A SIMULATION OF HELICOPTER AIRCRAFT IN AN ARMEDRECONNAISSANCE MODE, FOR THECDC 1604 DIGITAL COMPUTER

RICHARD RALPH JOHNSONAND

NEIL RAY VAN LEEUWEN

n1val

Rpostgradu^te school

MONTEREY, CALIF. 93940

A SIMULATION OF HELICOPTER AIRCRAFT

IN AN ARMED RECONNAISSANCE MODE, FOR

THE CDC 1604 DIGITAL COMPUTER

by

Richard Ralph Johnson

Captain, United States Marine Corps

B.S., Illinois Institute of Technology, 1957

and

Neil Ray Van Leeuwen

Captain, United States Marine Corps

B.S., University of Utah, 1956

Submitted in partial fulfillment

for the degree of

MASTER OF SCIENCE IN OPERATIONS RESEARCH

from the

UNITED STATES NAVAL POSTGRADUATE SCHOOL

May 1966

* 'D j-r \

ABSTRACT

A model is presented which is a computer simulation of a duel

involving two helicopter sections, a scout and an attack section,

and an armored mobile land target. Terrain features are considered

in the model by using a "least square" polynomial to represent the

terrain environment. The model was constructed in an attempt to

include the possible effects of terrain on tactics used by the com-

batants in the duel. The computer program, logic and model results

are included.

TABLE OF CONTENTS

Section Page

1. Introduction 7

2. Design of the model 9"

3. Helicopter and armored unit movement 11

4. Interacquisition 12

5. Attack 13

6. Destruction assessment 18

7. Comments 20

8. Conclusions 23

LIST OF ILLUSTRATIONS

Figure Page

1. Land unit weapon data, mission title, and

simulation parameters for entry into ATTACK 151

2. Time step simulation status 152

3. Historical tableau 153

4. Movement of Helicopter aircraft and land unit 154

5. HLMR mockup terrain grid square 5281 159

6. Coefficients of terrain approximating 160

polynomial

1. Introduction

The model presented in this thesis, ARMREC, is a time step com-

puter simulation of an armed reconnaissance flight of two helicopter

sections in search of a small stationary or moving armored land tar-

get. Simultaneous and independent movement of the participants is

provided for in the model and all movement takes place over terrain

simulated by a "least square" polynomial. The necessary data for

the terrain simulation in ARMREC is supplied by a separate program,

TERRAIN. The program, TERRAIN, is described in APPENDIX IV. The

flight paths of the helicopter sections in the model are either pre-

planned, and as such are included with the necessary input data for

the model, or they are generated as nap of the earth, NOE, flight

paths by the ARMREC program.

The interactions included in the ARMREC program, i.e., the

search and destroy mission of the helicopters and the ensuing duel

between the helicopters and the target, are designed to test the

efficiency of a helicopter anti-armored weapons system. The important

features of the model are its ability to simulate terrain such that

terrain effects on tactical changes by the participants are realistic,

and its ability to move any number of participants as independent

units over the terrain.

The authors' interest in the possible use of helicopters in an

anti-armored role was developed during their 1965 summer operational

tour with the Stanford Research Institute research group which sup-

ports the Army Combat Developments Command Experimentation Command,

CDCEC, at Fort Ord, California.

The authors wish to thank the staff of the Stanford Research

Institute group at Fort Ord, and specifically Mr. Richard Ferris, the

Project Scientist, and the members of Team IV on the CDCEC staff for

giving them the opportunity to assist in formulating proposed tactics

for helicopters in an anti-armored environment. The authors also

express their appreciation to Professor Alvin F. Andrus who provided

the encouragement and help necessary in completing this thesis.

2. Design of the Model

ARMREC was programmed in FORTRAN- 63 for the CDC-1604 computer and

consists of a time step movement of two helicopter sections involved in

a search and destroy mission against an armed mobile unit. The model

is designed so that Monte Carlo techniques can be used to generate ex-

pected outcomes of various tactics used in anti-armored reconnaissance

missions which may be assigned to helicopters.

The provision for weapons in the model is as follows: As many as

four weapon types, with their associated kill probabilities as a func-

tion of range to the helicopters, can be assigned to the armored unit.

The attack helicopters are armed with missile type weapons which can

have either nuclear warheads with an associated CEP as a function of

target range and crossing speed or conventional warheads with an as-

sociated kill probability.

Assigned to each participant in the model is a probability of

seeing opposing participants as a function of range given that the

opponents are in view of one another. The model begins the conflict

between the opponents by proceeding to move all forces according to

plan until an opponent is sighted by one of the participants. At

this time a decision to engage the sighted target is considered by

the participant making the sighting. If the decision is not to

engage, the computer model is time stepped until an engagement de-

cision is reached or the game run is completed. If, however, the

decision is to engage the sighted target, the attack phase of

ARMREC is executed. This phase of the program is described in

Section 5.

For location purposes all three participants are considered as

point forces, i.e., all elements making up the forces of any of the

three combatants are considered to occupy the same point, (X,Y,Z),

at any given time in the simulation. The routines that govern the

movement of the helicopter sections and armored unit until the attack

phase is executed are described in Sections 3 and 4.

At the conclusion of each attack phase or engagement, the ARMREC

program is designed to collect and print results which are necessary

for assessing the impact of parameter changes which can be made in

the program. A complete description of both the inputs to the program

and the printed results is found in APPENDIX III.

The scenario used with the ARMREC program consisted of an attack

section and a scout section each containing two helicopters. The

armored mobile land unit consisted of 3 tanks and 2 armored personnel

carriers. The flight path of the helicopters was both preplanned and

NOE generated by the program. The time step for the model was set at

one second.

10

3. Helicopter and armored unit movement

The tracks of the two helicopter sections and the armored unit

on the terrain are input values to the ARMREC program. The terrain

heights of points along each of the three tracks are computed using

the appropriate approximating polynomial expression generated by the

program TERRAIN. These heights are used to generate a nap of earth

flight path when desired. A nap of earth, NOE, flight path is defined

as i lying as close to the ground as vegetation and obstacles permit,

taking full advantage of the terrain to gain concealment and cover

from the enemy's observation and fire ( 8 ).

Helicopters proceed along their preplanned flight path and a check

is made during every program time step to determine if they can see the

land target. If it is determined that no line of sight has existed

between the helicopters and the land target for a specified period of

time, the scout helicopters perform a "pop-up" maneuver. This pop-up

tactic is described as suddenly ascending vertically from behind

terrain features in order to see any enemy ground units that might

be present. This tactic, combined with NOE flight, has been found

to improve the chance of successful mission completion by scout and

attack helicopters against a variety of targets ( 1 )

.

A helicopter while in the pop-up phase, is allowed to climb to

a predetermined height or until interacquisition is established.

If it is determined that no visual detection has occurred or is pos-

sible at the end of the pop-up ascent, the helicopter is programmed

to continue its NOE flight path.

11

4. Interacquisition

Inherent to the ARMREC program is the assumption that whenever

an unobstructed line of sight exists between two participants, they

both have the possibility of visual detection.

To determine if two participants can possibly see one another

a line, called the line of sight, is projected between them. If the

elevation of any point on the line of sight projected onto the terrain

surface is greater than the corresponding point on the line of sight,

the participants are considered not in view of one another. If all

points on the line of sight are higher than the elevations of their

respective projected points on the terrain surface, then the line of

sight is unobstructed and visual detection can occur. This computa-

tion is carried out in the ARMREC program by checking points 50

meters apart, on the average, on the line of sight.

If visual detection can occur, the detection probability as a

function of range associated with each participant is then compared

with a generated random number to ascertain if contact has been made

by one or both of the participants. If it is determined that a

visual contact exists, the ARMREC program executes the attack phase.

