NASA Contractor Report 4160 

Rule-Based Air Combat Simulation 

G. H. Burgin and L. B. Sidor 

Titan Systems, Inc. 

La Jolla, California 

Prepared for 

Ames Research Center 

Dryden Flight Research Facility 

under Contract NAS2-11990 

National Aeronautics 

and Space Administration 

Scientific and Technical 

Information Division 

1988 
FOREWORD 

While Titan wasunder Contract to the NASA Dryden Flight 

Research Center (Contract NAS2-11990), Titan was also under 

contract to the NASA Ames Research Center, Moffett Field 

(Contract NAS2-11824). Both contracts had as ultimate goals to 

improve the Adaptive Maneuvering Logic Air-to-Air Combat 

Computer program. 

The emphasis in the Moffett Field program was to improve 

the guidance laws, regardless of required execution time on a 

computer. In contrast, the Dryden effort was to provide a robust 

decision logic, guaranteed to work in real time. The logic 

developed for Dryden should eventually drive an actual aircraft 

in real flight. 

During the course of this work, it would have been 

unproductive to keep book which of the AML improvements should 

be credited to the Moffett Field contract and which ones to the 

Dryden contract. This final report on contract NAS2-11990 is 

therefore essentially the same as the final report on contract 

NAS2-11824 (Simulation of Modern Air-to-Air Combat). The present 

report has some material added in section 3 and a substantially 

enlarged section 5. It also contains an Appendix with the 

Fortran listing of the subroutines implementing the IIBasic 

Fighter Maneuverstt. 

i 
CONTENTS 

Section 

SUMMARY 

1 OVERVIEW OF AIR COMBAT SIMULATIONS AND 

METHODOLOGY 

2 

3 

1.1 Deterministic and Stochastic Models 

1.2 Offline and Real-Time Simulations 

1.3 Weapons Models 

1.4 Aircraft Models 

1.5 Decision-Making Process 

1.6 Performance Measures 

DEVELOPMENT HISTORY OF THE AML PROGRAMS 

2.1 NASA Langley DMS Program (AML 75) 

2.2 The DMS Control Model (AML 76) 

2.3 A One-Versus-Two Version of AML 

(AML 1V2) 

2.4 AML with Revised Equations of Motion 

(AML 84) 

2.5 Northrop Aerosciences Laboratory AML 

(Interactive Target) 

2.6 General Electric's AML version on the 

Simulator for Advanced Airmanship 

(AML 86) 

2.7 AML 87/Expert Ivan 

2.8 Missile Evasion AML (AML/SAM) 

2.9 Pilot's Associate D1 AML Program 

THE BASIC AML IF => THEN LOGIC 

3.1 Terminology 

3.2 Commonality with the Trial Maneuver 

Logic 

3.2.1 Timing Considerations 

Page 

vii 

1-1 

1-2 

1-5 

1-7 

1-11 

1-12 

1-16 

2-1 

2-1 

2-1 

2-3 

2-4 

2-5 

2-6 

2-6 

2-7 

2-7 

3-1 

3-1 

3-1 

3-1 

ii 
CONTENTS 

Section Page 

I 3.2.2 Maneuver Plane Concept 

3.3 Decision Hierarchy 

3.3.1 Ground Avoidance 

3.3.2 The Pointing Algorithm 

3.3.3 The Lead/Lag Maneuver Logic 

4 AIRCRAFT AND CONTROL SYSTEMS DYNAMICS 

4.1 Selecting an Appropriate Model 

4.2 Synopsis of the Current Attitude Control 

Mechanism 

4.3 Refined Calculation of Commanded Pitch 

Rate 

4.4 The Pointing Control System 

5 SAMPLE TRIAL MANEWERS AML VERSUS 

IF => THEN AML RUNS 

5.1 Region 2 

5.2 Region 3 

5.3 Region 4 

5.4 Region 5 

5.5 Region 6 

5.6 Conclusion 

6 ADDING BASIC FIGHTER MANEWERS TO THE 

IF => THEN LOGIC 

6.1 Opposite Turn 

6.2 Diving Overshoot 

6.3 Pull-up Overshoot 

7 CONCLUSIONS AND RECOMMENDATIONS 

8 REFERENCES 

3-2 

3-4 

3-4 

3-4 

3-5 

4-1 

4-1 

4-3 

4-5 

4-6 

5-1 

5-4 

5-8 

5-11 

5-23 

5-34 

5-34 

6-1 

6-5 

6-11 

6-17 

7-1 

8-1 

iii 
1-1 

1-2 

1-3 

1-4 

1-5 

2-1 

3-1 

3-2 

3-3 

4-1 

5-1 

5-2 

5-3 

5-4 

5-5 

5-6 

5-7 

5-8 

5-9 

5-10 

5-11 

5-12 

5-13 

5-14 

FIGURES 

Level of Detail in Simulations 

Gun Vulnerability Cone 

Typical Missile Envelopes for Maneuvering 

and Non-Maneuvering Targets 

Definition of Deviaton Angle and Angle-off 

Ambiguities in the Line-of-Sight/Angle-off 

Representation 

Development History of the AML Air-to-Air 

and Missile-Evasion Programs 

Illustration of Maneuver-Plane Concept 

Regions for Steering Laws 

Summary of the AMLB Control Laws 

Block Diagram of Pointing Control System 

Definition of Regions 

Region 2, X-Y Trace 

Region 2, PI Plot 

Region 3, X-Y Trace 

Region 3, PI Plot 

Forward Quarter Turn Options 

Forward Quarter Pass, Case 1, X-Y Trace 

Region 4, PI Plot 

Forward Quarter Pass, Case 2, X-Y Trace 

Case 2, Region 4, PI Plot 

Forward Quarter Pass, Case 3, X-Y Trace 

Case 3, PI Plot 

Forward Quarter Pass, Case 4, X-Y Trace 

Case 4, PI Plot 

1-3 

1-8 

1-10 

1-18 

1-21 

2-2 

3-3 

3-6 

3-7 

4-8 

5-3 

5-5 

5-6 

5-9 

5-10 

5-12 

5-13 

5-14 

5-16 

5-17 

5-19 

5-20 

5-21 

5-22 

iv 
5-15 

I 5-16 

5-17 

I 5-18 I 

5-19 

5-20 

5-21 

t 

5-22 

5-23 

5-24 

5-25 

6-1 

6-2 

6-3 

6-4 

6-5 

6-6 

6-7 

6-8 

6-9 

6-10 

6-11 

Region 5, Case 1, X-Y Trace 

Region 5, Case 1, PI Plot 

Region 5, Case 2, X-Y Trace 

Region 5, Case 2, PI Plot 

Region 5, Case 3, X-Y Trace 

Region 5, Case 3, PI Plot 

Region 5, Case 3, Line-of-Sight and 

Angle-off Plot 

Region 5, Case 4, X-Y Trace 

Region 5, Case 4, PI Plot 

Region 6, X-Y Trace 

Region 6, PI Plot 

Outline of the Implementation of Basic 

Fighter Maneuvers 

Opposite Turn Case 1 

Opposite Turn, Case 1, PI Plot 

Opposite Turn, Case 2, X-Y Trace 

Opposite Turn, Case 2, PI Plot 

Diving Overshoot, X-Y Trace 

Diving Overshoot, PI Plot 

Lead/Lag Overshoot, X-Y Trace 

Lead/Lag Overshoot, PI Plot 

Pull-up Overshoot, Case 1, X-Y Trace 

Pull-up Overshoot, Case 1, PI Plot 

5-24 

5-25 

5-26 

5-27 

5-28 

5-30 

5-31 

5-32 

5-33 

5-35 

5-36 

6-3 

6-7 

6-8 

6-9 

6-10 

6-13 

6-14 

6-15 

6-16 

6-18 

6-19 

V 
TABLES 

1-1 

1-2 

5-1 

Complexity in Air Combat Simulations 

Representative Values of Deviation Angle 

and Angle-Off 

Initial Values for Sample Runs 

1-6 

1-22 

5-1 

vi 
SIMULATION OF MODERN AIR COMBAT 

By George H. Burgin and Laurent B. Sidor 

Titan Systems, Inc., La Jolla Ca. 

SUMMARY 

This final report on Contract NAS2-11824 is organized 

in seven sections plus a list of 25 references. 

Section 1 provides an overview of current topics in the 

simulation of air-to-air combat, touching on such subjects as 

weapons simulation, aircraft modeling and performance measurement. 

In section 2, the history of a set of computer programs, 

developed over the last 15 years is traced. These programs are 

generally known as !!Adaptive Maneuvering Logic" (AML) programs. 

They exist in many versions: Air-to-air combat and missile 

evasion, real-time and non-real time versions. 

The air-to-air combat simulation exists in two basically 

different versions: The older version, the lttrial-maneuvertv 

version, is described in other NASA reports. The newer version, 

the "IF => THEN version, is the subject of section 3 of this 

report. 

Section 4 summarizes some important aspects of aircraft 

dynamics modeling. The interrelationship between the tactical 

vii 
decision process and the aircraft model is shown. For example, 

tactical performance can be significantly improved if the 

modelled aircraft can be controlled by a control system capable 

of orienting the aircraft's longitudinal axis into a desired 

direction (pointing control system). 

Section 5 compares the performance of the trial maneuver 

logic with the IF => THEN logic and demonstrates how each logic 

may be improved by 'lplaying" it against the other logic. 

To make the performance of the IF => THEN logic less 

predictable,some basic fighter maneuvers were added to AML which 

are invoked, when appropriate, under the control of pseudorandom numbers. These maneuvers are described in section 6. 

Finally, section 7 provides some suggestions for 

continued work in developing advanced guidance law for air-toair combat. 

viii 
1. OVERVIEW -- OF AIR COMBAT SIMULATIONS AND - METHODOLOGIES 

Simulation of air-to-air combat has become an 

indispensable tool for pilot training, for tactics development, 

for weapons systems evaluation and for a host of other 

applications. Air combat becomes more and more complex due to 

advances in electronic warfare. Air-to-air combat today begins a 

long time before the opponents have visual contact. Radar and 

other sensors provide critical input to the pilot at a range far 

beyond the visual range. It has therefore become common practice 

in the analysis and in the simulation of air-to-air combat to 

differentiate between a "Beyond Visual Range (BVR)" phase and a 

Ifclose In Combat (CIC) phase. 

I 

The present report is concerned primarily with simulating 

the CIC environment. Specifically, we will discuss in detail a 

series of computer programs generally known as "Adaptive 

Maneuvering Logic Program (AML). These models and simulations 

were developed under NASA sponsorship with the initial goal to 

have an intelligently interactive, real time opponenet on NASA's 

differential maneuvering simulator (DMS) at the Langley Research 

Center a 

pilot during air combat engagements. 

and with the long-range goal to provide assistance to 

A measure of the complexity of modern air war may be 

obtained by reading the account of Israeli air operations over 

Lebanon in 1982 (Reference 2). These operations involved air 

superiority fighters in strike escort and combat air patrol 

roles operating in concert with many other elements such as 

1-1 
SAMs, AWACS, ground-based radars and communication centers, 

stand-off jammers, and RPVs. Similarly complex operations are 

involved in the air defense of U.S. carrier task forces (see 

for example Reference 3). 

