum tactic against nuclear submarines.

thC. = Cost per unit of the i— sonobuoy type as tabulated in column (3)

of figure 7.

(C/E).= Cost per unit of effectiveness of the i— sonobuoy type where

effectiveness is defined later in this section.

(C/E).= (A.S.. + A_S_.) ^AP +A.P-.2 2i s^ 1 li 2 2i

A1P11

+ A2P21

C.i

(i = 1, 2, 3,)

V RESULTS OF EXAMPLE PROBLEM

The breakdown of the costs for each model is shown in Figure 7,

where all numbers represent millions of dollars. Column (1), Research

and Development, is self explanatory. Column (2), Initial Investment,

represents the cost of tooling up and producing the estimated number of

sonobuoys needed for ten years use, listed in column (7). Annual

Operations, Column (3), is the average cost of storing and maintaining

the dwindling supply of sonobuoys for one year, while column (4) repre-

sents those costs for the ten year study period. Column (5) is the sum

29

(1) (2) (3) (4)

Type Research and Initial Annual AnnualDevelopment Investment Operations Operations

Times Ten

SQS-AA $ .1 $ 1.8 $ . 08 $ . 8

SQS-XX . 3 7. 8 . 21 2. 1

SQS-YY .4 9.4 . 32 3. 2

(5) (6) (7) (8)

Type Cost of Ten Cost in 1967 Number of Cost perYear System Dollars Sonobuoys

to be Pro-duced and

Used.

Sonobuoy

SQS-AA $ 2. 7 $ 3. 6 40,000 $ 90

SQS-XX 10.2 10.2 60,000 ] 170

SQS-YY 13. 13. 60,000 217

FIGURE 7

COST OF THREE SONOBUOY TYPES(IN MILLIONS OF DOLLARS)

30

of columns (1), (2), and (4). It represents the ten year system cost in

1957 dollars for the SQS-AA, and 1967 dollars for the SQS-XX and

SQS-YY. In column (6) all costs are in 1967 dollars, where the annual

inflation between 1957 and 1967 was determined to be 3%. Column (8) is

the ratio of the entries in column (6) to the entries in column (7), and

represents the cost of one sonobuoy for each of the three models.

Figure 8 tabulates the numbers needed for the cost-effectiveness

model presented in section IV of this chapter, Columns (1), (2), and (3)

are taken from Figures 4, 5, and 6, and represent the Probability of

Detection for nuclear and conventional submarines when the optimum

tactics are used.

In the decade 1970-1980, during which this system would be

employed, it is estimated that the enemy will have a mix of six conven-

tional submarines for every four nuclear. So A = . 6 and A = . 4.

Column (3) then, is the weighted mean of the items in columns (1) and

(2). Columns (4) and (5) are the Average Number of Sonobuoys needed

for the tactic chosen, and column (6) shows the weighted mean of the

numbers in the previous two columns.

In column (7) the SQS-AA weighted mean probability of detection

from column (3) is defined to be one unit of effectiveness and the effec-

tiveness of the other two sonobuoys are computed in relation to it by

dividing the entries in column (3) by .074 to obtain column (7). In

column (8), the ratios of the respective entries in columns (6) and (7)

are listed, and represent the number of sonobuoys needed for one unit

of effectiveness.

31

(1) (2) (3) (4) (5)

i Type Pli

P2i

A.P, .+A P .

l li 2 2iSli

S_.2i

1 SQS-AA . 11 . 02 .074 10 18.

2 SQS-XX . 18 . 10 . 148 19 13

3 SQS-YY . 30 . 12 . 228 7 9

(6) (?) (8) (9) (10)

i Type A S..+A111 2

=x

2iA P +A P

1 li 2 2i

A1P11+A

2P21

=y

X

y

Ci (C/E)i

i SQS-AA 13.2 i. 13. 2 $ 90 $1190

2 SQS-XX 11. 2 2.00 5. 60 170 952

3 SQS-YY 7. 8 3.08 2. 53 217 549

FIGURE 8

DATA FOR THE COST -EFFECTIVENESS MODEL

32

Column (9) lists the cost per unit of each type of sonobuoy as listed

in column (8) of Figure 7. Column (10) is the product of the items in

columns (8) and (9) and is the desired result.