If contact is not established or the participants are not in view of

one another, then the participants repeat the cycle of events in the

next time step.

12

5. Attack

The attack phase of ARMREC provides the logic for the participants

during the engagement portion of the simulation. As mentioned in the

previous section, the attack phase commences when either of the oppos-

ing participants visually detects the other. The principal logical

divisions for this phase are as follows:

Armored Unit Movement

The armored land unit proceeds on the basis of three assumptions.

These assumptions are: The unit follows a predetermined route to a

selected destination with no deviation from the route allowed; the

unit must stop to fire; and elements of the unit will fire whenever

a helicopter is in view and ammunition is available.

Aircraft Initial Decisions

When one of the helicopter sections has sighted a target, a

firing point is computed for the attack helicopter on a constant

bearing from the target to the attack section at a given attack

range . ATR. . A scout observation position is then chosen along a

line perpendicular to the attack-target axis and at a distance

prescribed by ATR.

If the scout section can obtain an unobstructed view of both

the target and the attack section's computed firing point, a re-

finement of the firing position is made. This refinement consists

of selecting a point, if one exists, in the vicinity of the initial

computed firing point such that an uninterrupted line of sight,

LOS, exists to the target. If no such point exists a refinement

is not made. A major assumption in the computation of these posi-

tions is that the attack group verses armored unit speed ratio

ranges from 2.5 to 3.0.

13

Position Determination

During each time step the positions of the participants are

calculated and the lines of sight between the attack and scout sec-

tions and the armored unit are evaluated to determine whether or not

they are unobstructed. If the line of sight between the attack sec-

tion and the armored unit is discontinuous as the attack section

approaches the firing point, the scout section altitude is modified

to simulate a pop-up tactic. This tactic is utilized to insure that

the scout section will be able to assist the attack section in tar-

get position orientation.

Armored Unit Gunfire Control .

Subsequent to the calculation of positions and the lines of sight

evaluation, it is determined if the land unit could or would have

fired at the helicopters during the previous time step. The ability

of each weapon type to fire is predicated upon range, availability of

ammunition, whether sufficient time has elapsed to acquire the heli-

copter, i.e., time to train, sight and prepare the weapon for firing,

and when applicable, whether enough time has passed to simulate re-

loading and re-acquiring a helicopter.

If the armored unit is unable to fire at one or both of the heli-

copter sections due to the loss of a previously established visual

contact, a decision is made for the unit to remain in place or to

proceed to its destination at an emergency speed, TSPDM. This speed

is maintained until at least one of the helicopter sections is re-

acquired at which time the armored unit's movement is determined as

previously described, or until its destination is reached. The de-

cision to remain or proceed at emergency speed to the destination is

14

based upon the length of elapsed time before the lost contact can

again be seen. This is programmed to account for the momentary ob-

scuration of a helicopter section by a terrain feature. Time inter-

vals to re-acquisition of less than 15 seconds were arbitaraily

selected as a basis for the armored unit to maintain a fixed posi-

tion.

The armored unit will fire at a helicopter if the probability

of a kill as calculated by the following equation, is at least .15 .

NWP(helicopter kill) = 1-JT (l-P.(r) )

i=l i

Where:

NW = The number of weapon types

NWi= The number of weapons of type i

P.(r)= The probability of helicopter kill

by weapon type i at range r .

In the event the armored unit is able to fire at both helicopter

sections a predetermined firing doctrine, IKILL, is used in the model

to decide which target(s) the armored unit will fire at. The firing

doctrine gives firing priorities for the helicopter section type,

i.e., scout or attack, or it gives priority to the section with the

lowest probability of survival. The armored unit's weapons can also

be apportioned, by weapon type, to the helicopter section against

which it has the highest probability of a kill.

Aircraft Fire Control

In general, the attack helicopters are able to fire under the

following conditions: the armored unit is in visual contact and will

remain so for the time of flight of the helicopter's missile; a

period of time, HTF, simulating acquisition, has passed since visual

15

contact was made, and missiles are available for firing. Obscuration

of the target due to missile detonation does not affect the firing

capabilities of the attack section. In particular, a nuclear missile

can be fired at ranges in excess of 500 meters, and a conventional

rocket can be fired at ranges in excess of 100 meters from the target.

If the above conditions are not fulfilled or a helicopter has fired

a missile which has not yet impacted then the helicopter may not fire.

Once a helicopter has fired it must maintain the course and speed it

had at the time of fire until missile impact. Further firing or

evasive maneuver is then permitted. If the helicopter cannot fire

for reasons other than just having fired, evasive maneuver or move-

ment to press the attack is allowable. In either case, if missiles

are available, once evasive maneuver has been taken, another firing

point is selected and routes of flight are computed as described

before. If all missiles have been expended the program generates

a route from the attack section's position to a point of concealment

and then to a terminal point.

The scout section's route during the gunfire control phase of

the program is also subject to evaluation. Once the scout section

establishes visual contact with the armored unit a route is selected

to allow the scout to shuttle between an observation point and a

point concealed from the land unit's view. This continues until the

attack section is destroyed or has expended its missiles, or until the

land unit is destroyed. ARMREC then calculates a flight path from the

scout section's present position, via a concealed point to its term-

inal position.

16

A major assumption is that land unit weapons are considered

effective in the time step in which they are fired while the mis-

siles fired from helicopters have a time of flight extending over

multiple time steps.

17

6. Destruction Assessment

A helicopter is considered to be out of action if a number drawn

from a uniform distribution is less than or equal to the probability of

a kill for the weapons employed against the aircraft. No more than one

helicopter in each section may be destroyed in a time step.

As mentioned earlier, two missile types can be delivered by an

attack helicopter, one a conventional and the other a nuclear. The

conventional missile is merely delivered with a given kill probability.

That is, for conventional weapons the decision as to whether an element

of the armored unit is killed or not is a simple yes or no determined

by comparing the probability of kill with a generated random number.

In this sense the damage inflicted on an element of the armored unit

is either none or total and this must be reflected in the numerical

values assigned to the probability of kill. When a nuclear weapon is

delivered a CEP is generated in order to fit a normal distribution to

the distribution of points of impact about the aim point. The CEP is

generated as a linear function of range to the target in meters and

the relative crossing speed in meters per second. The functional re-

lationship of range and relative crossing speed to CEP used in ARMREC

was initially established to produce an average direct hit probability

of near .40 at target attack ranges of 900 to 1400 meters. However,

with minor program modification, known CEP's for weapons delivery

systems can be used. The missile aimpoint is determined as a function

of target speed and projected direction of motion of the target.

The relative position of the nuclear projectile impact point to

the center and end points of the armored unit, together with the tar-

get radius of destruction for the given weapon yield , provides the

18

information necessary to determine the extent of damage inflicted on the

target. An element, including its assigned weapon types, is considered

out of action if it lies within the target radius of destruction pro-

jected from the impact point of the missile.

Only surface bursts of small yield nuclear missiles are considered

in the ARMREC program. With the low yield projectile envisioned as

being used, it is felt that no detrimental nuclear effects would be

experienced by the helicopter weapons system at the attack ranges con-

sidered. However, provision is made in the ARMREC program to determine

the overpressure produced by the nuclear burst at various attack ranges

since overpressure is found to be the critical damage factor on air-

craft weapon systems ( 6 ) . First order mach effects were considered

the main augmenters in calculating the overpressure. The function

which estimates the overpressure from a nuclear blast of given yield

at varied ranges can be found in D.A.S.A. publications ( 9 ).