Due to the complexity of such air operations, individual 

air simulations must focus on a particular, limited area of air 

combat. We will briefly review the current state-of-the-art in 

air combat simulations in order to put a perspective on the area 

considered by AML. Some of the key issues addressed by this 

report will be: 

- Number of aircraft involved in the simulation 

- Types and properties of weapons employed by the 

combatants 

- Degree of complexity of aircraft and weapons models 

- How random effects are simulated 

- Off-line simulation versus real-time simulation 

1.1 DETERMINISTIC AND STOCHASTIC MODELS 

The common point of departure for air combat simulations 

are various scenarios of Air Force and Navy Missions. In the 

final analysis, their common evaluation point relies on pilot 

opinion. In the design phase, a basic trade-off must be made 

between the accuracy in modelling individual elements and the 

size and execution time of the code. Figure 1.1 attempts to 

portray this trade-off. Engineering simulations which model in 

detail physical mechanisms (such as warhead fuzing) are limited 

to one or two units. At the other end of the spectrum are 

1-2 
/ 

u 

z 

3 

W 

z 

H 

u 

z 

w 

m 

0 

4 
campaign or force-on-force models with hundreds of simulated 

units. In these models, the representation of physical 

mechanisms in the simulation is done in terms of aggregated 

performance measures. The simulation of even a minimally 

representative number of opponents in the case of NATO vs Warsaw 

Pact scenarios (2 vs 4) leads to an explosion in the 

computational requirements. 

The performance of many aspects of weapons systems is 

expressed in terms of probabilistic quantities, for example 

radar probability of detection or kill probability of a missile 

warhead against a target type. The combination of these 

probabilities can be performed in one of two ways: (1) Expected 

value method and (2) Monte-Carlo method. In the expected value 

method, the probabilities are combined using the law of 

probabilities for the particular probability law obeyed by the 

simulated process. For example, if there are N independent 

interceptors, each with a probability PD of detecting a single 

bomber over a period of time, then it may be shown that the 

expected fraction of bombers FDB detected at the end of the 

period of time will be : 

FDB = 1. - exp( N *PD/ M), where M is the total number of 

bombers. (Reference 15) 

In contrast, in the Monte-Carlo method, the outcome of a 

probabilistic event is assessed based on the draw of a random 

number. For this reason, these are described as "discrete 

events". Repetitive trials must be performed to obtain averages, 

1-4 
a process which multiplies computational requirements. In 

I addition, in Monte-Carlo simulations, the sheer volume of 

I information makes it difficult to trace causative factors. For 

I 

~ these practical reasons, Monte-Carlo models are popular up to 

the mid-range of Figure 1-1; for campaign models, only expectedI 

value models are practical. 

1.2 OFFLINE AND REAL-TIME SIMULATIONS 

The simulations discussed above consist of I1off-linefl or 

lvnon-real timet1 simulations. Even these non-realtime 

simulations may require execution times which limit their 

economical use for studies and analyses. 

In a real-time simulation, two tasks have to be performed. 

First, the equations of motion for each participant must be 

solved satisfying the condition that the CPU-time to perform the 

calculations for one integration step will not exceed the 

allocated frame time. The second task requires the simulation 

of the decision process for each platform. The required CPU time 

to perform this second task also must fit into the allocated 

frame time. Typical frame times for real-time close-in air-toair combat simulations with a human pilot in the loop are 

between 10 and 50 milliseconds. 

Table 1-1 illustrates the parameters involved at both ends 

of the spectrum in complexity in air combat simulations. The 

AML programs feature a high complexity simulation environment, 

moderate complexity in aircraft performance and tactics 

1-5 
Point mass 

!nstantaneous response 

------- UEaPOYS 

GUM: F'k, Vulnerability cone 

Yissiles: PI!, Launch envelopes 

Time-of-( light 

I 

I ey!gdjKs 

Radar, IE5T , visual detection ranges 

TKT!CS ------- 

1-on-1 

Pr e-progr armed 

Point mass 

Idealized guidance laws 

Generic production 

rules and 

qui dance 1 aws 

5 DN model 

Nan-1 inear aerodynamics 

Non-linear flight controls 

Guns, Hissiles 

5 DOF fly-out 

Riss distance 

Pk ior R!C vulnerable mas 

Detailed seeker, guidance and control 

and propulsion eodels 

Efiects of Jarming and/or IFXH 

Radar, IRST detection probab!!it!es 

Target g 1 i nt 

Counterreasures 

Bany-on-many; section tact its 

Production rules and tactics 

optimized for platfora!weaponltarget 

Trial maneuvers 

Coraand and control 

Integration with SAHs 

Real tire flight simulator 

Terrain 

d t maspher i c vi si bi 1 i t y 

1-6 
representation, and low complexity in weapons and avionics. 

1.3 WEAPONS MODELS 

The armament considered in air combat simulations consists 

of guns, guided missiles and, recently, lasers. Because of the 

research nature of these simulations, a significant amount of 

effort has been spent on simulating air-to-air lasers, while 

this weapon has yet to see operational use. They will not be 

discussed further here. 

The basic requirement to achieve a gun firing position is 

to point the nose of the aircraft at the target. Steerable guns 

would alter this requirement, but presently there are none 

operational on fighters anywhere in the world. In general, to 

achieve a kill will require several hits on the target. For this 

reason, an off-tail position is preferable (Figure 1-2). In AML, 

the conditions to achieve a gun firing position are a line-ofsight angle less than 10 degrees and an angle-off tail less 

than 60 degrees and a range less than 3000 feet. (These 

quantities are defined in the paragraph IIPerformance measurestt 

below.) Some models provide the option of integrating the 

trajectory of an individual bullet. The point of impact is 

calculated so that the effect of the hit can be accurately 

estimated using a vulnerable area approach. 

The requirements that must be satisfied for a missile 

launch are customarily summarized in terms of a "firing 

envelopell or "launch-acceptable region (LAR) I*. A representative 

1-7 
Cone of Vulnerability 

(1.5oom) 

Vulnerability 

COW 

Above: range Most successful Y gun 

attacks are made from astern at 3(r 

angle-off or less, the lethal cone. 

Vulnerability cone is45'angle-off 

and 1,Wyd (1.S00m)range. 

Figure 1-2: Gun Vulnerability Cone 

(from Reference 24) 

1-8 
envelope, with the target at the center, is shown in Figure 1-3 

for a typical radar doppler-homing missile (Reference 10). These I 

I 

I envelopes are used by most m on n air combat models. They have I 

! also been used in various studies using AML (Reference 13). 

I For non-maneuvering targets, an envelope has a maximum 

range with a roughly elliptical shape which reflects the aeropropulsive limit of a typical missile. The maximum range varies 

strongly as a function of altitude and target speed. Figure 1-3 

b also illustrates the seeker limit, which in the illustrated 

case is smaller than the maximum range of the missile. The 

seeker limit is dependent on the target's radar reflectivity 

I characteristics (a function of the target aspect as seen from 

the firing position.) Figure 1-3 also indicates an inner zone 

(minimum range or "dead zone"). It will be noted that the headon maximum range is much greater than the off-tail range -- 

typically four to five times. The greater area means that there 

are more engagement opportunities in the forward target quarter. 

But it should also be remembered that the target's sensors are 

effective only in its forward quarter. 

The llmaneuvering envelopeuu, as illustrated in figure 1-3b, 

represents the effect on the intercept capability of the missile 

when the target begins a level left-hand turn just as the 

missile is launched. The envelope typically assumes a shape that 

is distorted in the direction of the turn. The maximum range 

expands in the direction of the turn, as the target is flying 

towards the missile. It contracts in the direction opposite the 

1-9 
MAXIMUM 

RANOf 

TARQ~ 

a) Non-maneuvering Target 

MAXIMUM 

b) Maneuvering #Target 

Figure 1-3: Typical Missile Envelopes for Maneuvering 

and Non-maneuvering Targets (from Reference 10) 

1-10 
turn as the target is flying away from the missile. These 

I effects are proportional to the number of GIs pulled by the 

I 

target. In spite of the magnitude of the effect due to 

I maneuvering on the shape of the envelope, none of the models 

I 

I 

listed 

based on this effect. 

in the references appears to modify the decision to fire 

I 

After the missile has been fired, the damage to the target I 

I must be assessed. Detailed simulations simulate the fly-out 

I 

I 

I 

trajectory to the target, compute the miss distance and 

resulting survivability of the target. Less detailed simulations 

simplify this problem by computing a time-of-flight and 

survibability of the target based on a probability of kill and 

I 

I Monte Carlo draw. 

1.4 AIRCRAFT MODELS 

The simplest aircraft model used in air combat simulations 

consists thrust 

and drag forces. This provides a starting point, for instance to 

compute the endurance of an aircraft in the simulated 

engagement. This type of aircraft model is limited to 

"instantaneous turns", and cannot represent the attitude and 

turn capability of a fighter. Yet this limitation is often not 

recognized until realistic graphics are available, or the 

simulation is run in a flight simulator. 

of a point mass to which are applied the lift, 

A full 6 degrees of freedom (6 DOF) model is required to 

under simulate realistically the behavior of a fighter aircraft 

1-11 
the air 

combat. All the lift, drag and thrust characteristics as well as 

moments should be represented. In particular, roll performance 

is of primary importance in fighter aircraft tactics and would 

alone justify the use of a 6-DOF model (see for example 

Reference 18.) 

high-Gs and very large angles of attack encountered in 

The model currently used in AML is described in Reference 

14. It is a "performance modelt@, in which 6-DOF dynamics have 

been preserved, but in which the calculation of aerodynamic 

moments and control and stability derivatives has been omitted 

to meet execution time requirements on minicomputer-based flight 

simulators. 

1.5 DECISION-MAKING PROCESS 

The objective of the decision-making process is to derive 

maneuvers which will bring one's own weapons to bear on the 

target while at the same time minimizing exposure to the other 

side's weapons. It is essentially a representation of the action 

of the pilot during combat. In simulations involving multiple 

aircraft, the decision-making process also involves pairing 

groups of opponents. 

The real-life approach to the solution of the problem of 

steering an individual aircraft relative to an opposing, 

dissimilar aircraft is known as the "Basic Fighter Maneuversll 

(BFMs). Examples of training manuals describing BFMs for 

particular aircraft may be found in References 11 and 12. 

1-12 
Reference 10 is a more general treatment of this field. The 

objective of BFMs is twofold: (1) Gain and maintain a positional 

advantage with respect to the enemy allowing employment of 

armament, and (2) Gain and maintain sufficient energy to have 

maneuvering potential. BFMs are not exact maneuvers, but rather 

combinations of the three elementary actions that an aircraft is 

capable of -- roll, turn, and accelerate/decelerate -- used to 

gain advantage in a particular situation and against a 

particular opposing aircraft type. Well-known examples of BFMs 

are: the Immelman, the lead/lag turn, the Lufbery, the highspeed yo-yo. 