Using the criteria "Minimize Cost Per Unit Effectiveness", the

SQS-YY would emerge as the "best buy" despite its higher cost. This is

in consonance with intuition because its range of detection as input to the

program was approximately four times that of the SQS-AA, and twice

that of the SQS-XX.

*

.

33

CHAPTER VI

SUMMARY AND CONCLUSIONS

I SUMMARY

The problem was to find a means of comparing active sonobuoys of

different performance and cost, and find a way to determine the relative

cost-effectiveness of each type. From playing manual war games in

which one helicopter was pitted against one submarine, it became

apparent that the initial tactics employed by the helicopter were of para-

mount importance in determining the effectiveness of each type sonobuoy,

and yet the "optimal" tactic for each was not known.

A computer war game utilizing Monte Carlo technique was written

when it was discovered that there was no model available in the litera-

ture to test tactics for active sonobuoys.

The model is documented in chapters II through IV, and is illustrat-

ed by means of a complete cost-effectiveness example in chapter V.

II CONCLUSIONS

The computer war game developed is capable of doing two main

tasks.

It will evaluate the tactics of any aircraft using active sonobuoys

so as to arrive at one or more useful tactics for each type sonobuoy

studied.

Once the optimum tactic is decided upon, the numbers of sonobuoys

used for each type may be used, together with cost information, to

compare the sonobuoy types for cost-effectiveness.

34

The model has been thoroughly analysed by the statistical and

geometrical methods presented in the Appendices. In addition ten hours

of production runs yielded preliminary data which approximately agreed

with the manual war games and coincided both with intuition and experi-

ence. That data is classified secret and has not been included in this

unclassified report, which concentrates on the underlying technique.

35

BIBLIOGRAPHY

1. Andrus, Alvin F. A Mine Sweeper Computer Simulation. Monterey,

California: Naval Postgraduate School Technical Report/

Research Paper No. 64, 1966

2. Campbell, William F. Form and Style in Theses Writing . Boston,

Massachusetts: Houghton Mifflin Company, 1954

3. McCraken, Daniel D. , and Dorn, William S. Numerical Methods

and Fortran Programming . New York: John Wiley and Sons,

Inc. , 1964

4. Mood, Alexander M. , and Graybill, Franklin A. Introduction to

the Theory of Statistics . New York: McGraw-Hill Book

Company, Inc. , 1963.

5. Parzen, Emanual. Modern Probability Theory and Its Application.

New York: John Wiley and Sons, Inc. , I960.

6. Tiedeman, John A. "Digital Program for Surface Missile System

Expected Kill Analysis. " Unpublished paper, Naval Postgraduate

School, Monterey, California, 1967.

36

APPENDIX A

GENERAL FLOW CHARTS

END —

—

(input CARDS

>

HEAD A..D ..RITE INPUTS WRITE RESULTS

GENERATE SUBM RiNECOORDINATES AND CUU ibE

\

CALLTACN

CALLT \CM

<HELICOPTER ITH1N MA~d\RANGE OP SUBMARINE _J

N

END OF GAMEHELICOPTEu WINS

ADVANCE TIME ONE SECONDl

(game time up)—

to

f SONOBUGY DATA \yCOLLl^C ION TIME/

END OF GAMESUBMARINE INS

N ULCALLHDET

CALLSDET

(HELP ACHIEVED ^ y /lF1..-:ST DETECTION^/ \*

i£L

CALLTACA

,2, 3 i S NOBUOYSACHIEVED DETECTION

ICALLTAC1

CALLT*C2

CALLTAC3

N ( SUBMARINE ACHIEFIiiST" DETECT

eved\ION J

FIGURE 9

MAIN PROGRAM

37

cCHECK EACH SONOBUOTWHICH HAS LIGHTED OFFFOR SUB DETECTION >ELIMINATE HELICOPTERTACA PROM FURTHERUSE

RECORD COORDINATESOF SONOBUOYS ANDRANGE FROM SUBMARINE]

(*THREE DETECTIONS^ N

<r.