It is also assumed in the computer model that the area within the

target complex is flat earth. This may affect the damage assessment

since the armored unit critical damage factor in determining the

target radius of destruction was the nuclear radiation intensity in-

flicted upon the personnel within the target complex ( 3 )

.

It is also assumed in the model that armored unit destruction

and aircraft damage is simultaneously known to all participants.

19

7. Comments

In addition to comments pertaining to assumptions made earlier,

this section contains remarks that are considered significant.

All participants described in the model moved on or above the

terrain without regard to natural vegetation or man made obstacles.

No attempt was made in the model to degrade sighting probabilities

as a result of the masking or camouflaging effects that are produced

by these elements. Cover afforded by vegetation could be simulated

by allowing ground elements to operate below the terrain surface in

areas where masking is prevalent. Area extent would be controlled

to approximate light or heavy coverage. Background concealing

effects by terrain or vegetation on helicopter acquisition by ground

targets could be simulated by sensing terrain along the extended line

of sight between ground and airborne elements. A diminishing factor

could then be applied to the probability of aircraft acquisition.

In the nuclear effects assessment portion of the program it was

assumed that the vehicles of the armored unit were spaced 50 meters

apart and in single file. Modification of the damage part of the

program would be necessary in order to calculate the damage inflicted

upon other target types.

It is also the case that the model scenario has been described

in terms of two sections of helicopters and an armored unit. Actually

the structure of the model is such that other participant types may

be used in place of those described by changing the input parameters

which determine the operating envelopes of the participants. As a

result many other conflict type scenarios may be investigated by this

model. Fixed ground participants, such as those used in Capt. J. L.

Harrison's thesis ( 2 ) , may be incorporated into ARMREC with a mini-

20

mum of programming.

The previous sections have described the model in terms of the

logical development of actions and reactions. It has not been

specifically mentioned that all of the previous sections describe

parts of an integrated complex computer program. The ARMREC program

is composed of a main program and eleven sub-routines. The main

program initiates each run, directs the movement of the participants

to the attack phase, and directs the execution of the historical

print out tableau at the completion of each run, Fig. 3. The names

and functions of the sub-routines are as follows:

BNDCK checks for out of bounds conditions as routes are computed

for each of the moving participants. If a route is found to extend

beyond the map area upon which the duel is designed to take place,

BNDCK initiates a program stop.

RANGE is used to calculate the position of each participant on

its computed path at any time step, and senses when a participant

reaches its terminal position.

ALOS calculates the range between two positions and determines

if an unobstructed line of sight exists between them.

ELEV uses the input coefficients of the terrain approximating

polynomials to calculate the elevation at any surface point (X,Y)

within the game boundaries.

CONTOUR computes a nap of the earth flight path between points

along the track of an aircraft.

TGSE selects a position such that a LOS exists, or one in which

a LOS does not exist between the position and another specified

point.

21

RTE determines the X,Y coordinates of a path such that nap of the

earth flight is possible between any two specified points. It enables

an aircraft to simulate a spiraling climb to elevations which normal

nap of the earth flight as simulated in CONTOUR does not allow.

PL0T1 provides the necessary data for the graph output desired.

ATTACK provides for the functions mentioned in Section five. It

also calculates the aircraft damage due to land unit fire as described

in Section six.

PRINT1 controls the printed historical output.

NUC determines damage inflicted upon participants by nuclear and

conventional missiles as described in Section six.

DRAW, which does not appear in the program listing, produces the

output on tape necessary for the plotting of graphs. A brief descrip-

tion of DRAW is included within APPENDIX IV.

A complete listing of program ARMREC and a complete set of flow

charts presenting the initial program logic are included as APPENDIX

II and I respectively. A description of all computer input and output

data appears in APPENDIX III.

22

8. Conclusions.

The real value of this simulation, as felt by its authors, is the

insight gained while trying to represent the important ingredients in

the simple duel developed in this thesis. An awareness of the pit-

falls and difficulties inherent in a simulation and the necessary com-

promises with reality to obtain manageable scope within a limited time

are important and invaluable aids in evaluating the results of this

and other simulations. The modeling or simulation of an event, even

of comparatively little magnitude, is the genesis of an almost unend-

ing sequence of investigations into all of its ramifications.

In particular, the authors feel that more sophistication is

required before the model can be called complete. Airborne and

ground element capabilities must be extended to more nearly approxi-

mate their operating envelopes. Several variables treated as deter-

ministic in the model should be considered as probabilistic, e.g.,

all type weapons fire as a unit and pop-up' s occur at definite time

intervals. It should also be noted that data used to generate the

program results is not assumed to be accurate. Kill probabilities

and sighting probabilities, for example, are but very rough estimates

assumed by the authors.

Time was not available to use program ARMREC in making a detail

analysis of the results of the interactions between the opposing

participants by changing the parameters and tactics in the thesis

scenario. However, some general observations can be made. Excluding

the effects of vegetation and man made obstacles, NOE flight with a

pop-up tactic seemed to enhance the helicopters' capability to detect

and successfully engage the land unit. Based on missile speeds of

23

350-370 meters per second firing at ranges of 1000-1500 meters and an

acquisition time required by the helicopter in excess of three to four

seconds, program results also indicates the requirement that a heli-

copter have a continuous LOS during missile flight significantly

lowers the probability of helicopter survival because of the time

available for the firing of land unit weapons.

24

BIBLIOGRAPHY

1. Hoppes, H.N. An evaluation of helicopter pop-up tactics .

Research Analysis Corporation, RAC-T- 464, November 1965.

2. Harrison, J.L. A computer simulation of an aircraft penetrationover hostile terrain , Thesis U. S. Naval Postgraduate School,May 1965.

3. Ethridge, N.H. Blast effects on simple objects and militaryvehicles (Secret), Operation Sunbeam, Little Feller, BallisticResearch Laboratories, POR-2261, September 1964.

4. Hoppes, H.N. Reconnaissance techniques for light observationhelicopters in a summer environment - A two sided field play ,

Research Analysis Corporation, RAC-T-433, August 1964.

5. Staff officers field manual - nuclear weapons employment ,

FM 101-31-2 ^Secret) and FM 101-31-3, Department of the Army,February 1963.

6. Glasstone, S. The effects of nuclear weapons , U.S. DefenseAtomic Support Agency, April 1962.

7. Von Senger Und Etterlin, F.M. The worlds armoured fightingvehicles , Doubleday and Co., 1962.

8. Armoured cavalry platoon and troop, air cavalry troop, and

division armored cavalry squadron, Department of the Army,

December 1961

.

9. Moulton, J.F., Jr. Nuclear weapons blast phenomena , Volumes

I and II (Secret), Defense Atomic Support Agency, March 1960.

25

APPENDIX I

This appendix contains the flow charts of the ARMREC computer

program logic. The following conventions will be used within the

chart.

Symbol Symbol definition

Read the input data listed

PRINT statement

A FORTRAN statement, the number 4

on the upper right hand corner is

the statement number. If the rec-tangle contains a call statementthe page on which the subroutinestarts, immediately follows thesubroutine name, e.g., P-4 meansflow for subroutine also starts onpage 4. Rectangle may be of any size,

LOGICAL IF statement.

COMPUTED "GO TO" statement

IF statement

26

DO statement,eg., "Do 6 1=1,10"

Used for BEGIN, END, RETURN, or

STOP statements

Connector between statementsin the same program or subroutinewhich appear on different pages or

cannot be connected by an unbrokenline.

A= connector symbol163= statement number to which it

connects if there is oneP70= connector appears on page 70.

Continue

CONTINUE statement

11

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34

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36

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37

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ARMK£C0Ac,mJOofJ3

JL—

N

m\4SPQ(/*3)J

icflc;* o

J.C&

iqFiq *Z

4JC7

$ SPT(P3)j

\y m.