In spite of the admittedly inexact nature of BFMs, they 

nevertheless constitute a sourcebook of possible maneuvers which 

has been used as the basis for the decision logic of models such 

as PACAM (Reference 8), AASPEM (Reference 7) and TACBRAWLER 

(Reference 9). As an example of this approach, a partial list of 

such maneuvers available in the AASPEM model includes: 

chandelle, split-S, high-speed yo-yo, barrel roll. The 

decision logic for selecting a maneuver is based’for the most 

part on user-specified geometry rules. There is an amount of 

guesswork involved in specifying these maneuvers. For example, 

the user must insure that the energy state of each aircraft is 

sufficient to complete the specified maneuver. Otherwise, 

unrealistic and unacceptable maneuvers may result. 

The specification of these maneuvers depends on the current 

phase of the engagement. For example, AASPEM considers seven 

1-13 
phases: 

- Neutral: no threat detected 

- Late set-up: setting-up phase near completion 

- Early set-up: setting-up phase near completion 

- Pre-attack: final set-up and preparation for attack 

- Attack: attacking threat 

- Post-attack: initial attack complete 

- Disengage: engagement complete 

For each of these phases, AASPEM requires specifying 

positional tactics, information-gathering tactics and 

information-denial tactics. 

This approach suffers from the disadvantage which was noted 

in the original AML report (Reference 5) , and is echoed in some 

training manuals (Reference 11) that fighter pilots learn these 

basic fighter maneuvers in training, but they rarely complete 

them in a dogfight because of the continuous interaction and 

changes in the relative situation. 

Another type of approach consists of programs which apply 

such disciplines as optimal control theory, and the theory of 

differential games to obtain control laws. Such approaches work 

best for idealized situations (e.g. co-altitude, analytic lift 

curves, etc.. . ) . 

The trial-maneuver approach was introduced by AML to remedy 

the problems with these approaches. The AML technique determines 

the next tactical maneuver as it contributes to the goals of the 

pilot. It uses the concept of a situation matrix describing the 

tactical decision options in terms of various values assigned to 

each cell. The maneuver selected is the one which maximizes this 

value (References 5 and 6). 

1-14 
The trial-maneuver approach, originally published by Burgin 

et a1 (References 5 and 6) proved to be quite successful for a 

real-time decision logic. It does require, however, considerable 

computer resources. Pedotti and Hignard (Reference 22) 

plagiarized the above mentioned work. They used almost an 

identical set of trial maneuvers and had a real time version of 

their It Logique Adaptive de Manoeuvre Aerienne" running on an 

UNIVAC 1100/82 mainframe computer. 

Austin et a1 ( Reference 23) used a very similar trial 

maneuver technique in the simulation of air-to-air combat 

between two helicopters. This program is operational in real 

time on the NASA AMES VerticaL Motion Simulator. 

The trial-maneuver approach -- as the name implies -- 

involves searching over a series of flight paths. The 

computational requirements were found to exceed the capacity of 

VAX 11/780-class mini-computers for real-time applications. To 

remedy this situation, a different approach was devised: the 

rule-based AML (RB/AML). The rule-based AML uses a combination 

of production rules (i.e. IF ... THEN statements) and guidance 

laws as an alternative to the trial maneuvers. These rules will 

be discussed in greater detail in Sections 3. 

In m-on-n simulations, the decision process must in 

addition pair various groups of opposing aircraft. The doctrines 

found in the tactics manuals are the welded-wing, free-engaged, 

and the double attack system. These tactics have been emulated 

in air combat models such as PACAM and AASPEM. In the welded1-15 
wing doctrine, the wingman attempts to maintain a loose 

formation with his leader. He does not make independent maneuver 

decisions, but nevertheless he fires his weapons on his own 

initiative when such opportunities arise. In the doctrine of 

free-engaged tactics, the two fighters exchange the roles of 

leader and wingman as the tactical situation requires. 

1.6 PERFORMANCE MEASURES 

Three levels of performance measures can be found: 

(1) Individual aircraft performance, e.g. turn rate or 

energy maneuverability as a function of Mach number and 

altitude. The ability to change state is a recently introduced 

performance measure in this category (Reference 18.) 

(2) Differential aircraft performance measure, e.g. 

the difference in turn rate. These are commonly used in training 

manuals. The implicit assumption is that both opponents enter 

the combat arena under the same initial conditions. 

(3) Tactical performance measures, which are made possible 

only through air combat simulations of the type analyzed in this 

report. 

The relative position of two opposing aircraft, llA1@ and lrB1l 

is conventionally described in terms of the deviation angle 

lambda and angle-off epsilon. These have been illustrated, from 

the point of view of sBrl, in Figure 1-4 , where they are 

indicated as lambda(B) and epsilon(B). The deviation angle 

1-16 
lambda(B) is the angle between llB1lls velocity vector and the 

line of sight from I1B1l to I1AV1. For this reason, it is sometimes 

referred to as the Itline-of-sight angle". This deviation angle 

is an indication for l1Bl1 of whereollA1l is: lambdab = 0 degrees 

means I1AV1 is directly in front of llB1l; lambdab = 180 degrees 

means I1A1@ is directly behind OB1l. 

The angle-off epsilon(B) is measured between the line-ofsight vector from I1Al1 to IrBll and llA1lls velocity vector. It tells 

IIBn where llA1l is going relative to llB1l: epsilon(B) = 180 degrees 

means I1A1@ is coming directly at IIBa; epsilon(B) = 0 degrees is 

going away from I1Bl1. Alternate names for angle-off are: angleoff-tail and aspect angle (Reference 11, page 2-2). 

Similar angles can be defined for I1A1@. Inspection of figure 

1-4 shows that lambda(B) = 180 deg - epsilon(A) and lambda(A) = 

180 deg - epsilon(B). 

The line-of-sight angle and the angle-off are 

fundamentally important in air-combat; both for the tactical 

decision process as well as for the assessment of the current 

situation. A few clarifying remarks are therefore in order. 

First note that the AML program carefully differentiates 

between line-of-sight angle and deviation angle. In the following discussion, we reference all the angles to aircraft llB1l, in 

other words, when we say, line-of-sight angle, we mean aircraft 

I1B1l1s line-of-sight angle. By AMLIs definition, the line-ofsight angle is the angle between the vector from llB1lls cg to 

llA1lls cg (the line-of-sight vector) and llB1lls body x-axis. The 

1-17 
''B"'s Perspective: 

o 

o 

The deviation angle AB tells "B" where " A If is. 

The angle-off &B tells "B" in which direction "A" is 

going with respect to "B". 

Figure 1-4. Definition of Deviation Angle and 

Angle-of f ("B" ' s View) 

1-18 
deviation angle, on the other hand, is defined as the angle I 

I 

1 between the LOS vector and "b"'s velocity vector. Line-of-sight I 

angle and deviation angle therefore are only identical if there I 

I 

I 

I 

I 

exists no sideslip and no angle of attack. 

I 

1 From a tactical point of view, both the deviation angle and 

I the angle-off are important. For gun-firing, the line-of-sight 

is of primary importance, because the guns are mounted such that l 

they point in the direction of the aircraft's longitudinal axis. 

t For missile firing, both the line-of sight angle and the 

deviation angle are important, the missile is mounted parallel 

to the aircraft's longitudinal axis, the initial missile 

I 

I velocity, however, is determined by the aircraft's velocity 

vector. 

One last point: The line-of-sight vector can be changed by 

the pilot much more rapidly than the deviation angle, because 

modern fighter airplanes allow very rapid changes of angle of 

attack of the order of 10 to 20 degrees. This translates 

directly into a line-of-sight angle change of the same 

magnitude. The velocity vector however can not be changed that 

rapidly. 

Although these definitions (or equivalent definitions) are 

widely in use air training manuals as well as air combat 

simulations, it should be noted that there are ambiguities 

arising from the fact that the values of the line-of-sight angle 

and the angle off are between 0 and 180 degrees and always 

1-19 
positive . 

For example, if one expresses the situation in the 

lambda(B)-epsilon(B) plane, both situation 1-5 a and 1-5 b will 

be represented by the same point in that plane, namely lambda(B) 

= 90 degrees, epsilon(B) = 90 degrees. 

Similarly, the two situations 1-5 c and 1-5 d fall into the 

same point in the lambda-epsilon plane, lamda(B) = 90 degrees, 

epsilon(B) = 45 degrees. 

Since 1-5 a represents a tactically different situation 

from 1-5 b, these ambiguities should be removed if one wants to 

base the tactical decision on the two angles lambda and epsilon. 

One possibility would be to introduce, in addition to these two 

angles, also the line of sight angle rate. Assuming equal 

velocity for the two aircraft, the line of sight angle rate 

would remain zero for situation 1-5 a, but a large rate would 

result in situation 1-5 b. Similar observations can be made 

between situations 1-5 c and 1-5 d. 

Notwithstanding these limitations, it has been found useful 

to introduce a performance index which combines these two angles 

into a single measure: 

PI(B) = 50*(1 - lambda(B)/180) + 50*(1 - epsilon(B)/180) 

PI(A) = 50*(1 - lambda(A)/180) + 50*(1 - epsilon(A)/180) 

Values of PIB and PIA are illustrated in table 1-2. 

For example, during its AML tests (Reference 4), 

1-20 
1 

1-5 a 1-5 b 

1-5 c 1-5 d 

Figure 1-5 Ambiguities in the Line-of-Sight/Angle-Off 

Representation 

1-21 
0 

ln 0 

0 

d 

0 ln 

hl In 

1'5 

0 

co 

d 

0 

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d 

0 

co 

d m 

ru 

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0 

co 

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0 

rn 0 Lu 

P ar 

0 

0 

rl 

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1'5 5: a, 

d 

30 

C 

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0 

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Q) 

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sa, "$ l2- 

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1-22 
NASA/Langley considered that a pilot (say "B") enters a gun zone 

if does 

not exceed 60 degrees (and the range is less than 3000 feet). 

This condition corresponds to a performance index PI(B) of 80 

or better. (Correspondingly, PI(A) would be 20 or less.) It 

should also be noted that this value of the PI is a necessary 

but not sufficient condition for a gun-firing position. 

lambda(B) does not exceed 10 degrees and if epsilon(B) 

The integrated performance index is the time-averaged value 

of the instantaneous values of the performance index: 

IPI = ( PIl*DT + PIZ*DT + .......+ PIN*DT ) / T 

Offensive - time 

The offensive time is defined as the accumulated time 

during the 

reference aircraft. This was one of the figures-of-merit used 

during the original AML test runs at Langley (Reference 4). 

which the opponent was in front of the wing line of 

The offensive time with advantage is the accumulated time 

during which the opponent was in front of the reference 

aircraft's wing line and the reference aircraft was behind the 

opponent's wing line. AML also used a more restrictive 

definition of the offensive time, consisting of the accumulated 

time during which the reference aircraft's deviation angle was 

less than 60 degrees and its angle off less than 60 degrees. 