ALL CHECKEDD

C DETECTIONS V-

RESET DETECTIONCOUNTER TO NUMBEROF DETS. MADE ONLAST SUCESSFULINTEROGATION OF

SONOBUOYS

N

150 SECONDSSINCE TAC1 ORTAC2 CALLED

-»| RETURN J

ENABLE TAC1.TAC2,TAC3 TO BE USEDAGAIN

FIGURE 10

HBLXCOPTER-SONOBUOT DETECTION SUBROUTINE

m

CHECK EACH SONOBUOYWHICH HAS LIGHT EDOFF FOR SUBMARINEDETECTION

ELIMINATE SUBMARINETACM FROM FURTHERUSE

ADD BEARING OFSUBMARINE TOTOTAL OF OTHERSONOBUOYS DETECTING

N-»f ALL CHECKED)

(DETECTIONS) N

ESET SUBMARINECOURSE TORECIPROCAL OFAVERAGE BEARING

£RETURN

FIGURE 11

SUBMARINE DETECTION SUBROUTINE

39

(ALL SONOBUOYS ALLOTT1FOR TACA DROPPED

N

5CALLSQSE

ADVANCE HELO TOINPUT POSITIONOF NEXT (OR FIRST)SONOBUOT TO BE

DROPPED

cAT POSITIONF>JL

DROP SONOBUOY ANDCOMPUTE LIGHT OFF

TIME

M return]

FIGURE 12

HELICOPTER INITIAL TACTIC SUBROUTINE

40

(taci complete)

N

DETERMINE IF HELICOPTERIS INSIDE OR OUTSIDE

RING

ADVANCE HEL COPTERTOtfARD RING

(^AT RING?)N

CALLECONZ3Z

ADVANCE RINGCOUNTER

IRING CROSSEDTWICE

N

CAUSE HELICOPTERCOURSE TO BETOWARD OPFOSITESIDE OF RING

CALLSQSE

DECLARETACICOMPLETE

tSTURN

FIGURE 13

HELICOPTER TACTIC ONE-RING SUBROUTINE

41

(TAC2 computed)

JUL

TAC2 USED SINCELAST DETECTION

MADE

CALLSQS*

COMPUTE TWOINTERSECTIONSOP RINGS ANDLABEL POINT ONEAND POINT TWO

(point one closer) M

DESTINATIONIS POINT ONE

ADVANCE HELICOPTERTOWARD DESTINATION

( AT DESTINATION)—**-

CHANGE DESTINATIONTO OTHER POINT

CALLECO* <

DESTINATIONIS POINT TWO

J

SECOND DESTI-NATION REACHED

y

>^

TAC2 COMPLETEj

-

Jreturn

FIGURE 1%

HELICOPTER TACTIC TWO-RING

AZ

rBEGIN>lTAC3

(tac3 complete) f

DETERMINE MUTUALINTERSECTION OFTHREE RIxNGS

ADVANCE HELICOPTER

CALLECON=3Z

TAC3 COMPLETE

CALLSQSE

( AT INTERSECTION) -

:! f\ RETURN

FIGURE 15

HELICOPTER TACTIC THREE-RING SUBROUTINE

43

N

CALUCATE TIMETO COMPLETE SIDEOF SQUARE

^1

HELICOPTER STARTS AT ZEROAND TAKES COURSESAS SHOWN

ADVANCE HELICOPTER

cTIME TO TURND*

TURN LEFT ASSHOWN

return]

FIGURE 16

HELICOPTER SQUARE SEARCH SUBROUTINE

44

ADVANCE SUB ALONGINITIAL COURSE FROMINITIAL COORDINATES

•;turn

(a)

ADVANCE SUB ALONGEVASION COURSECALCULATED IN SDET

RETURN

(b)

FIGURE 17

(a) SUBxMARINE FIRST TACTIC SUBROUTINE

(b) SUBMARINE SECOND TACTIC SUBROUTINE

45

'BEGIJTlECON

CHECK EACH SONOBUOYWHICH HASBEEN DROPPED

WITHIN ONE-HALFDETECTION RANGEOF PROPOSEDDROP POSITION

N

IT QALL SONOBUOYS CHECKED)

ADVANCE SONOBUOYCOUNTER, COMPUTELIGHT OFF TIME,RECORD SONOBUOYCOORDINATES

ADVANCE COUNTEROF SONOBUOYSWITHIN DETECTION

RANGE'

XN ONE OR MORE

SONOBUOYS WITHINRANGE

| RETURN

1

FIGURE i*

SONOBUOY ECONOMIZING SUBROUTINE

46

1 SET COUNTERS

GENERATE RANDOMNUMBERS, SORT INTOINTERVALS , COMPUTESAMPLE MEAN

GENERATE SAMERANDOM NUMBERS,SORT, COMPUTE SAMPLEVARIANCE, MEANVARIANCE, ANDINTERVALS.