JSFMi+l

si

J£9

38

ARMR£CPac,£ UoFjj

ICO

I':

' r-r«u£

49

CALL.PRTNTl

39

*,!*

AXMRGCpA**JZoFt3

40

'.

ARMREC r*ttr J3ofJ3

)

17

V-v£i

1*0

TJ : rr4

117 <*N"»H6**A»«| ^^^.^J^

41

S^^Aoi/r/iVe

8MDC K

fi£G/A/

X.3 JCMAX y5

r* (,c 1 erf t

42

8 t <*ld

1 70

PciD

f/PZ :

.- Ta*LSM=. o.

'r

/o

/W ioFi

t

VyTJ- r*UVO

x.l^pl

PJST> £tiP

.*_*

yVsX

J &

Cormuvt

1*

f fi£TuKM

ILO

jKTsi

43

BfbtKl

?A(,€ t**i

0j*= g"o#TF((v4-yrz<»

4t Of*"***?)

Jfc

no

Xt ,XTX- I?*>«£!*

Ih ^ez. —H

Hbtao

gU>z &u)**0.

^.

linn- r

XTSc sft

140

?TS€z 1

ICATz D&/i«M

Retu*.*i

44

S u3Aout2u€

ELEV

Begirt

I~.rHi*y*(Xrtt~i)

el

|_1

h

zl*

£*•y<VT~sty x

—+• ycy7 - BCi%

9jO V: XT-/5CX^v-yr- fic/3

K

x->t - ecxl

; X, XT- 01*3

I y--y? -gey

4

X- XT- 6'CXi

y; yr - 3CYS.

X--XT- ffcxi

v- > t- gey3

X--XT- »CK3

X:»fT- 6 t*3 ,5?

Uttl

45

£„;»

101

K'-t^MAMj

Ztz. AlMAx('i)+t-K

XL- A/MAXX

±I OS

——f

loo

L I1 'I'V^

c^ajr

ZC4MP siUMi

fA t>c 2.0*3.

tftTUtfA/

46

Pk<.e to<iX

n

F=lTLi)tl t

tt> t

?TU)< ¥T(l+l)

yes

Xo

Qni)<zT(x*i)p£+ IMAfl<%Z

IMA&Kz 1

i >1

F-. ir(X)4/o.

^'

47

.' '

Contour

?*<,£ Hotz.

iov

2*TF

VS-

Fr HO>J)

—r

—

vs

H(JTjs F

W^12**/ See NotF fi

y«

*..?

Co/triMi/?

</8o

Ron

* If***,

ns ro/°

ft6TU&N

48

So8/LouTltiC

7&sr/^AfeC I 0^3

Be d>iA/

(A-B)ltVtTF ( U -<*.)*

It

XFf:triiAr%»

A

.• TrO

yFic = yFi

yFZz^FP

yftsyLCall£l6i/

49

S"t/afit<3<jn a/ t

TQSEk^o/J

zFir =

/£

* *- soCall, alos(X7£, YT£

tZTr,

XFI, Yfil, 2Fl)\

Call ALOS(xrs

tYTjr

tzrr

t

S^Z, /FIt2FI)

/v

1 yPN ~ xpn+j.

50

TQSC

/MS

JOXPN = O

ATA?*fyr/?-S"0 «(-!)+ -IA

„/3

Yn-- Yfic

/y

AZXB r

*A<* 3 of

3

©RETURN

51

Bec 1 A/

RA^e 1 of

4

OXBF(AtB

tCtD) =

X/ECF(AJB£&) s.

(A ~6)/DX&F(A£pp)

Yn)KS(MA

PRINT*RRor

//V

>0 \ RTF

E J^

YQ(NQh YQI

1

Sro

52

RTE

Kz. Ni.fl C

CALL £~Lt"/

26(fejit-c —

Pkb£ AoFf

8P5X

iMfi/iilA&JlXX

A

IAA :IAA+1'

53

D

Pa*>€ 3oF*/

R eraAN

CAlLCoMToug

10

CoHT/AiVt

5X

54

'

SustiouTj/ije

> I

?A<>€ H ofti*

1

X<r(A/«* XKlk+l'Ll) '.

II

rAA-ZAA+l

55

ATTACK

&S<7

LLylt l/v>eTtfj

KttUfcJsO

rrU*)ro

Bean

Vt(.P(Afi,CP)4K'B)/

ASzcOcOI«SCrX0J*l

——a—— ii ii i

mt> ;Trt«.> s //'iff <l>s7«U)

T»tu>» *ft*f-t- fix*CffK*l4X*(.H.t\T«*('JjTo4t(t;,o TidiestJT7»;l »•#» t 2T01 O

56

'

Sugroutr *v rA TTA.GK(XNZTIAL A/C

**<ke Zofft

rpTT « ATTCir

+ HTA + PCror

l>l 9

! *\JT*1TDTT)

Call. Ranc>£

XLiX YL*YCall El.cv

Call Alos

57

SuGGOUTZME

Attack/'AqBSoFSZ

6SOO

CalculateXSI j YSIXS Tl , YS Tl

tokDeTEfrt/ne Roure** xsi

} Ysi, zsrTHENce t° xro

trro

t

zro

Oe TERM!n£ Rou reTo fS£

AVS£, ?5e

Wt

6J.ho

0e reiZMiue

ffoure Toxfi> yit, zfi

OerenM£r^eRoorc To

XttiyYnijtrxi

pEr&fZMXNERoure To

Xt£) Yq£>zc,£r

58

AttackPA(,m 4oF3Z

r

<°o3

log"

CoTiAft/s 4- -C^qM + jjr)- IOOt

(eOL

to

D'rERMlHC*

y<s^ y<Si/

59

S L>SAOur,'nff

ATTACK

Pm*>£ 6 0*33

y*'> » CTJ, ylf|£ „ TJ,iW£Call aJot (x ft. vF*.* rr *f TJ

m -- px fB(x u, x rlity%t

4rru

call rt$e<*TtttyrU,/4L**Sy«,*M, Vm, tiU,t rx£t j

call Alt>i(xr£yrrter x*Tit

XSXr XTII

y?i s ysrx

jrr/*x*s •

*M

Attack

>o

Co"*

' Xtl> YAl, f.FI i tz,j.)

ytf. ztsv 1

10 9O

**£, VS£t /srj.,

YST±

i3S

r&, xtr, yet *rtt vfi

r° Xf=-£t yrX, i?r

/V< +ZAA

(rU.

xsr- xsnysr* ysrj.

ser Pa^k xq

6,18

C/M. L At. OS

^"•fyt^rf-r^sr 'r

> xs-rr

I

bl

'•..

tATTACK

1V>

t>Tr*ATT+rsylCALL ttAMCitfflhZ/ijXiVA

UUALil(KAlf yni i 'i4I .

P4t ttAT

/W 7**33

X£*xrr = x

CALL £LEV

rr» rr+iCALL KlANGB(*T,yr,iT xrtA*i +

rr.rtrA

62

ATTACK

XPP- Ipfi+t

w, iaij

fit' It AT

Pttxrse

iPfizIPP+t

*.OO*O%0 tPP

rCALLALdSdrc

ZAllz tkl

fiiitCAT

pAte&*f35

Hob

lAti 2AIX +

TPP

CALlAL(b$(xrxyrtjirrxAr

PLiTCAT iTPPzO

pi*rrse

63

ATTACKfate f of 33

4t&

?A(I/4AX<tl-lY)=.

Jtt---XA(#$J:XAZ

CALL £L€i/

rSfUztSFif,

Cl.X.