-- Time to first - kill 

Other performance measures account for the weapon 

1-23 
probability of kill. The time to achieve the first kill is an 

attractive measure of this kind. However, its drawback is that 

it aircraft 

state at the time the first kill i& achieved and its subsequent 

capability to engage more targets. An initial firing position 

may be achieved by turning at maximum instantaneous load factor 

in order to gain an angular advantage. However, this will result 

in the aircraft losing rapidly energy and thus position itself 

unfavorably for a subsequent engagement. In typical air-to-air 

scenarios, it is precisely the purpose of the leader/wingman 

team concept to take advantage of such situations. 

does not properly reflect the future impact of the 

Accumulated probability of kill 

A commonly used measure of military effectiveness is the 

loss exchange ratio, defined as the ratio of the number of enemy 

killed divided by own losses. In a one-on-one duel in which 

multiple weapons are exchanged, this reduces to the ratio of the 

accumulated probabilities of kill. Neuman and Erzberger used 

this measure (Reference 13) as an alternative to the measures 

of effectiveness previously discussed. 

The common procedure to calculate the exchange ratio is to 

use the Monte-Carlo method. An alternate method was used in 

Reference 13 in which the engagement continues independently of 

the outcome and these trajectories are recorded. A postprocessing program uses these trajectories to identify firing 

opportunities and to compute the accumulated probability of 

kill. This method was used to avoid the problem often 

1-24 
encountered in air combat simulations that small changes in 

I 

I initial conditions or in the flight path somewhere in the 

I engagement propagate into large differences in outcome. However, 

I this method is limited to lvl, since in m on n there are 

cooperative effects which depend on the sizes of the forces. 

~ 

1-25 
- 2. DEVELOPMENT HISTORY THE AML PROGRAMS 

2.1 NASA LANGLEY DMS PROGRAM (AML 75) 

Development of the AML program started in 1969 under the 

sponsorhip of the NASA Langley Research Center. The original AML 

program was developed to operate on NASA Langley Research 

Center's Differential Maneuvering Simulator (DMS). It is shown 

in figure 2-1 as the root of the AML program family. It was 

designed to be an interactive air-combat opponent operating in 

real time. This original version of the AML program is 

documented extensively (for example, References 5 and 6). 

2.2 THE DMS CONTROL MODEL (AML 76) 

In the original version operating on the DMS, AML would 

Itdrive" the displayed aircraft by providing body rotational 

commands p, q, and r to the DMS display program. AML calculated 

the values for p, q, and r such that the displayed aircraft 

would achieve an attitude compatible with the following 

conditions: 

- resultant force vector ( aerodynamic forces, propulsive 

forces and gravity force) must 

lie in the desired maneuver 

plane 

2-1 
AML 75 

RT. 

(DW 

AML 76 

RT. 

(DW 

AML 1V2 

N.RT. 

1 

AML 84 

51 AML 86 

AML 071 

EXPERT IVAN 

N.R.T. 

AMUSAM 

N.RT. 

(NELLIS) 

I 

SAML D1 

(NORTHROP) 

R.T. = Real Time 

N.R.T. I Non-Real Time 

Figure 2-1. Development History of the AML Air-to-Air and Missile-Evasion Programs 

2-2 
2.3 A ONE-VERSUS-TWO VERSION OF AML (AML 1V2). 

- the angle of attack is such that the desired lift is 

produced 

- sideslip is zero 

The AML program then filtered these commanded body rotational 

rates in order to achieve a smooth motion of the displayed 

aircraft. However, when a pilot lost an engagement with the AML, 

he had a tendency to claim that the AML driven aircraft would 

perform flight maneuvers which were outside the performance 

envelope of the real aircraft. To counter this argument, a 

control system was developed which would actually move the 

simulated aircraft's control surfaces in exactly the same manner 

as the pilot did it with the stick and the rudder pedals. These 

commanded control surface deflections were then fed into the 

identical set of equations of motion as the were used to drive 

the human piloted aircraft. The development of this control 

system is described in reference 20. A thorough comparison 

between the performance of the original AML (called the 

performace-model AML) and the AML with a control-system is 

contained in reference 4. 

The Human Research Laboratories of the Air Force (AFHRL) 

sponsored subsequently an extension of the one-versus-one AML 

version to a one-versus-two version Here AML represents the 

single aircraft opposing two bogeys. This lead to a batchversion of AML which handles the one-versus-two situation based 

2-3 
on a set of value functions taking into account the relative 

situation between all three combatants. This version also 

replaced some of the binary value functions of the original AML 

by continuous functions, thus giving' a better resolution between 

trial maneuvers and avoiding ambiguity in the scoring of 

different maneuvers. 

2.4 AML WITH REVISED EQUATIONS OF MOTION (AML 84) 

The original AML (AML 75) had a number of known 

deficiencies. The most serious one was an abnormal behavior of 

the AML aircraft when it approached 90 degrees in a vertical or 

in a near vertical turn. This anomaly was not due to the 

singularity of the Euler angles at theta = 90 degrees ( AML uses 

quaternions for the attitude integration and consequently there 

is no singularity at any attitude). The problem rather had to do 

with the decision logic and it may be explained in somewhat 

simplified form as follows: Most maneuvers in AML are executed 

in nmaneuver-planesl'. A maneuver-plane always passes through the 

aircraft's velocity vector. Certain other parts of the decision 

logic are based on the line-of-sight angle, in part, 

determined by the direction of the aircraft's body-x axis. In a 

vertical loop, under high angle-of-attack conditions, it will 

happen that the body axis has already exceeded the 90 degrees 

pitch angle, but the velocity vector's pitch angle is still 

below 90 degrees and still increasing. Under such a situation, 

it can occur that the AML reverses its maneuver command 

inappropriately. Specifically, it will command a maneuver plane 

which is, 

2-4 
rotation angle of 180 degrees (or close to 180 degrees) when in 

reality, the maneuver-plane rotation angle for the intended 

maneuver should be zero (or close to zero). This reversal can 

take place during several subsequent decisions. The result in a 

flight simulator is that it looks as if AML wouldn't know what 

to do. The long range effect is a hammer-head stall of the AML 

aircraft. Section 4 of this report explains briefly how this 

problem was solved. 

2.5 NORTHROP AEROSCIENCES LABORATORY AML (INTERACTIVE 

TARGET). 

The Aerosciences Laboratory of the Aircraft Division of the 

Northrop Corporation, which had an early version of AML 

installed on ther moving base simulator, was interested in an 

AML implementation with the new equations of motion, which 

eliminated completely the "over the top" problem explained in 

the previous paragraph. However, the computer hosting AML was a 

Harris Slash 4 minicomputer whose computational capability was 

inadequate to support AML in real time, not even with a frame 

time as large as 50 milliseconds. To reduce execution time, we 

abandoned the concept of trial maneuvers and of selecting the 

most promising of these trial maneuvers. Instead, we developed a 

logic which resembled closely the production rules of the then 

popular expert systems. This not only allowed us to perform a 

tactical decision well within the allocated frame time, but it 

also gave AML the flavor of an AI program. 

2-5 
2.7 AML 87 / EXPERT IVAN 

2.6 GENERAL ELECTRIC'S AML VERSION ON THE SIMULATOR FOR 

ADVANCED AIRMANSHIP (AML 86) 

At the time of this report, this is the most advanced real 

time version of AML. logic 

as the Northrop version, with some added improvements for low 

speed, low energy avoidence. The host machine is an SEL 32/97 

computer and the visual display is a General Electric Compuscene 

I11 computer generated image. AML86 has a number of additional 

features, such as minimum allowable altitude for the AML 

aircraft, a choice between three different aircraft (F-4, F-5 or 

F-15), a large number of selectable Ilcanned" maneuvers for the 

AML aircraft and most interesting, a selectable skill-level for 

the AML aircraft. The skill level of the AML aircraft can be 

selected to be ItACE1l, l1AVERAGEt1, or lgGRAPE1g. 

It uses basically the same decision 

Presently, there is an in-house effort going on at Titan 

with the two objectives of: 

1. - Expand AML's decision logic to BVR 

2. - Expand AML's decision logic to handle multiple 

aircraft on both sides. 

AML 87 is strictly a production rule based system, the rule-base 

being built by Navy fighter pilots with current experience in 

air-to-air combat in F-14's and F-18's. 

2-6 
2.8 MISSILE EVASION AML (AML/SAM) 

The initial success of the AML program as an Ifiron pilotll 

in the DMS created confidence that the AML decision logic could 

be changed to llflyll AML such that it would avoid a surface-toair missile. This work was initially sponsored by the Tactical 

Fighter Weapons Center at Nellis AFB, Nevada. The obvious 

required change to AML was to replace the value functions (which 

favored achieving a six-olclock position with respect to the 

opponent) to functions which favored achieving a large distance 

between the missile and the AML aircraft. Obviously, the type of 

trial maneuvers also had to be changed. Less obvious is the fact 

that in case of missile evasion, a short term maneuver 

optimization (as it is performed in the air-to-air combat 

version) will not generate maneuvers with accepable missdistance. It is necessary to carry out the optimization from the 

decision time all the way to the impact (or the point of closest 

approach of the missile). The decision logic of the AML program 

was modified to implement these requirements and very successful 

evasive maneuvers against surface-to-air missiles, such as the 

SA6 were generated by AML. The program ran in non-real time on a 

CDC Cyber computer. 

2.9 PILOT'S ASSOCIATE D1 AML PROGRAM ( SAML D1) 

The Aircraft Division of the Northrop Corporation 

participated in the demonstration phase of the Pilot's Associate 

2-7 
D1 program. The AML/SAM program was modified to work in real 

time on a flight simulator. AML determined suitable evasive 

maneuvers for the aircraft. These maneuvers were generated based 

on a set of production rules. The AML generated maneuvers were 

either used to provide cues displayed to the pilot on the 

heads'up display or they were fed directly into a flight control 

system. AML successfully avoided, at very low altitude, two SAMs 

simultaneously. For further details, see reference 21. 

2-8 
3. - THE BASIC ---- AML IF => THEN LOGIC 

3.1 TERMINOLOGY 

The purpose of this section is to give an overview of the 

tactics currently implemented in the IF => THEN version of AML 

which is in use at various flight simulation facilities. To 

avoid confusion, we will first clarify some terminology. In a 

real-time, one-on-one environment on a flight simulator, the AML 

driven aircraft is called A/C llBll, or for short, AMLB. When the 

program operates in a batch environment, the opponent of AMLB is 

AMLA. Each of AMLA and AMLB can implement either the "trialmaneuver-logicll or the IF => THEN logic. The following 

discussion assumes that the aB1l aircraft is driven by the IF => 

THEN logic. In the rest of the report, AMLA is a ntrial-maneuver 

logic AML. 

3.2 COMMONALITY WITH THE TRIAL-MANEWER LOGIC 

3.2.1 Timing Considerations. 

In the IF => THEN logic as well as in the trial maneuver 

logic, two time-intervals are used for maneuver decisions. The 

first one, which is the smaller of the two is equal to the 

integration stepsize ( alternatively called frame-time or cycletime). The AML maneuver logic subroutine (TACTICB, see figure 3- 

3) is invoked every integration step. At each invocation, the 

AML logic unconditionally checks for the necessity of either 

initiating a dive recovery or to continue a dive recovery 

currently in progress. If no dive recovery requirements exist, 

3-1 
then the logic tests whether there is time to perform a new 

tactical decision. This second time-interval between tactical 

decisions is called decision-interval. For close-in, one-on-one 

air-to-air combat, it is typically between 0.5 and 1.5 seconds. 