PRINT DATA

RETURN

FIGURE 19

RANDOM NUMBER TEST SUBROUTINE

47

APPENDIX B.

DICTIONARY OF PROGRAM NAMES

AA, BB No meaning attached; For reading in title of data set.

A(I) Input X coordinate for (1-1)— sonobuoy of helicopter's

initial tactic.

AK Floating point equivalent to counter K in subroutine TEST.

ALFA Initial course of Submarine.

thAMAN(I) Mean of the I— interval in Subroutine TEST

thBE (I) Lower endpoint of I— interval in subroutine TEST.

B(I) Input Y coordinate for (1-1)— sonobuoy of helicopter's

initial tactic.

BRING Input value of one half the side of the square in whichsubmarine is contained initially.

CUS Computes escape course of Submarine in Subroutine TACN.

ECON Subroutine which drops new sonobuoys in TAC1, TAC2,and TAC3 only i« there are not one or more sonobuoyswithin detection range.

HDET Subroutine which queries sonobuoys for detection of

submarine.

IIR Input argument for random number subroutine. Enteredin octal.

IR Equivalent to IIR.

JA Counter for submarine and helicopter data collection.

KCK Prevents KTLIT(I) from being calculated more than once.

KMEAN Tells if sample mean has been computed. Done on first

pass through random numbers.

KSB The number of sonobuoys (plus one) which have beendropped at any given time. | £KSB ^ 101

48

KSBCK Counter which prevents helicopter from dropping a sono-buoy if there are one or more within one-half of the

detection range of the intended drop position.

KTEST Input which determines whether or not subroutine TESTis called.

KTIME Game time in seconds. O^KTIME^KTMAX

KTLIT(I) Light off time of (1-1)— sonobuoy.

KTMAX Fixed point equivalent of TMAX ' 3600.

LL Prevents TAC1 and TAC2 from being started over unless150 seconds have elapsed.

M Number of sonobuoys achieving detection at a given intero-

gation time.

MCK Prevents helicopter from using TACA after a detection

has occured.

MS Determines what side of square search helicopter is on.

MT Counter of seconds of helicopter advancement along a

side of the square search.

MTA Number of seconds helicopter advances for one-half the

side of the square search.

MU Determines if TAC1 has been completed.

MX Records value of M at start of subroutine HDET and

assigns its value to M again if no detections occur.

NCK Prevents TACM from being used after submarine first

detects a sonobuoy.

NN Determines secondary tactic within TAC1

.

NP Distinguishes between two arms of ambiguity in TAC2.

NR Counter for number of replications

NRAN Input which determines how many random numbers are

evaluated. 1355 is the most it is necessary to call.

NREP Maximum number of replications desired.

Maximum needed is 271.

49

NS

NSB

NT

PROB

PSUM

R

RANDOM

RANI

RDET

RMAD

RSB

SDET

SMEAN

SQSE

SUM

SVAR(I)

TACA

TAC1

TAC2

TAC3

TACM

TACN

TEST

Determines if TAC3 has been completed.

Number of sonobuoys in a full TACA pattern.

Tells helicopter what to do within TAC2.

Number assigned when TMAX or MAD occurs.

Numerator of average probability of detection fraction.

Random number in FORTRAN IV

FORTRAN 6 3 equivalent of R.

Random number subroutine.

Radius in nautical miles from each sonobuoy achieving

detection to the submarines.

"Cooky Cutter" range of MAD gear in nautical miles.

"Cooky Cutter" range of sonobuoys, in nautical miles.

Submarine's subroutine for detection of sonobuoys.

Sample mean of an interval of width one -tenth in sub-

routine TEST.

Subroutine which moves helicopter in a square pattern to

attempt MAD detection.

Numerator of average course fraction.

Sample variance of each interval in subroutine TEST.