H£*

+\rsrL(*s t%ru

*o8

64

Su&Aoi/TitJt

ATTACK Pa <*e io 6F33

<tz4 ,?Z3

EfzkTT

prr- att+to

(ATTAC< PottTj

I *^ J

1CAILA14>%(X6I

}

ft/zinc j Mb-.N+i

65

•

iTA^A/ri

v.

m

66

9"

.'* '

'

r #S?

SudfLouriuE

ATTACKPa<*£ IfLottZ

o

b7

ATTACKfh<.€ 13 oF32

\<oO

IPzO

©HIXZa

18

VTT' ATT+

CALLeAti&fCx^yi

PST€A*")/</£ (x t. r, yn___26r*

-Z,

uLCALL 4U SCt 1,1)

r?rr- 4Tr+

CALL JfAAJ^e

prrt ti m)

^LLAL0S(XAZt

y*hWtXrt,yTS.

Pl'tCAT

68

Si/QAootiaJ£

ATTACK

TiarjzATT

i

I

PftC£ IHoC&

A'

X8i

O

\

o

I

tycipj-att

1r

r?AVS(tFj;1

I

— ATTzATT-

IPAUSCTF):

o

69

ATTACK( A/C ATTAC*.

flit.€l$ of 3i

lot,

4f3

ZHUCi

70'

ATTACK?*<*€ If, of3S

A/'A* /YC+ tAk

Compart £outc To

TM>»X --A/A +IM

71

Si/StcovxiNe

ATTACKP*ue II of 31

$l.U

i-i

/o

P<./TJ,f-i

6o

)fKl.-XTX

y*ir yrz

jm,

8X7

ZfllNii):

VS3

n-.x m»y ^cau. «•!€•

^o

91t

r<t>Kay-o

XA/OCzZ

72

ATTACKF*<*e IS of 33

217

t%TS %

73

>*e 19 or33

h&tsJLiukyMLLW \i

74

S<s84oUT itlS

ATTACK

mi74LWTT T\pt>y *

~XL-.K t TfU.y ( CALL ftf/

>o

>H%

</S8

p<,/T4>r-i

tzo

Wi

Tt><(jl)zO

?o

<vvo

xKi=xrr

*f »*,N

-2

7 5

ATTACK ph<*€%\ 0*33

tUTpfit*

ZTDziO

Co"V 7S'Q I

rrrfimi -

IZ:TAPI>A*\:

i Z££*

TnPti)*TriP&j

9STf(H%\-

TOAM

Ji^-

+ STP--Z

7toV

rro= ZTOfto*

76

ATTACKPk<*€ Z% 0P33

Hfo

CULNULlit TDAtA

7goL

775/

i <0 776Q

V?l

t4 fc CU o

nzoH

Try pit):rrvpw -

/ryAHJ*r»l»OA»A

Htl

T4 fc ti) s

77

ATTACH

OAiAACe)

Ph1,e 23©P33

78

'suetLouTitJt Phue XV of £3

ATTACK

co-o

79

ATTACK

AfS«4PfctJ

P*(,e if*? 32

fTH

-j^ continvp

f>(L\HT

atmc*.

80

Attack

fW ftfcof33

31

ATTACK

Pa«.G Z?o<33

p$--o £ Pbzf**t13 =

tKlLLzZtP

TKXLl:Xtt£

AP^APCr

82

ATTACK

P*<*£*&<* 71

/U.<r</Kj£0

±~J1

frtp(pK)

j

S3

ATTACKf>At.€ 2,9 of 33

rsFzz- 4 I *

%o

rsfS 3

11

rMLLz.3

IdrFiZ

84

S(S&/t,OJTlA/£

ATTACK(mm AtTto fit

PkbctOeFlS

'-***•

call ptnnri

» *3L _ IPI'Z

CALLP&ltITi<?3*

L rpr=3

?vt

CALL f>HINT

i

WqHH

CH.L P&iMTl

85

'I

ATTACK( Mi st.)

pR<,e 3lcF%2

U

tTflsiW-OiJ

86

ATTACK

/W ^to^SZ

t$FL*>+l

87

^U0AOOTlKl£

ATTACK1°*** ?J o?33

88

Pau icP ?

BcC-riN

ASF(8,C,0)iASMF(8*C/c>)

r°i

TPAWxTPAfA41

Ct'^:P/ST7fo/xou, + XS^i?/

<?'?

T:ij2

3

1 I

2£*X6iXT«t/?<fc«»C«4F

/{IfcT-. DJSTS.S/

/?FtLOZ>F(I6O0,(

84

-;v

NUCpAqeZors

901

<&x)

+ z

INO -hi

90V

(OY)TNO^JND+Z

THE 7A =

A TNF(DY/OX)

r/JETA =\3.1Hlt> +

THETA

TNETA =

fHETA

t-22?

90

SvdKoLrriue

> NUC

11

r*t€TAT:THeJA

ETAi.

TM£7kT-T«6TA<,

*&it*«« Coif (£TA}

I

T«rrAr+rHfA6.

1i<*

s/wrjeTAj)

?A(,£.3otf

<?>A

ruerhQ- * T/itTA

tUQ'O i 2%: py ;0

PiiKTA- *T

Z>7S>T4 -vt

91

fi/VC

pAce 4 of?

«xT-*s>/yT-y6))

/Vtfc-.V&fc** /V^Sa/l/firJtj;

VrA;;c.»*(xrA-)(T/s«.(fKr4-rr^VW-rOi

rTAs»«t»ilVTA-vr/ » „ ^

CO:So«xTA-)faj(yrA«ytj;

J

£0* SDztcro

il

Xff>X8-VT

TPA*\'.TAf>OAMZb

JA/rO

, i

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92

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MS

TM-.THtrAIN or. O

©_1_

TMPzO

OK s *T5

1*3

9 3

PkG£ &0f9

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THteTHFTA

IOI<t /OHO

CTHzfHX'THi

lott

CTU: TM-TH1

CTH-S fe.183 2

IQU

-TUi + T»Z

t

94

SveAOuTtHt

hJUC/W 7 0F1

/ 079

TDAH\*TDAM*1

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iReruZN 4

95

NUC

J12$Al Hz AUiAB,

JL

lArS>A»P<£T«J*.

4101

C*TM s 4Sr{C0,

/.As S»«P(tTW)#

K*4

*M*JN4 4

Pkge Sof?

(AThtcrH)

AP/SJWF(AT«)

>lol

P«CXTW = A$F(P0,

JlVlATKJ^Q

£TH;3.'V/4-(Artf

/.As S/VP(tTM}HAo/tmrWty

96

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Su3£,OUTtNt

NUC

10(0$

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WPANwTaWa*1*1

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TQfirt-.rOAn+l

iOk,7

n

Ti?AM a T04ml

TAPPA^TVPAAHi

97

APPENDIX II

This appendix contains the FORTRAN listing of the ARMREC

computer program. All major divisions of the program are ident-

ified and comments are inserted into the listing where appropri-

ate.

98

rHrgcn^ir\vot^oo^o>^ogro^(i^vOf^oo<>o»^rg<^<fir\^r^oo(>o»--if\icri-^-ir\vOOOOOOOOOOHHHHHHHHHHMrVI(\J(\J(\l(\J(MMf\|fy|mm(0(f\(f\{f|(flOOOOOOCCCC OOOOOOOOC CCOOOOOOOOOOOOOOC5oooooooooooooooooooooooooooooooooooo

uLUasrr

-I

:•

•T

a13otl

co<

'

c I

o

< <

»

•I

uII

t

1,1

inV,

vO

s.