(For 

situation it may be considerably longer). 

missile evasion it is shorter and for a decision in a BVR 

3.2.2 Maneuver Plane Concept. 

A significant contribution to the success of the early 

versions of the AML program came from the concept of the 

maneuver-plane. Strictly speaking, one should not call this 

plane a maneuver plane, but rather a maneuver half-plane. (As it 

is properly called in reference 22). It is the half plane in 

which, ideally, the next segment of the AML aircraft velocity 

vector will lie. It extends through the AML driven aircraft's 

velocity vector towards the side of the cockpit. The maneuver 

plane provides (1) a convenient mechanism to specify AML 

maneuvers ( both in the trial maneuver and in the IF =-> THEN 

version) and (2) a computationally efficient way for prediction 

of the aircraft's future position and attitude. In the IF => 

Then logic, the maneuver-plane serves to specify the parameters 

for lead or lag pursuit maneuvers. The maneuver plane and its 

associated maneuver plane coordianate system are illustrated in 

figure 3-1. 

The crucial problem in both AML versions is to control the 

aircraft's body rotational rates in such a manner that: 

3-2 
aJ 

X 

C 

.I4 

0 

al 

al 

u 

C aJ 

bl 

a 

u-c 

aJ 

e: 

aJ 

X 

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aJ 

N 

u 

a 

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0 

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U 

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3-3 
a) they are physically executable under the prevailing 

flight conditions and 

b) the aircraft's velocity vector remains in the 

specified maneuverplane. 

3.3 DECISION HIERARCHY 

3.3.1 Ground Avoidance 

The ground-avoidance logic is executed every integration step. 

This reflects the fact that ground-avoidance has higher priority 

than any other tactical decision. In both AML versions the 

decision on whether a ground-avoidance maneuver is required is 

based on a two dimensional table of the dive recovery angle. 

This angle is a function of airspeed and altitude. In the IF => 

THEN logic, it is a 

roll to wings level followed by a maximum instantaneous g 

pullup. The throttle is controlled such that the aircraft is 

going to fly at corner-velocity. The dive-recovery maneuver may 

therefore succintly be described as a maximum g turn in a 

maneuver-plane whose rotation angle rho is zero. 

a dive recovery maneuver leaves no choice, 

3.3.2 The Pointing Algorithm 

If dive recovery is not required, the program performs a 

test whether the aircraft should be controlled in such a way 

that its nose (i.e. its longitudinal axis) will point at the 

opponent or at a specified point in front of the opponent. This 

3-4 
is the only maneuver in the AML program (except of course 

the ltcannedI1 maneuvers in certain versions on flight simulators) 

1 

, where the maneuver is not based on a maneuver plane, but where 

directly body rotational rates which will bring the aircraft 

intothe desired attitude, are calculated. The pointing algorithm 

is described in more detail in section 4. 

3.3.3 The Lead/Lag Maneuver Logic. 

These maneuvers form the heart of the basic AML maneuver 

decision logic. They implement one of the basic rules of air 

combat: Point your nose towards the opponent. The refinment 

consists in the determination of the exact point in reference 

with the opponent towards which we want to point the aircraft 

(behind = lag, in front = lead or exactly at the opponent = pure 

pursuit); the other refinments being the rate of turn by whcih 

we want to achieve this goal ( in other words, the loadfactor) 

and finally how much thrust we will apply (throttle setting). 

The decision on whether to fly lead, lag or pure pursuit is 

based on the values of the line of sight angle and the angle 

off, as illustrated in figure 3-2. 

Load Factor Selection The load factor is also selected 

as part of the LLG. This selection process, however, is 

primarily determined on the basis of airspeed considerations. A 

high load factor results in a high turn rate, which is desirable 

to achieve a firing position as quickly as possible. However, 

turns at the maximum load factor create a lot of drag which 

causes the airspeed to drop rapidly. This is actually desirable 

3-5 
iaoo I 

Pure Pursuit 

X(B) degrees 

b 

Evasive 

Maneuver 

I 

90" 

30" 

0" 

\ Lag Pursuit 

0" 45" 90" 180" 

-E: (B) degrees 

'Figure 3-2. Regions for Steering Laws 

3-6 
I when the current airspeed is above corner velocity, the velocity 

which yields the highest turn rate. For this reason, when the 

current airspeed is above corner velocity, the maximum load 

factor is commanded. When the current airspeed is near or below 

corner velocity, the sustained load factor is commanded to avoid 

losing further energy. In B's forward sector (LOS < 60 degrees), 

an additional test is performed which compares the load factor 

described previously, which is airspeed-oriented, to the load 

factor corresponding to the desired flight path, i.e. the flight 

path which intercepts the reference point. This Ilintercept 

trajectory" load factor is selected if it is lower than the 

airspeed-oriented load factor. 

I 

! 

I 

The pointing algorithm could generate negative. load 

factors. An option to command negative load factors in the 

maneuver-plane method has been partially implemented. The load 

factors commanded in the original AML were always positive. The 

equation for the maneuver plane is given by (p 53 of Reference 

6) : 

There are two solutions to this equation, Rhos and Rhos + 

180 degrees. The second solution corresponds precisely to 

negative a load factor, and is calculated in this version of 

AML. A negative load factor will be chosen if all these 

conditions are satisfied: 

3-7 
(1) B's airspeed must be lower than A's 

(2) A must be in Bls forward quarter and low 

(3) Bls current roll angle must not exceed 30 degrees; 

otherwise, it is preferrable to roll inverted under a positive 

load factor. 

(4) the negative load factor yields the smallest 

variation in maneuver plane rotation angle (and therefore in 

roll angle.) 

These conditions are restrictive and favor the well-known 

pilot preference for positive load factors. They will however 

make possible the use of a negative load factor for the purpose 

of bringing Bls nose onto A while avoiding a high positive load 

factor and, hence, unnecessary loss of airspeed. 

Throttle Control The throttle control laws are set 

independently and can be summarized as follows: 

(1) In dive recovery, set the throttle to bring the 

airspeed near the corner velocity. 

idle if the airspeed is above corner velocity. 

Thus, the throttle is set to 

The throttle is 

otherwise set to afterburner. 

(2) Under other conditions, the avoidance of an 

overshoot takes precedence over the rule enunciated above. This 

will occur if A is in front of B and B has a high overtake 

velocity. In this case, the throttle is set to idle. 

3-8 
SUBROUTINE REACTB 

Figure 3-3. Summary of the AMLB Control Laws. 

3-9 
4. AIRCRAFT AND CONTROL SYSTEM DYNAMICS 

4.1 SELECTING AN APPROPRIATE MODEL 

What constitutes an appropriate model depends on the purpose of 

the simulation. As illustration, consider the two extreme cases: 

(1) Development of evasive maneuvers against an air-to air 

missile (2) Training of pilots in ECM tactics in a BVR 

environment. To capture the intricate dynamics between a highly 

agile missile and a fighter aircraft, it is necessary to 

simulate aircraft response to control surface deflections. This 

will rotate the aircraft in such a way that at any instant of 

time, the missile seeker head "seest8 the aircraft under the 

proper aspect angle. In the BVR case, representing the aircraft 

as a point-mass may be adequate. Close-in visual air-to-air 

combat in a flight simulator lies somewhere between these two 

extremes. To achieve the necessary accuracy for the CIC 

simulation, two key performances of the aircraft must be modeled 

accurately: 

1) The Normal Acceleration 

2) The Roll Dynamics 

Normal acceleration determines how tight the fighter can turn 

and whether or not he loses energy during the turn. Roll 

performance determines how quickly the fighter can change the 

direction of the lift. In AML, roll performance is the 

determining factor in how fast the flight path can be changed 

from one maneuver plane to another maneuver plane. The two 

important parameters for roll performance are maximum roll rate 

4-1 
and maximum roll acceleration. As Shaw (Reference 10 ,page 414) 

points out: 

In air combat, continuous rolls of more than 180 degrees 

are seldom required. Because a certain length of time is 

necessary to acclereate the roll rate from zero to its 

maximum value, maximum stabilized roll rate may not be 

reached during such short periods of roll. Therefore, roll 

acceleration is often the controlling factor in combat 

performance . 

Shawls quote is certainly true for air-to-air combat and even 

more so for evasive maneuvering against missiles. 

The problem of properly simulating roll performance is 

complicated by the fact that a change in bank angle has often to 

be achieved under high angle of attack or that coupled with a 

change in bank angle is a large change in angle of attack. In 

AML, a maximum roll rate and a maximum pitch rate is specified. 

Both are a function of the particular aircraft type represented 

by AML. If a maneuver command requires both a large change in 

the pitch angle (Theta hat) and the roll angle (Phi hat) the 

details of how this maneuver is performed depend a great deal on 

the ratio between maximum pitch rate and maximum roll rate. A 

proposed method, which, due to lack of funding never has been 

implemented, is to calculate the maximum available pitch and 

roll acceleration every time one of these extreme maneuvers has 

to be performed: 

As a first approximation, we suggest to calculate and 

max 

H as follows: 

4-2 
rolling moment due to aileron deflection and "9 is the 

maximum available aileron deflection. To be accurate, f; would 

have to be known as a function of Mach number and of the angle 

of attack. Herin lies the problem: It is often difficult to 

obtain these control derivatives for the extreme flight 

conditions which occur so often in air-to-air combat. Analogous 

remarks apply for 6, (control derivative for pitching moment 

due to elevator deflection) 

\ 

N 

f? &a, 

If the AML maneuver command is fed into a simulated (or 

eventually, into a real) flight control system, the problem of 

properly simulating pitch and roll performance under high angles 

of attack is greatly simplified. The aircraft (F-X) in 

Northropls Pilot Associate Program D1 was controlled by feeding 

AML provided load-factor and bank-angle commands into the flight 

control system. It can therefore be assumed that the dynamic 

response of the F-X to AML maneuver commands was very realistic. 

4.2 SYNOPSIS OF THE CURRENT ATTITUDE CONTROL MECHANISM 

A detailed account of the new equations of motion can be 

found in reference 14 where all the mathematical background 

underlying the treatement of the attitude control equations is 

presented. For' the sake of completeness of this report, the 

significant changes between the AML-75 and AML-84 are summarized 

below. 

As an introduction, a few words about #'degrees of freedomll 

of an airplane model may be in order. If we consider the 

4-3 
aircraft to be a rigid body, then, by definition of classical 

mechanics, the number of degrees of freedom is equal to the 

number of independent coordinates required to uniquely define 

the position and the attitude of the body. A single rigid body 

can have at most six degrees of freedom (3 translational, 3 

rotational). If we constrain the motion, the number of degrees 

of freedom is reduced, e.g. an aircraft whose cg could only move 

in in 

that plane, has 3 degrees of freedom (2 translational, one 

rotational). How many degrees of freedom does the AML model 

have? The answer is this: We try to make it a five degree of 

freedom motion, by postulating that the sideslip angle and the 

rate of the sideslip angle (not the yaw angle and the yaw rate!) 

be zero. But during a transition from flight in one maneyuver 

plane into some other maneuver plane the calculated values of p 

q and r do not necessarily exactly guarantee a zero sideslip 

angle. The model is therefore a true six degree of freedom 

model. 

a planeand whose longitudinal axis is constrqaint to lie 

Most of the maneuver commands in AML are triplets defining 

- a maneuver plane ( by means of the maneuver plane 

rotation angle rho) 

- a load factor 

- a throttle setting 

Given the above three parameters, one can calculate what 

the aircraft's attitude, at the present time, (or one 

integration stepsize ahead) should be for the aircraft to fly in 

the commanded maneuver plane with the commanded load factor and 

4-4 
1 with zero sideslip. 