Helicopter

Helicopter

Helicopter

Helicopter

Submarine

s initial tactic,

s one-ring tactic,

s two-ring tactic,

s three-ring tactic

s initial tactic.

Submarine's evasion tactic,

Subroutine which tests random numbers for randomness

50

TMAX

TPROB

U(E)

VAR(K)

VH

VSS

XDET(M)

XH

XHH

XI

X(I)

XKSB

XNR

XP

XP1

XP2

XS

XTIME

YDET(M)

YH

Submarine's escape time in hours.

Average probability of detection of submarine by helicopter,

Upper endpoint of I— interval in subroutine TEST.

Term needed to compute sample variance.

Helicopter airspeed in knots.

Submarine patrol speed in knots.

X coordinate of Mt— sonobuoy detecting submarine, in

nautical miles.

X coordinate of helicopter in nautical miles.

X coordinate of helicopter initial position in nautical

miles.

Denominator of CUS.

.thX coordinate in nautical miles of (1-1)— sonobuoy whichhas been dropped. Also serves as a counter in subroutine

TEST.

Floating point equivalent of KSB.

Floating point equivalent of NR.

X coordinate in nautical miles of one point of intersec-

tion of two circles. (XP=XP1 or XP=XP2).

X coordinate of one point of intersectionfof two circles

in TAC2 and TAG 3.

X coordinate in nautical miles of the other intersection.

(See X PI)

X coordinate of submarine in nautical miles.

Floating point equivalent of KTIME.

Y coordinate in nautical miles of M— sonobuoy detecting

submarine.

Y coordinate in nautical miles of helicopter.

51

YHH

Y(I)

YKSB

YP

YP1

YP2

YS

YTIME

Z

Y coordinate in nautical miles of helicopter's starting

position.

tVi

Y coordinate in nautical miles of (1-1)— sonobuoy whichhas been dropped. Also serves as a counter in subrou-tine TEST.

Numerator of average number of sonobuoys used.

Y. coordinate in nautical miles of one point of intersection

of two circles. (YP=YP1 or YP=YP2).

Y coordinate in nautical miles of one point of intersection

of two circles in TAC2 and TAC3.

Y coordinate in nautical miles of the other intersection.

(See YP1).

Y coordinate, in nautical miles, of submarine.

Numerator of average time fraction.

Term needed to compute sample variance in subroutine

TEST.

Note: This program was originally written in FORTRAN IV, then

altered to FORTRAN 63. Several terms, such as EQUIVALENCE (R,

RANDOM), and FUNCTION SQRT, were inserted to avoid much rewrit-

ing of complicated expressions.

52

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68

APPENDIX D

STATISTICAL EXAMINATION OF MODEL

In order that the user of the model may decide on the degree of confi-

dence to place in the model's results, two critical features are examined

statistically. Those examinations are presented in this appendix.

I RANDOM NUMBERS

Five random numbers are generated in each replication. They

control the area of the square the submarine is contained in at the start,

and the initial course of the submarine. The random number generator

is assumed to be uniform between zero and one but, as is well known,

the numbers from a random generator are not random at all, but are

instead a rigid sequence of numbers determined by the program which

generated them and the intial argument specified by the user. The

user should examine those random numbers which his program uses,

to determine if they are close enough to true randomness to meet the

requirements of his problem. If they are not, one standard procedure

to effect a change is to change the initial argument until a nearly ran-

dom sequence of numbers has been obtained. That has been done for

this model and the results and statistical methods follow.

As will be explained in the subsequent section of this appendix, 271

replications are the most runs necessary to achieve eighty one per cent

confidence that the probabilities of detection of two games which differ

by one-tenth are statistically different. 1355 random numbers are the

most which will ever be needed, and sequences of that length have been

examined. The input values of KTEST = 1 , NRAN=1355, and

.69

IIR=47532352 (octal field) were used and the results were as presented

in Figure 3 of Chapter IV.

Subroutine TEST called 1355 numbers, sorted each into 10 intervals

of one-tenth width each (arbitrary) counted the numbers in each inter-

val and computed their sample mean as (4):

n

where n is the number of random numbers which fell into a given inter-

thval and X. is the value of the i— number in that interval,

l

The same random numbers were generated again and this time the

sample variance was computed as (4):

where the symbols n, X., and X have the same meaning as before.