COv.

o*

o»•

1/5

zo"*>

_J

z>

aoou

I

J

Q»

c*

•

( J

Q

Q

><

CO

f J

(ll

< V

c

Q

O I h-_J o o.

•

I/) * *~ C> h-* >- Ll.

- : i-

»- o *»- x s:. . fl

iS> X Q.»— fNl CO• • h

H- <r •>

t- > _l-

urr

r j

>

CO

»

rr

*

U

— <l'' XM *» CL—

• >

>- Q

«M >

>

>

u I

x m•- Q

< 10>- CO- o< HX O.

15Z.'

or

lu oror UJ5." OQT LU< H-z

<QT LUo ao >-

or »-

Q-

rv

U 1

a•s

ZO:>

>ou

1Q

I—

(

>LU_J

LU

>

ii

*

Ua

Vi

a u-

5" oror »-» I> •-

ri

or J

r^

_J *or o

•> zt— •

U_ cO* z

•• <x •*

I—

1

f\l

I- Q.M •- O— ai— co

I- cOX Li>

i-< 5t- Z>I- z< z\ or

— a~- <t coc ~ *

c a ~en >- lT,

— I— CMx -> ~rsj •> <* — Q_~ <1" COc «- •O CO —f Z vO— CL .-I

<r y. ~rsj + O* -^ _j -»

— <t uj <fo — — —o U_ X

< I-

> <f <}•

O1/5

<-•

QQ<1

C

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— oc c-O c*>

C«"i —— X< oX INI

o »_J XLu <

i- x

a u;>- ot— •>

~> X* (—X r< u_

•> >X I/)

< t- »-

S! * fsj

o o *•— Cl vO 1-

tO Cl >-

Q

< or•• LU

CO —

i

•

—

* *>

O _)• <I- u< or

u •—»-i *>

» oLU <CO

O h- l_;

—. — <» \w \ <-l

or co »-- o z> -J oz < u

o cC C

>

u <N) m ir, vO r^

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i- ae o _i *o o

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<

x c o<r c o5: en mx >- —>v h- Or-l X X^r

u zcu O\ •—

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or — r\j

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— r\i >•^ -- z— o —»— CL •>

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— (NJ > O< *- Z II

H- I- •— 0.» * Q.

MII

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1/

Qo o o o a^> i-H <\i m <t

LUCJ a3 Oz: >

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< zrr oMD 1—

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H UD i—,

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1

aft LUl~- orcr;

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r u<

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LU _lX z;*r lu

a

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99

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i

o LU S"

u UlX LU

oz

Q \~ r>: >-

z , _i •

< a:

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•

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cc

U.UJ

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u. 1—

1

< a. '

i I i—

i

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< ui3 1— < U'

a: DQ UJ a • Q LU ct <UJ O >— o a (- UJ 2CO oc h- a h- < h- >—

1

5: • a i—

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h-idz

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Q-LU Q. 1—

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< z • ~ X CC aI o 1— Cfj *—« *-"» • < a U. <1— u X O cc to • U 5: CL o Ui

l-H CD o- 3 cr -~ LU >- < c UJ •-> U^1

0- _J >—

.

a O UJ • to •> UJ o ID to D> UJ t/i 1- U X o ID UJ a Ul a <r

_l X • UJ UJ Ui a: < h- Q LU ID z 3LU u lO • O 2 tO LU ZL Ul 2: O O O> V o h- tO u_ z -~ -~ 0_ X tO o K- UJ u to•—

i

u Z q: o < UJ UJ •v _J h- h- X UlH- < to U_ UJ t— X o 2 tO z < U. h- o D_ to yu 1— LU 2 H- » u z t—

«

CC •—1 ¥—* Ul O 1—1 o >-• t—

«

LU t— . U UJ UJ q: < 1- UJ s: s: _l CD ct h- <a < o t 4 _J s: i— ui cc h- to >- o _i rtto a ct LU X Q Z UJ z » z U. U u. Ll < ctUJ X m h- o •> 3 V o s: 3 z > o C o O > UJ

> ct u » < V o a: 1— U l-H ^- Ct l-H _l ct h-z « < t— > U lT\ i— «-" < h- o 51 o UJ UJ Ui UJ Lu CM*-* LU u. Q. < rg < 1— H- i—

i

LU u_ X a 1— h- h- h- i— u •—

i

»

DC U) LU t- * _J H- 10 LU o * < < < < z O 1— r-H

KJ < Q w> 0£ h- O > < <L —

•

o_ z X u. z z z Z (—

(

-—

> a: < < < o _i 3 tO 3 a: < o >—< t—

1

l-H t—-t z \ (Xi

Z > <r a H LU s: q O Ct Lu s: Q C3 Q c UJ o l-H

>—

i

Z O to ID O o 3 UJ < Ul z CO v cc Ct Ct ct ct 5" 1—1 _l •

•> l—

i

CO • a Z 10 » s: cc _l •> ^ * LU O O O o 1—

1

to h- 1— r\i

O < (\i Uj < h- vf i—i .—

i

o to o 3 o CO O o o o 1— z •—

i

ID Oen o o »• Z o X to _J Ul o Z o s: u u u L; UJ # • Oo z CO o »- •> Ul o < UJ UJ •—> o o 3 Ul 2 X i—l

•—

1

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APPENDIX III

This appendix contains a complete list and card format for the

input variables to the ARMREC program. Following the input descrip-

tion is an example and description of the program output.

It should be noted that in the input description the variable

name is the name of the input variable as it is used in the program.

It is not necessary to punch this name on input cards, only the

values or symbols assigned to the variable names are punched on the

cards.

Input data cards for program ARMREC should be prepared as in-

dicated. The values of all input parameters are right justified in

the fields assigned and the value of each variable whose name begins

with I,J,K,L,M,N is a fixed point number while all others are float-

ing point unless otherwise indicated.

142

DataGroup

Numberof cards

1

VariableName

ITL

INVC

INV

SPA

SPT

SPG

DELV

ATR

HTR

TOF

Columnsof card

1-2

1-10

11-20

21-3031-40

1-50

1-50

1-50

1-10

11-20

21-30

31-40

Description of

Variable

Time length of game, less

than 99.

The number of nuclear missiles

carried by each helicopter in

the attack section.

The number of conventional

anti-armored missiles carried

by each helicopter in the

attack section.

The probability of sighting

by the helicopter scout air-

craft.

The probability of sighting

by the armored unit.

The sighting probability of

the attack helicopter air-

craft .

The change in elevation of

a helicopter in the pop-up

mode

.

The proposed helicopter

attack range.

The helicopter acquisition

time.

The missile time of flight.

143

DataGroup

Numberof cards

VariableName

NRUN

KMAX

XMIN

YMIN

XMAX

YMAX

TI

TPD

MNAX

NMAX

Columnsof card

1-10

1-10

11-20

21-30

31-40

41-50

51-60

61-70

1-10

11-20

Description of

variable

The number of runs to be

made.

The number of polynomials

to approximate the terrain,

KMAX less than or equal to

12.

The X coordinate of the left

edge of the terrain.

The Y coordinate of the bot-

tom edge of the terrain.

The X coordinate of the right

edge of the terrain.

The Y coordinate of the top

edge of the terrain.

The game time interval.

The dimension of a terrain

square approximated by one

polynomial.

The degree of X in the poly-

nomial which approximates the

first terrain square.

The degree of Y in the poly-

nomial which approximates the

terrain in the first map

square.

144

Data NumberGroup of cards

8 As manycards as

necessary

VariableName

PHI

Columnsof card

1-80

Descriptionof variable

The coefficients of the first

approximating polynomial in a

(4E20.10) field as obtained

from the terrain simulation

program.