Once we know the aircrafts desired attitude, we can 

calculate body rotational rates which will rotate the aircraft 

from its present attitude into its desired attitude. The 

important contribution of the "new equations of motion" is the 

way how these desired body rotational rates are calculated. To 

determine values of p q and r Euler angles Psi hat, Theta hat 

and Phi hat are calculated.These angles are expressed in the 

aircrafts present body axis system and not, as in the '#old 

equations of motion" in the inertial reference system. 

Therefore, only Phi hat ever can become really large, Theta hat 

and Psi hat will always be relatively small ( Theta hat will 

never be greater than the difference between maximum and minimum 

allowable angle of attack) Consequently, there will never be a 

singularity in the set of Euler angles Psi hat, Theta hat and 

Phi hat, and as a consequence, the previously encontered problem 

of Iqgoing over the top will no longer occur. 

4.3 REFINED CALCULATION OF COMMANDED PITCH RATE 

The procedure to determine p q and r as developed in 

reference 10 appeared to work reasonably well in the AML-84 

program, but occasionaly, the AML driven aircraft would fly into 

the ground even though dive recovery was inititiated at the 

appropriate time. Careful analysis of trajectories during dive 

recovery revealed that the aircraft never achieved the commanded 

load factor but consistently flew with a load factor less than 

4-5 
the commanded load factor during the pull out maneuver. At first 

we thought that the problem lies in the first order transfer 

function between q command and q achieved. But even as the time 

constant in this transfer function was reduced to a very small 

value, the problem persisted. The real reason for the 

discrepancy between commanded angle of attack and achieved angle 

of attack lies in the fact that. the calculation of the ttdesiredll 

aircraft attitude is based on the present velocity vector. 

However, if the aircraft undergoes a large normal acceleration, 

the velocity vector will rotate during the next integration step 

and therefore, the commanded pitch rate must be increased by the 

rotational rate of the velocity vector which is: 

w=a 

V 

- n 

In a hard turn, a better value for q commanded therefore is: 

min (q , abs ($/at)) sign (6) + Lift 

g*v qcom = max 

4.4 THE POINTING CONTROL SYSTEM 

One of the most significant additions and improvements to 

the solution of the AML driven aircraft attitude control is the 

incorporation of a llpointingll control system. In several studies 

with AML, it was found that the AML controlled aircraft 

performed quite well to get behind the opponent, but once there, 

it lacked the capability to reduce the line of sight angle to 

the small value required for a gun solution. Controlling the 

aircraft by means of maneuver planes and loadfactors is indeed 

not a suitable way to point the aircraft's nose in a desired 

4-6 
direction. Therefore, a control system was implemented which 

would directly command roll and pitch rate to point the 

aircraft's longitudinal axis into a desired direction. Figure 4- 

1 illustrates in form of a block diagram the pointing control 

system. This control system is a modification of a control 

system suggested for use in surface-to-air missiles (Reference 

25,page 37). It is highly effective in controlling the AML 

driven aircraft. The problem is to find appropriate values for 

the various gains in the control system if a new fighter 

aircraft is implemented in AML. 

4-7 
AIM-MINT 

COORO IN ATLS 

RESOLVE DESIRED 

Poiru NO VECTOR &TAN2 (OYeO, INTO A/C BODY 

A /C BOOY AXES 

ORIENT AT ION 

CHANNa 

r zFKR.6 

eo m 

FKO 

ELEAR. FKP 

y ELERR 0 cam A2lRR P comm 

‘X e * 

- - 

Ga Go 

0 - FEEDBACK 

- FEEDBACK 

Figure 4-1. Block Diagram of Pointing Control System 

4-8 
5. SAMPLE TRIAL MANEWERS - AML VERSUS IF r> THEN AML RUNS 

A series of test cases was conducted to exercise the 

AMLB logic described in section 3. In this series of runs, the 

llA1l aircraft was an F-15 controlled by the trial-maneuver logic 

I 

AML (AMLA). The IIBII aircraft was an F-4, controlled by the IF => 

THEN AML logic (AMLB). The initial conditions selected for these 

cases are shown in Table 5-1. A variety of initial velocities, 

altitudes and initial ranges were used. Initial velocities of 

M.77 at 20,000 feet were selected because they represent a 

typical entry conditions into the air combat arena. On the 

other hand, initial velocities of M.46 correspond to typical 

corner velocities at 10,000 feet. The initial angular conditions 

vary from neutral to very unfavorable to the F-4 : the initial 

PI range approximately from 50 to 90. Since in addition the F-4 

is a considerably less performing aircraft than the F-15, which 

has a smaller turning radius, one would expect that the 

situation would develop in favor of the F-15. 

5-1 
Table 5-1 

Initial values for sample runs 

Region Mach Altitude Relative Mach Altitude Eps(B) Lmbd(B) 

/Case No. Range No. 

ft ft ft deg deg 

2/1 .46 10,000 1000 .46 10,100 90 90 

3/1 .46 10,100 1000 .46 10,100 90 135 

.77 20,000 2250 .77 20,000 154 30 4/1 

4/2 .77 20,000 2000 .77 20,000 180 45 

4/3 .46 10,000 1000 .46 10,100 135 0 

.46 10,000 1000 .46 10,100 135 45 4/4 

5/ 1 .46 10,000 1000 .46 10,000 135 90 

.46 10,000 1000 .46 10,000 135 90 5/2 

.76 16,000 3500 .77 20,000 135 90 5/ 3 

.77 24,000 3500 .77 20,000 135 90 5/4 

6/1 .46 10,000 1000 .46 10,100 135 135 

5-2 
A natural way of classifying these runs is to define 

regions in the epsilon(B)- lambda(B) plane which is used for 

AMLB maneuver selection (Section 3). This plane was divided in 

the regions shown below: 

Figure 5-1. Definition of regions 

5-3 
These runs were made for a fixed period of time, typically 

20 seconds, which only allows the observation of the development 

of the initial maneuvers. The X-Y traces of the trajectories 

were plotted for that period of time. Also, additional pertinent 

information such as altitude and airspeed have been indicated as 

labels on these plots. For all these runs, the performance index 

for aircraft ttAtt , PI(A), and the integrated performance index, 

IPI(A), were plotted as a function of time. These were discussed 

in Section 1.6. Since PI(B) = 100 - PI(A) , only PI(A) was 

plotted. The PI yields an indication of the relative angular 

attitude between the two aircraft and complements the 

information from the X-Y trace. It will be recalled that a PI of 

80 is required (but not sufficient) to achieve a firing 

position. 

5.1 REGION 2 

A run was made in this region corresponding to neutral 

conditions in all initial variables (angles, velocities and 

altitude.) These results are shown in Figures 5-2 and 5-3. 

It would be expected that the superior-turning F-15 would 

gain advantage. However, the performance index plot indicates 

that the situation remains essentially neutral throughout the 

simulated engagement. It will be noted that there is loss of 

airspeed on both sides (but is more severe for AMLA), and that 

the engagement remains approximately co-altitude. 

An examination of the X-Y traces in Figure 5-2 contrasts 

5-4 
7,000 

6,000 

5 , 000 

X 

(feet) 

4,000 

3 , 000 

2 , 000 

1,000 

0 

TCE: Tail Chase 

Evasion 

P: Pursuit 

LCP: Lag Pursuit 

"A" 

M .46 

1 I 10,000 

-3 , 000 -2,000 -1 , 000 0 1,000 2,000 3,000 

Y (feet) 

Figure 5-2 

Region 2 (A.(B)=90 deg., 0 €(B)=90 deg.) X-Y Trace "A" (F-15) 

A "B" (F-4) 

Time marks in seconds 

Mach No./Altitude 

(in boxes) 

5-5 
100 

90 

80 

70 

60 

50 

40 

30 

20 

10 

0 

0 12 3 4 5 6 7 8 9 10111213141516 

Time.scc 

PIB + lPlB 

Figure 5-3 Region 2 

PI Plot 

5-6 
the initial behavior of AMLA/F-15 and AMLB/F-4E. AMLB begins to 

I turn immediately, while AMLA reacts very little until t = 7 

seconds. Then AMLA begins a turn reversal during t = 7 seconds 

to 16 seconds. As indicated in Reference 10, this tactic should 

be expected from an aircraft with a smaller turn radius such as 

the F-15 compared to the F-4E. It will be seen again in more 

simulated runs. This tactic fails in the present case probably 

due to the small initial range (1000 ft). 

The steering laws used by rlB1l have also been indicated in 

Figure 5-2. The pursuit law is used intermittently (t = 0 sec to 

1 sec; 12 sec to 13 sec; 14.5 sec to 16 sec) The lag pursuit law 

is used during the rest of the simulation. 

Both the IrA1* aircraft and the llBn* aircraft rapidly lose 

airspeed, but remain approximately co-altitude during the 

simulated engagement. This trend will be observed in other 

engagements starting co-altitude and not involving tail-chase 

evasion. 

5-7 
5.2.REGION 3 

The initial conditions used ( Lambda(B)= 135 degrees, 

Epsilon(B) = 90 degrees) put AMLB at a significant disadvantage 

with an initial PI(B) = 37. 

The trajectory, shown in Figure 5.4, exhibits flat scissors 

for the first 9 seconds of the engagement, during which the 

pursuit law is used. This part of the engagement is similar to 

the Region 2 case previously discussed. The F-15 has brief 

firing opportunities between t = 8 and 10 sec. Unlike the region 

2 case, AMLB cannot initiate a second scissor and is forced 

instead into the tail-chase evasion mode after t = 9 seconds, 

which accounts for its fluctuations in altitude. AMLB has a 

slight speed advantage during the major part of the simulated 

engagement. In a real-life engagement, this might be exploited 

to disengage, a maneuver not included in the present AMLB 

disengagement maneuver. 

5-8 
7,000 

6,000 

5,000 

X 

(feet) 

4,000 

3,000 

2,000 

1 , 000 

0 

TCE: Tail Chase 

Evasion 

P: Pursuit 

LCP: Lag Pursuit 

0 "A" (F-15) 

A "B" (F-4) 

Time marks in seconds 

Mach No. /Altitude 

(in boxes) 

Figure 5-4 

Region 3 (h(B)=135 deg., 

E(B)=90 deg.) X-Y Trace 

5-9 
100 

90 - 

80 

70 

60 

50 

40 

30 

20 

10 

0 

0 2 4 6 8 10 12 14 16 18 20 

TIME (SEC) 

PIA + IPlA 

Figure 5-5 Region 3 

PI Plot 

5-10 
5.3.REGION 4 

Referring to Table 5-1, the range of initial epsilon(B)- 

lambda(B) values considered in region 4 corresponds to forwardquarter passes. This means that the initial position of each 

aircraft is in the other's forward quarter. As indicated in 

Reference 10 (p77), there are two turn options available for 

fighters meeting in forward-quarter passes: the nose-to-nose 

turn option, and the nose-to-tail turn option. These are 

illustrated in Figure 5-6, adapted from Figure 2-11 in Reference 

10. The terminology refers to the position of the fighters at 

the end of the maneuver. These options were compared to the 

results obtained with the AMLA/AMLB logic in this series of four 

cases. 