Next the mean (5),

where a is the lower limit of the interval and b it's upper limit, was

computed for each interval. The variance as determined by (5):

/^

was then determined to be a constant in all intervals.

The upper and lower limits were then computed and all the above

information presented in the following order: Interval limits; Number

of random numbers which fell into this interval; Mean; Sample mean;

Variance; and Sample variance.

The numbers in Figure 3 are the result. Since the number in each

interval is close to 135. 5 and there is close agreement between the

mean and sample mean, and the variance and sample variance, these

70

random numbers are regarded by the author as sufficient for the pur-

poses of this model, hence the initial argument shown is recommended.

II PROBABILITY OF DETECTION

The outcome of each replication is a one if MAD occurs and a zero

if it does not. The only things which change from one replication to the

next are the submarine's starting coordinates and course. These are

determined by the random numbers which, we have seen, are reason-

ably random. So the outcome of each replication, or "experiment" may

be considered belonging to two categories, called "successes" or

"failures" and represent independently repeated, or "Bernoulli trials"

(5).

The maximum likehood estimator for the mean of the Bernoulli

distribution is (4) ^

A large enough sample (271) is present for the normal approximation to

Abe accurate. A ninety per cent confidence that P is within + . 05 of the

"true" population mean is desired. The model for the large sample

confidence interval of the normal approximation of the Bernoulli distri-

bution is (4): P(90% of sample means will be between P+. 05 and P- . 05)

-MM*/5*5 *" ^/ajlp) = .io

71

1st r = p + .os

p t .os- ± P + i.c<f£-fh^p)

p(l-p) £ >0F

P(i-P) * f' 0S \

(>-H K .»* J

A A

n 2 211 (at P s a )

So the most replications ever necessary is 271, and that only if the

probability of detection is . 5. If the probabilities are different, the

number of replications required for the same confidence interval is

Aless. For example, if P = . 1, then n 2 98.

AThe estimator P will fall within . 05 of the "true" value of P 90%

of the time. But we wish to know if a probability that differs by . 1

72

from another represents a "better" tactic. In order to resolve the two

points each of which is 90% certain, each must lie within +_ . 05 of it's

true mean. So if the points are separated by . 1 we may be (. 90)(. 90) •

100 = 81% confident that the two points are "statistically different".

Assuming the model does not bias one tactic over another, we may be

81% certain that the tactic with the higher probability of detection is

"better" than the other. The author sees no evidence of such bias.

73

APPENDIX E

ANALYSIS OF MODEL'S LOGIC

A complete analysis of one replication is presented geometrically

in Figure 20 and in the following text. The solid line in the Figure

represents the helicopter's path and the broken line that of the sub-

marine's. The arcs with numbers on them indicate the detection time

from the sonobuoy in the center of the arc. Presented at the top of

Figure 20 is a write out of the input to this game. This is a replication

which the helicopter "won", and illustrates many of the model's

features.

Cards were inserted into the program to cause certain critical

values to print out every one second of game time. These values

represent the positions of the helicopter and submarine at all times ls

positions of the sonobuoys, the positions and ranges to the submarine

of all sonobuoys up to a total of three achieving detection at any given

time, and the current game time in seconds.

TIME EVENT

sec. Helicopter starts at (x, y) = (0, -20), (not shown).

Submarine starts at (2.2, .2).

478 Helicopter lays sonobuoy No. 1 at (0, -4. 1).

648 Helicopter lays sonobuoy No. 2 at (4.0, -. 1).

658 Sonobuoy No. 1 lights off.

660 Submarine detects sonobuoy No. 1, changes its=course

to go away from it, and doubles its speed.

818 Sonobuoy No. 3 is dropped.

74

1L10.0 6.0 4.05

-4.0 4.0

N

0-20.0 1.0 .2 3.0 ^75^23528 u oo 6 4 • o • -4 • o o o o

LEGEND

elicopter track

—* Submarine track

ff7 Game time in seconds

(jj) Sonobuoy No. 3

jonobuoy detection onivo

this arc at this time

(-1) Distance from datumin nautical miles

L

FIGURE 20

A PLAY vHICH THE HELICOPTER "WON"

75

TIME EVENT

828 Sonobuoy No. 2 lights off.

840 Submarine detects sonobuoy Nos. 1 and 2 and alters course,

Helicopter detects submarine on sonobuoy No. 2 and alters

course as directed by TAC1.