NOTE: Data groups 7 and 8 are repeated KMAX times.

in

11

12

A 1-20

B 21-40

C 41-60

W

PK

TRD

61-80

1-10

11-20

NWPTYP 1-10

WPNAWPNB 1-16

The coefficients of the ex-

potential function which

estimates the overpressure.

(See DASA pubs)

.

The nuclear weapon yield in

kilotons

.

The kill probability of a

conventional anti-tank mis-

sile .

The target radius of damage

for a nuclear weapon of

yield W.

The number of weapon types

located with armored unit.

The name of the weapon, e.g.,

Red Eye.

145

Data NumberGroup of cards

13

VariableName

JTYP

TA

FT

RLT

RMAX

RMIN

TFT

Columnsof card

21-25

26-30

31-35

36-40

41-50

51-60

61-70

1-8

9-16

17-25

etc.72-80

Descriptionof variable

The number of weapons of this

type. JTYP is proportional

to the number of units in the

armored unit.

An integer, the time required

to acquire the target by this

weapon. (Seconds)

.

An integer, the firing time of

this weapon before reloading

is required. (Seconds)

.

An integer, the reloading time

of this weapon. (Seconds)

.

The maximum range of this

weapon in meters.

The minimum range in meters of

this weapon.

The total firing time available

for this weapon. (Seconds)

.

The probability of a kill by

this weapon for a range of

0-2500 meters in 100 meter

increments

.

NOTE: Data groups 12 and 13 should be repeated NWPTYP times for each

of the NRUNS

146

DataGroup

L4

Numberof cards

L5

lb

VariableName

AFIELD

GMAX

RC

Kb

GS

TSPD

GSG

TSPDM

IMARK

Columnsof card

1-16

1-10

11-20

21-30

31-40

41-50

51-60

61-70

1-10

Descriptionof variable

These four cards have the

title of the run to be

printed at the top of the

output page.

The maximum positive G force

to be used by the aircraft.

Aircraft maximum rate of

climb . (f t . /min.

)

Aircraft maximum rate of

descent . (f t . /min.

)

The estimated ground speed

of the scout helicopter,

(knots)

.

The estimated speed of the

armored unit. (mph)

.

The estimated ground speed

of the attack helicopter

element (knots)

.

Emergency speed of the armored

unit (mph)

.

This flag determines the type

of flight path flown by the

helicopter scout and attack

elements during the recon-

naissance phase.

147

Data NumberGroup of cards

VariableName

Columnsof card

ISEP

IPOP

IKILL

11-20

21-30

31-40

Descriptionof variable

NOE = nap of the earth flight

PP = preplanned flight

scout attack

IMARK= 1 PP PP

= 2 NOE NOE

= 3 PP NOE

= 4 NOE PP

The starting time separation

between the scout and attack

helicopter sections.

The minimum elapsed time

between pop-ups.

This flag aids in determining

which aircraft to fire at.

IKILL= 1 Fire all weapons at

scout aircraft if

possible.

= 2 Fire all weapons at

attack aircraft if

possible.

= 3 Fire all weapons at

aircraft with high-

est kill probability,

= 4 Fire available weap-

ons at both aircraft,

148

Data Number Vari able ColumnsGroup of cards Name of card

1 / As manycards asnecessary

XA 1-20

21-30

31-40

ISTP 41-45

L8 As manycards as

XG 1-20

necessary YG 21-30

ZGH 31-40

ISTP 41-45

1M As manycards as

X'l 1-20

necessary YT 21-30

ZT 31-40

ISTP 41-45

Descriptionof variable

Each of the cards of this group

contains the X, Y and Z co-

ordinates of the helicopter

scout section in consecutive

time intervals.

ISTP=1 on last of these data

cards and is zero otherwise.

It is the only variable ap-

pearing on last card indicat-

ing all data for scout air-

craft has been read in.

Contains the same type of

information for the helicop-

ter attack section as found

in data group 17.

Contains the same type of

information for the armored

unit as found in data group

17.

NOTE: Data groups 11-19 should be repeated NRUN times

149

Output of Program ARMREC

Output from program ARMREC is illustrated in Figures 1, 2, 3,

and 4. Figure 1 contains the land unit weapon data, the mission

title and the simulation parameters for entry into ATTACK. Figure 2

shows the simulation status for each time step. Figure 3 represents

the printed historical tableau containing the important interaction

data. Figure 4 is a graphical presentation of the various phases

of the duel simulation. Description of the variables which appear

in Figures 1 and 2 is given on pages 155 and 156.

150

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FIGURE! 1

Land unit weapon data, mission title, and

simulation parameters for entry into ATTACK151

ATT = 33.000000

XAI = 72955.929 YAI s 75454,399 ZAI « 379.235

XQI = 71661,661 yd « 76336,125 2Q 1 > 345.946

XTI = 73075,801 YTI * 767Q0.000 ZTI » 297.862

SCOUT s 1251.3555DIST. TO TGT FROM

A-Q * 1460.2043

SCOUT s

LOS, TGT TOA-Q a 1

PR08 OF SCOUT SURVIVAL = 1.00000

PROB OF A-G SURVIVAL = 1.000 00

ISF = 1 IGF a J 1

KSS = 0,~

K G G__f __0 0.

TF =

IT = ..____o

3 IGFLG =

i

ISFLG s__

TOK =

INVC =2

ITMV 81 ISO , o IGO • ~

J J YP*3 3 2 2

FIGURE 2

Time step simulation status

152

i

SUMMARY OF RUN NUMBER, 1

DAMAGE RESULTS

ELEMENT TIME POSITION RANGE WEAPON(S) DAMAGE12 3 4 EXTENT

SCOUT A/C

1 87 _ x «. 732o6 . 1218 1

Y s 75489

ATTACK A/C1 X =

Y

2 X « 0000Y =

ARMOURED UNITTANK 91 X a 73o76 n5i 1 I

Y s 767qo

TANK 92 X * 73o76 n82 1 2Y 3 767 o

APC 92 X * 73 76 n82 1 2Y c 767 00

0X« 0000_ Y » .

ox« 0000Y «

FIGURE 3

Historical tableau

NOTE: Should be read as follows: One tank damaged at coordinates(X,Y) during the 91st second of game time. Weapon 1 indicatesdamage to tank by a nuclear missile, Weapon 2 indicates damageresulted from a conventional weapon. Aircraft damage can beinflicted by Weapons 1 through 4 which appear in the summaryof target weapon data, Figure 1.

153

77000

76OO0

7SOOQ

74000

7 7*'dO *~

-pieoo

7SOOO

7*000

rron

'OCO 72009

FIGURE 4

MOUEMENT OF HELICOPTER fl/C

AND TANKS fJOHNSON. UflN LEELUEN)

154

Definitions for the variables appearing in FIGURES 1 and 2 are

given below:

Variable Definition

XAI,YAI,ZAI Present coordinate positions of the scout heli-

XGI,YGI,ZGI copter section, attack helicopter section and

XTI,YTI,ZTI ground unit respectively.

ISF.IGF Results of ground unit fire on respectively the

scout and attack helicopter sections.

= 1 no fire

= 2 fired and missed

= 3 fired and hit

KSS.KGG Depicts the ability of the land units weapons

1 through 4 to fire respectively at the scout

and attack sections.

= 1 can fire

= cannot fire

TF The length of firing time since reloading for

the land units weapons 1 through 4.

IT The number of times that the ground units

weapons have been reloaded.

ISFLG, IGFLG Defined with comments in program ARMREC

.

TOK Estimated impact time of the attack helicop-

ter section's missiles.

155

Variable

INC.INV

ITMOV

ISD,IGD

JTYP

P2,P4

P1,P3

Definition

The number of nuclear and conventional missiles

expended by attack helicopters one and two.