Case 1 is illustrated in Figure 5-7 and shows a nose-totail conversion generated by the present AMLB. The instantaneous 

steering maneuver has also been indicated on Figure 5-7. llPrr 

indicates that IIBlr follows a pure pursuit maneuver between t = 0 

seconds and t = 8 seconds. IIU;Pt' indicates that a lag pursuit 

maneuver is used between t = 8 seconds and t = 21 seconds (end 

of the simulated engagement.) In this particular case, the AMLB 

steering law provides the F-4 with both a good defensive 

maneuver and a good maneuver for repositioning for attack. In 

contrast, the AMLA-controlled F-15 does not exhibit a 

repositioning tactic and seems instead to "wander off". The 

performance index plot (Figure 5-8) indicates that the situation 

evolves in favor of the F-4 from initially neutral conditions. 

5-11 
'h 

h 

8 

U 

C 

h 

W 

P 

8 

m 

0 

z 

I 

0 

U 

I 

8 

m 

0 

z 

5-12 
0 

0 

0 

9 

0 

0 

0 

lrl 

0 

0 

0 * 

0 

0 

0 

cc) 

0 

0 

0 

rJ 

0 

0 

0 

rl 

0 

0 

0 

0 

1 

d 

0 

0 

0 

rJ 

1 

0 

0 

0 

m 

1 

0 

0 

0 * 

1 

0 

0 

0 

Ln 

1 

0 

0 

0 

9 

I 
n 

a 

n 

z 

W 

X 

W 

w 

P e 

B 

U 

w 

a 

100 

70 i 

60 

50 

40 

30 

20 

10 

0 

0 2 4 6 8 10 12 14 16 18 20 

I 

(TIME SEC) 

a PIA + IPlA 

Figure 5-8 Case 1, 

Region 4, PI Plot 

5-14 
Case 2 represents a slight variation in initial conditions 

compared to case 1: Lambda (B) = 45 deg; epsilon(B) = 180 deg. 

I 

1 It is illustrated in Figure 5-9. In contrast to the previous 

run, this results in a nose-to-nose conversion. This conversion 

mode offers the F-4 the potential for a subsequent head-on 

firing opportunity when the range closes to less than 3000 feet 

(but this is beyond the internal simulated). 

~ 

The maneuvers used in Case 2 have also been indicated on 

Figure 5-9. Pursuit (P) is steered between t = 0 second and t = 

1 second; between t = 2 seconds and t = 12 seconds; and between 

t = 14 seconds and 15 seconds. Lag pursuit (LGP) is steered 

between t = 1 second and t = 2 seconds; t = 12 seconds and 15 

seconds; and between t = 15 seconds to the end of the simulated 

engagement. 

The initial angular conditions for cases 3 and 4 also 

correspond to forward quarter passes, with slight variations in 

epsilon and lambda compared to cases 1 and 2. However, the 

initial altitudes (10,000 feet) and speed (M.46) are very 

different. The initial speed was selected so that both aircraft 

start near corner velocity, the velocity at which both aircraft 

have their best turn performance. The X-Y traces for both cases 

(Figures 5-11 and 5-13) rapidly develop into well-defined 

ttscissorstl. The effect of the F-15Is smaller turn radius is 

apparent: llA1l turns well within ItBt1. However, in spite of this 

visible advantage, the PI plots for both cases indicate that ItAtt 

does not attain a gun-firing position. The situation remains 

5-15 
3 ,OOC 

2 ,ooa 

1,000 

-1,000 

X 

(feet) 

-2,000 

-3,000 

-4,000 

-5,000 

21.649' 

0 1,000 2,000 3,000 4,000 5,000 6,000 

A I'B" (F-4) 

Time marks in seconds 

Mach No./Altitude 

Y (feet) 

Figure 5-9 Forward Quarter Pass, 

Case 2 

X(B)=45 deg., ~(B)=180 deg.) 

X-Y trace 

5-16 
100 

90 

80 

70 

60 

50 

40 

30 

20 

10 

0 

0 2 4 6 0 10 12 14 16 18 20 22 

TIME (SEC) 

a PIA + IPlA 

Figure 5-10 

Case 2, Region 4, 

PI Plot 

5-17 
essentially stalemated. 

The steering laws have also been indicated on Figure 5-11 

and 5-13. The pursuit law is used the most frequently, as would 

indeed be expected from the domains specified in Figure 3-2. 

5-18 
I I I I 

5-19 

0 

0 

0 

c\1 

0 

0 

0 

rl 

0 

0 

0 

0 

4 

I 

0 

0 

0 

C.l 

I 

0 

0 

0 

m 

I 

0 

0 

0 

U 

I 

0 

0 

0 In 

I 

0 

0 

0 

9 

I 

m 

al 

cn 

a 

u 
0 2 4 6 8 10 12 14 16 18 20 

(nME sEc) 0 PIA + IPlA 

Figure 5-12 

Case 3 PI Plot 

5-20 
7 50 

600 

500 

X 

(feet) 

400 

300 

200c 

l0OC 

C 

0 "A" (F-15) 

A "B" (F-4) 

Time marks in seconds 

Mach No. /A1 t itude 

-2000 -1000 0 1000 2000 

I 

Figure 5-13 Forward Quarter Pass (feet) 

Case 4 (X(B)=45 deg., ~(B)=135 deg.) 

X-Y trace 

1 i V 

(in boxes) I 5-21 
100 , 

60 

50 

40 

0 2 4 6 0 10 12 14 16 18 20 22 

(TIME SEC) 

a PIA + IPlA 

Figure 5-14 

Case 4 PI Plot 

5-22 
5.4. REGION 5 

A series of 4 runs were made in this region which 

corresponds to a slight angular advantage in favor of the F-15. 

In case 1 of region 5, shown in Figure 5-15, the F-15 eventually 

gains angular advantage after t = 13 seconds, but also loses 

more airspeed than the F-4E in the turn. 

Case 2 of region 5 was run to highlight the influence of 

the turning ability of the F-15 on the result of an engagement 

with the same initial conditions as in Case 1. The thrust/weight 

ratio of the F-15 was reduced by increasing the weight from the 

nominal 40,000 lbs to an artificial 50,000 lbs, thus yielding a 

thrust-to-weight ratio of approximately 0.8 which is comparable 

to the F-4E. The results are illustrated in Figures 5-17 and - 

18. This run shows that the F-4E now has a firing opportunity 

between t =11 and 12 sec. 

Cases 3 and 4 illustrate the effect of an initial altitude 

difference on the same initial angular conditions as in Case 1. 

In case 3, IlAlI has an initial altitude advantage of 4,000 feet 

compared to llBll. The results have been illustrated in Figures 

5-19 and -20. The present AMLB logic commands a pursuit course 

with the aimpoint located at the altitude of I1Al1. As a result, 

lrBrl rapidly loses altitude. The situation at the end of the 

simulated engagement shows that ltB1l ends up in a defensive 

position. Thus, the initial altitude advantage has not improved 

I1B1l I s situation. 

5-23 
r 1,000 

"A" 

16 

15 

8,406' 

TCE : 

P: 

LGP : 

Tail Chase 

Evasion 

Pursuit 

Lag Pursuit "B" IT 10,000 

0 I I I 

-3,000 -2,000 -1,000 0 1,000 2,000 3,000 

Y (feet) 

A "B" (F-4) 

Time marks in seconds 

Mach No./Altitudc 

(in boxes) 

Figure 5-15 Region 5, 

Case 1 (X(B)=90 deg., 

c(B)=135 deg.) 

X-Y Trace 

5-24 
100 

90 

80 

70 

60 

50 

40 

30 

20 

10 

0 

TIME (SEC) 

0 PIA + IPlA 

Figure 5-16 Region 5, 

Case 1, PI Plot 

5-25 
8,000 

7,000 

6,000 

5,000 

X 

(feet) 

4,000 

3,000 

2,000 

1,000 

0 

TCE : 

P: 

LGP : 

Tail Chase 

Evasion 

Pur sui t 

Lag Pursuit 

-3,000 -2,000 -1,000 0 1,000 2,000 3,000 

Y (feet) 

Figure 5-17 Region 5, Case 2 

(),(B)=90 deg., ~(B)=135 deg., 

modified F-15) X-Y Trace 

5-26 
70 

60 

50 

40 

30 

20 

10 

0 

0 2 4 6 8 10 12 14 16 19 21 

(TIME SEC) 

0 PIA + lPlA 

Figure 5-18 Region 5, 

Case 2, PI Plot 

5-27 
6,000 

5,000 

4,000 

X 

(feet) 

3,000 

2,000 

1,000 

0 

TCE: Tail Chase 

Evasion 

P: Pursuit Il*" 

LGP : 

__ 

Lag Pursuit 

-1,000 0 1 .owl 2,000 3,000 4,000 

Y (feet) 

Figure 5-19 Region 5, Case 3 

(X(B)=90 deg., e(B)=135 deg., 

Z(A)=16,000 ft., Z(B)=20,000 ft.) 

X-Y Trace 

A "B" (F-4) 

Time marks in Second8 

Mach No./Altitude 

(in boxes) 

5-28 L I 
The PI at the end of the simulated engagement ( Figure 5- 

20) was much higher than one would expect at first from an 

examination of the X-Y trace. For this reason the line-of-sight 

and angle-off were plotted individually in Figure 5-21. A 

careful examination of the run shows that the ttAtt aircraft is 

strongly pitched down. This attitude explains the obsewed 

variation in these angles. This highlights the utility of the PI 

in summarizing the angular situation of the engagement. 

Case 4 assumes an initial altitude disadvantage of 4,000 

feet for ItBtt. In this case, illustrated in Figure 5-22, the AMLB 

logic commands a climbing turn in IIAttts direction, resulting 

from the pursuit law which is used between t = 0 seconds to 7.5 

seconds. This maneuver brings trBtt in trAttts forward quarter, but 

the PI plot in Figure 5-23 shows that tlA1l does not have a firing 

opportunity as a result of the altitude difference. The 

engagement ends up with ttAtl overshooting ItB1l, without I1Btt having 

a gun-firing opportunity due to the altitude difference. 

Following the overshoot, the F-15 does not appear to be 

reacting. 

In both cases 3 and 4, both ltA1lts and @IBttts tactics could 

be improved by the inclusion of negative GIs. 