947 Helicopter drops sonobuoy No. 4 on the ring of TAC1, at

(2. 3,1. 2).

990 150 seconds delay time has elapsed since first detection.

Helicopter reverses course to restart TAC1.

1020 Submarine detects sonobuoy Nos. 1, 2, and 3 and alters

course.

1036 Helicopter reaches ring of TAC1 but is prevented fromdropping because sonobuoy No. 4 is nearby. Reversescourse.

1140 Submarine detects sonobuoys No. 1, 2, 3, and 4 and alters

course. Helicopter detects submarine on sonobuoys No. 2

and 4 and alters course toward the nearest intersection of

the two rings as in TAC2.

1241 Helicopter, at (2. 0, . 8) detects submarine, at (1. 9, . 9),

by MAD and replication ends in favor of the helicopter.

76

INITIAL DISTRIBUTION LIST

No. Copies

1. Defense Documentation Center 20

Cameron Station

Alexandria, Virginia 22314

2. Library 2

Naval Postgraduate School, Monterey, California

3. Office of the Chief of Naval Operations (OP96) 1

Navy Department, Washington, D. C. 20350

4. Prof. John A. Tiedeman, Dept Ops Research 1

Naval Postgraduate School, Monterey, California

5. Lt Robert F. Harvey, SMC 1767 1

Naval Postgraduate School, Monterey, California

6. Systems Analysis Staff, Naval Ordnance Laboratory 1

Silver Springs, Md. 20910

77

UNCLASSIFIEDSecurity Classification

DOCUMENT CONTROL DATA • R&D(Security clarification ol tltlo, body ol obatract and indaxinj annotation muat bo ontotod wtion tho orotmll raport io cloaaitiod)

1. ORIGINATING ACTIVITY (Ccrporata author)

Naval Postgraduate School

Monterey, California 93940

2a. REPORT SECURITY CLASSIFICATION

Unclassified2b eroup

3. REPORT TITLE

A Computer War Game for Determining the Cost-Effectiveness of ActiveSonobuoys

4. DESCRIPTIVE NOTES (Typo ol roport and Inctuairo dmioo)

Thesis, Master of Science in Operations Research5 AUTHORCS; (Loot nana, Htot nmmo, initial)

Harvey, Robert F,

« REPORT DATE

June 1967

7«- TOTAL NO-4S9 F PA1II

79

7b. NO. OF REFS

to. CONTRACT OR BRANT NO.

b. PROJECT NO.

9«. ORIGINATOR'S REPORT NUMEERfS.)

9b. OTHER REPORT NO(S) (A ny othat rmmbora that may ba aaaifnod

10. AVAILABILITY/LIMITATION NOTICES

Off*pp^h

11- SUPPLEMENTARY NOTES 12 SPONSORING MILITARY ACTIVITY

Office of the Chief of Naval Operations

(OP96), Navy Dept, Wash. D.C. 20350

13- ABSTRACT

In order to evaluate the relative effectiveness of different active non-

directional sonobuoys, a computer war game is developed. One submarine,employing one evasion tactic, is opposed by one helicopter, using five prosecu-

tion tactics. The tactic of the helicopter prior to the initial detection of the

submarine is seen to be critical, and this simulation aids in determining an

optimum tactic.

A cost-effectiveness model to use data from this simulation is developed.

An example, using hypothetical but realistic data, is presented to illustrate

methods of determining the cost-effectiveness of each sonobuoy type when used

with its optimum tactic.

DD .KB- 1473 UNCLASSIFIED79 Security Classification

UNCLASSIFIEDSecurity Classification

key wo R OS

Sonobuoy

Helicopter

Simulation

Monte Carlo

Tactics

Aircraft

Cost -Effectiveness

War Game

.

; ./y

o. .;

DD ,

F°oR:. 81473 ^ack,

-

§/N 0101 -807-6821UNCLASSIFIED

Security Classification A-31 409

_

thesH29634

3 2768 00404583 1

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