= 1 tank stopped , = tank moving

The number of scout and attack helicopters dam-

aged.

Number of effective ground unit weapons.

Indicate the existence of an LOS from the scout

to the ground unit and the attack section to the

ground unit.

=1 no LOS

= 2 LOS exists

The ranges from the scout section and the attack

section to the ground unit, rounded up and in

terms of 100 meters.

156

APPENDIX IV

Comments on Program TERRAIN

In order to adequately simulate the effects of terrain on the

movement of the engaging units in ARMREC , the program TERRAIN, as

presented by Capt. J. L. Harrison, USMC, ( 2 ) with a few minor

modifications was used. With this program the elevation of any point

in the area of movement of the combatants can be computed.

Terrain elevation for this model is found by using an approximat-

ing polynomial function, Z = F(X,Y) , in which the coefficients of the

polynomial are computed by the program TERRAIN. Use of the approximat-

ing polynomial appears to be the most accurate way of simulating ter-

rain and eliminates the need for the large computer storage necessary

when average elevation squares are used to represent terrain surfaces.

With a set of input points (Z,X,Y), the program, using the least

squares method, fits a polynomial of the form Z=F(X,Y) to approximate

the three dimensional surface from which the input points were taken.

In this thesis, input points were obtained from terrain squares of

2100x2100 meters in order to adequately fit the 2000x2000 meter square

centered inside. Eight of these squares were used to provide the

maneuvering area for the scenario in ARMREC.

The surface from which the input points were taken was a mockup

contour map closely resembling the Stoney Valley area of the Hunter

Liggett Military Reservation. Elevations varied from 1100 to 1900

feet within this area. Polynomials of the form, Z= /_ „/_ c? X /

which were fitted to each terrain square in the mockup area contained

as many as 400 terms with the power of X and Y reaching a maximum of

20.

157

In order to provide the storage area required by the input data,

program TERRAIN was written in FORTRAN 63 as a main program with three

overlays. The main program's function is to call the separate over-

lays into operation. Each overlay provides the extra storage neces-

sary by using a magnetic tape as auxiliary storage.

A facsimile of the terrain program output data which includes a

printed list of the coefficients Anm and a plotted 2000x2000 meter

mockup terrain square appear in Figures 5 and 6 in this Appendix.

The coefficients Anm also appear on punched cards for input to ARMREC.

Potential users of Program TERRAIN should be aware of the changes

necessary in the spacing data and parameters throughout the program

when map squares larger than 1000x1000 meters are used. This is nec-

essary so that the number of equally spaced grid lines, used in the

program overlays for finding terrain elevations at equally spaced

points, do not exceed 45.

When the CDC-1604 at the USNPGS computer facility is used, it

is necessary that the terrain program and input data cards be read

onto tape using the CDC-160. This tape is then used as the input

tape on the CDC-1604. Failure to follow this procedure will yield

FORTRAN 63 computer diagnostics peculiar to the system which will

delete program execution.

158

FIGURE 5

UflN LEEUWEN, JOHNSONHLMR MOCKUP TERRAIN GRID SQUARE 5281

i

159

COEFFICIENTS OF APPROXIMATING POLYNOMIAL

CEGREE

CF X_0

69

12-1518

OEGREE CF

_2_c

en17

1.3235205812E 03-9.088667628UE-06-1 .6213201266E-13U.4225802512E-213.08R9917657E-30

-1.1U87293172E-38-2.772731U690E-M9

-2.7191879898E-01-3.88195515143E-08-9.528958G221E-161.3i47E993178E-231.151 1775U1UE-32

-3.97711493299E-41-7.8370136028E-52

6.1153U63628E-021 .6539701U27E-081. 1350730M76E-151 .9981628979E-2M1.39866R1291E-321 .3651765C55E-429.7OO7M73202E-52

1 .U4R5669925E-031.3116 5U3FJ71E-1C3.37R6960197E-188.3779206C92E-274.6527106563E-35U, 186*4 722*497E-453.581C691393E-54

7.290307796UE-CM1.5602717169E-107.6244207965E-191.01 1U873960E-262.7949186522E-365. 15103301R4E-45

6.87695390S7E-06U.89777620ROE-133.6870C90048E-213.2189376366E-299.39U8519852E-391 .8U61950799E-47

3.588G35157OE-0U_ 1...199M126548E-101. 1093652E64E-18

-3.952U054C82E-26-1.951 17i42975E-35

. __ 9..M366923S45E-4U1.373651076UE-5I*

3.4529136C88E-06•9.680C867394E-1U1 .0927755537E-201.3U67812133E-291.1636337C65E-377.3329C131M1E-U87.9U777U79U0E-57

1.0115470708E-09•1 .68630C9345E-15_5.3231709518E-2U8.635913818UE-321 .6312499313E-U1M.2\MU1tt£tSE~5Q_

FIGURE 6

INITIAL PRINT OUT OF THE COEFFICIENTS OF THEPOLYNOMIAL WHICH APPROXIMATES GRID SQUARE 5281

•.

160

INITIAL DISTRIBUTION LIST

No. Copies

1. Defense Documentation Center 20

Cameron StationAlexandria, Virginia 22314

2. Library 2

U. S. Naval Postgraduate School, Monterey, California

3. Commandant of the Marine Corps (Code A03C) 1

Headquarters, U. S. Marine CorpsWashington, D. C. 22214

4. Prof. Alvin F. Andrus 4

Department of Operations AnalysisU. S. Naval Postgraduate School, Monterey, California

5. Team IV CDCEC 1

Fort Ord, California

6. CAPT Richard R. Johnson, USMC 1

4517 North Monticello, Chicago 25, Illinois

7. CAPT Neil R. Van Leeuwen, USMC 1

3747 South 645 East, Salt Lake City, Utah

161

Unclassified

Security Classification

DOCUMENT CONTROL DATA - R&D(Security clmmmttlcmtlon ol title, body ol obttrect and Indexing annotation muat be entered whan the overall report ia claaatlied)

1 ORIGINATING ACTIVITY (Corporate author)

U. S. Naval Postgraduate SchoolMonterey, California

2a REPORT SECURITY CLASSIFICATION

Unclassified2b CROUP

3 REPORT TITLE

A SIMULATION OF HELICOPTER AIRCRAFT IN AN ARMED RECONNAISSANCE MODE,

FOR THE CDC 1604 DIGITAL COMPUTER

4 DESCRIPTIVE NOTES (Type of report mnd Inclusive dataa)

ThesisS AMTMORfSJ (Lmat name. Ilret name, Initial)

Johnson, Richard R. , CAPT, USMCVanLeeuwen, Neil R., CAPT, USMC

• REPO RT DATEMay 1966

7e TOTAL NO OF PAGES

161

7 b NO OF REFS

• a. CONTRACT OR GRANT NO.

b PROJICT NO

9* ORIOINATOR'S REPORT NUMBERfS,)

9b OTHER REPORT NOfS) (Any other numbera that may be aaalgnad(hi* report)

10 AVAILABILITY/LIMITATION NOTICES

13 ABSTRACT

A model is presented which is a computer simulation of a duel involving

two helicopter sections, a scout and an attack section, and an armored

mobile land target. Terrain features are considered in the model by using

a "least square" polynomial to represent the terrain environment. The

model was constructed in an attempt to include the possible effects of

terrain on tactics used by the combatants in the duel. The computer pro-

gram, logic and model results are included.

DD FORM1 JAN «4 1473 16: Unclassified

Security Classification

Unclassified

Security Classification

14.KEY WORDS

ComputerHelicopterSimulationArmed Reconnaissance

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