5-29 
X 

100 

90 

80 

70 

60 

50 

40 

30 

20 

10 

0 2 4 6 8 10 12 14 

(TIME SEC) 

0 PIA + IPlA 

Figure 5-20 Region 5, 

Case 3, PI Plot 

5-30 
180 

170 

160 

150 

140 

130 

120 

110 

100 

90 

80 

70 

60 

50 

40 

30 

20 

10 - 

0 1"'1'"1"'1'"1"'1'"l" 

0 2 4 6 8 10 12 14 

TIME (SEC) 

0 LOS ANGLE + ANGLE OFF ANGOFA 

1 

Figure 5-21 Region 5, Case 3 

Line-of-Sight and Angle-off Plot 

5-31 
10, ooc 

9 ,ooc 

8,000 

7,000 

6,000 

X 

(feet) 

5,000 

4,000 

3,000 

2,000 

1,000 

0 

P: Pursuit 

TCE: Tail Chase 

- Evasion 

LGP: Lag Pursuit 

- 

I I 1 I 

TCE: Tail Chase 

Evasion 

P: Pursuit 

LGP: Lag Pursuit 

- 

18,192' 

I 

-3,000 -2,000 -1,000 0 1,000 2,000 3,000 4,000 

A "B" (F-4) 

Time marks in seconds 

Mach No. /Altitude 

(in boxes) 

Y (feet) Figure 5-22 Region 5, Case 4 

(X(B)=90 deg. ; ~(B)=135 deg. 

Z(A)=24,000 ft.; Z(B)=20,000 ft.) 

X-Y Trace 

5-32 I I 
n 

X 

a 

x 

v 

z 

w 

0 

f 

[r 

0 

LL 

E 

a 

100 , 

90 

70 

60 

50 

40 

30 

20 

10 

I 

0 2 4 6 8 10 12 14 16 

(TIME SEC) 

PIA + IPlA 

Figure 5-23 Region 5, 

Case 4, PI Plot 

5-33 
5.5. REGION 6 

This region corresponds to a severe initial angular 

disadvantage for llBll. The case illustrated in Figures 5-24 and 

5-25 exercizes the AMLB evasive maneuver during the entire 

simulated engagement. The PI plot indicates that there is no 

improvement in lgB1l Is angular position. However, the X-Y trace 

indicates that the relative range increases from an initial 1000 

feet to 3500 feet. This is due to ItA1fts rapid loss of airspeed 

during the turn. This result shows suggests that rrBrt might have 

an opportunity to disengage. 

5.6. CONCLUSIONS 

In all cases, a wide difference in outcomes has been 

observed for small variations in the initial angular conditions. 

This result has often been observed in ACM simulations. 

Furthermore, this wide difference in outcomes occurred in spite 

of a small variation in initial PI. The use of the initial PI to 

classify and predict the entire engagement outcome does not 

appear promising. 

In all cases, both AMLA and AMLB command initially high 

load factors which result in a rapid loss of airspeed. In all 

cases starting co-altitude, the fight remains roughly in the 

initial horizontal plane unless tail-chase evasion is initiated. 

The lag-pursuit and pure pursuit laws involve essentially a 

series of level turns, or an "angles fight" to use the 

terminology of Reference 10. In this fight, the F-4 cannot gain 

an advantage due to its lower turning capability compared to the 

5-34 
I I < 

0 

hl 

=P 

n 

0 U 0 

0 PI 0 

0, 

d 

xG U 

0, 

CJ 

0 

- 

u 

PI 

PI 

Iu 

w 

OW 

0 

0, 

pz 

0 

0 

ro 

0, 

0 

0 

ul 

0. 

0 

0 

e 

0. 

0 

0 

m 

0. 

0 

0 

0. 

cu 

0 

0 

rl 

0, 

3 

0 

0 

0 

4 

I 

5-35 
90 - 

c 

so - 

.a W 70- 

X 

W 

6o i n 

z 

0 !. - ~I'"1"'l''~l'''l'"l'~'l"'l~~~l"~l 

0 2 4 6 8 10 12 14 16 18 20 

TIME (SEC) 

PIA + lPlA 

Figure 5-25 Region 6 

PI Plot 

5-36 
F-15. In many cases, surprisingly, the fight does not rapidly 

evolve to the disadvantage of the F-4, as might be expected from 

the disparity in performance, and remains approximately neutral. 

Finally, it will be noted that the cases investigated did not 

present any opportunity to exercize the Itpointing algorithm" 

dsicussed in Section 3. 

Throughout the history of air combat, skilled pilots have 

been able to win engagements in spite of having the lowerperforming aircraft. In this situation, they would avoid a 

turning fight as simulated above. In the next section, we 

describe an alternative approach to angular conversion which 

attempts to trade off altitude to gain an angular advantage. 

5-37 
6.ADDING BASIC FIGHTER MANEUVERS TO -- THE - IF --- => THEN LOGIC 

The maneuvers generated by the IF => THEN AMLB and 

discussed in Section 5 are realistic and have generally enjoyed 

good pilot acceptance in flight simulators. However, the 

predictability of the maneuvers it generates has been criticized 

because it makes it possible for a person to anticipate AMLB's 

future maneuvers after a few sessions in a simulator. To enrich 

the variety of maneuvers generated by AMLB, additional maneuvers 

based on the "basic fighter maneuvers" (BFMs) of the type found 

in ACM training manuals (for example, references 10, 11, 12) were 

added to the existing AMLB logic. It will be recalled from 

Section 1 that such an approach had been rejected at the time of 

the development of the original AML program. However, BFMs were 

used in the present effort because they improve the variety of 

maneuvers generated by AMLB, not only in flight simulators, but 

also against AMLA in offline programs, and has proven useful in 

these respects. 

In examining samples of such BFMs, it was found that in 

general each of these maneuvers is appropriate under a narrow set 

of circumstances based primarily on relative geometry, and 

additionally on other situational parameters such as closing 

velocity, relative airspeed, relative altitude, to name just a 

few. While all these maneuvers have their individual, specific 

objective, the majority of them share with AMLB the underlying 

purpose of angular conversion on the opponent, except in the case 

of the disengagement maneuver, which does not exist in AMLB. This 

observation suggested keeping the underlying AMLB angular 

c -a6-1 
conversion logic, and to replace it only when an opportunity for 

a BFM arises. when a choice between a 

BFM and AMLB is available, the selection of the maneuver is 

decided by the means of a random number. 

To reduce predictability, 

Due to the limited scope of this work, only a set of three 

BFMs was investigated: a lldiving overshoot", a Wertical 

overshoot1*, and Ilopposite turn". This terminology and the results 

obtained will be discussed in detail later in this section. 

The features discussed above were implemented in a new 

subroutine called SELECTB. The particular requirements for the 

BFMs were (1) to identify when a particular BFM can be executed: 

(2) to execute that maneuver for a specified amount of time, or 

until conditions specific to that BFM are no longer met, and (3) 

to terminate the maneuver under the specified conditions and 

return control to the underlying AMLB. Function (1) is presently 

performed in a added subroutine called SELECTB, while functions 

(2) and (3) are performed in individual subroutines, as 

illustrated in Figure 6-1. 

6-2 
SUBROUTINE SELECTB 

Figure 6-1 OUTLINE OF THE IMPLEMENTATION 

OF BASIC FIGHTER MANEWERS 

6-3 
----- 

I 

V 

REACTB logic 

I I I Lead/Lag algorithm decision I 

I I 

Figure 6-1 Concluded 

6-4 
6.1 OPPOSITE TURN 

Several cases of @#forward passes" were discussed in Section 

5. It was found that the AMLB logic would generate either a noseto-nose conversion, or a nose-to-tail conversion, depending on 

the initial conditions. Reference 10 (p 79) outlines the 

potential advantage of a nose-to-nose turn, which could result in 

achieving offensive advantage. To execute such a maneuver in Case 

1 of section 5 would require I@Bf1 to turn away from his opponent, 

as was illustrated in Figure 5-1. This maneuver was 

implemented in SELECTB as the "opposite turn" BFM. 

Sample results are shown in Figure 6-2 and 6-3. The effects 

of the superior turning ability of the F-15 over the F-4 is 

clearly demonstrated by the AMLA-controlled F-15 performing a 

"turn reversal" to gain a firing position on the F-4. This 

possibility of this situation is in fact predicted in Reference 

8, Figure 2-12. In this case, AMLA derives the Iftextbook 

solution1#. The F-4 does not gain anything by performing an 

opposite turn with the initial conditions considered. 

To underscore the role of the turn rate, another case was 

run with the same initial conditions as in case 1, but now with 

the F-E initially at corner velocity (M .41), and the F-15 

remaining at the same initial velocity of M .77 . Case 2 has been 

illustrated in Figures 6-4 and 6-5. The F-E clearly achieves a 

nose-to-nose offensive position against the F-15. The F-15 also 

achieves an offensive position. 

The results of these cases would encourage us to consider 

6-5 
the differential turn rate between the 

of the decision for the next maneuver. 

this feature would be fairly simp 

two aircraft at the time 

The implementation of 

e from a computational 

standpoint. Furthermore, AML presently does not differentiate 

between a l1defensiva1l aircraft and an tloffensivell aircraft. The 

inclusion of the differential turn rate might be a good way to do 

so. 

6-6 
0 

0 

0 

0 

6-7 

0 

I 

0 

0 

0 

fi 

0 

0 

0 

\D 

0 

0 

0 

LA 

0 

0 

0 

3 

0 

0 

0 

m 

0 

0 

0 

hl 

0 

0 

0 

4 

0 

0 

0 

0 

hl 

I 
n 

4 

W 

X 

100 

0 2 4 6 0 10 12 14 16 18 20 22 

(TIME SEC) 

a PIA + IPlA 

Figure 6-3 Opposite Turn, 

Case 1 PI Plot 

6-8 
0 

P4 

P 

co 

d 'p 

Q) "B 

h 

u 

6-9 

0 

0 

0 

b 

m 

0 

0 

0 

9 

m 

0 

0 

0 

m 

m 

0 

0 

0 

-3 

m 

0 

0 

m 

0, 

0 

0 

0 

P4 

m 

0 

0 

0 

d 

m 

n 

U 

aJ 

aJ 

cu 

W 

? 

0 

0 
100 

90 

80 

70 

60 

50 

40 

30 

20 

10 

0 

0 2 4 6 8 10 12 14 16 18 20 

TIME (SEC) 

0 PIA + IPlA 

Figure 6-5 Opposite turn, 

Case 2 PI Plot 

6-10 
6.2 DIVING OVERSHOOT 

I 

This BFM is a gun defense maneuver described in Reference 10 

(pages 26-27). The defending aircraft dives in order to force the 

opponent to overshoot. For brevity, it is referred to in this 

document as a "diving overshoot". It is activated under the 

following conditions: 

1. 120 deg <= Epsilon(B) <= 180 deg AND 

2. 60 deg <= Lambda(B) <= 120 deg AND 

3. ABS(ZEA - ZEB) <= 1000 feet (i.e. approximately 

4. Relative Range <= 6000 feet 

It is implemented in subroutine OVRSHT. The diving effect is 

co-altitude) , AND 

accomplished by steering the B aircraft on a pursuit course which 

uses an aimpoint 10,000 feet below the A aircraft, i.e. with 

coordinates XEA, YEA, ZEA + 10000 (z positive downwards). The 

commanded load factor is 95% maximum. In spite of the dive, the 

commanded throttle setting is A/B because of the anticipated 

speed loss due to the high-G turn. Due to the anticipated loss of 

altitude, the maneuver can ony be executed above a minimum 

altitude. 

This maneuver was only tested against a non-interacting I1Alg 

aircraft, i.e. flying straight and level. The results are shown 

in Figures 6-6'and 6-7 (Case 1). A case with the original AMLB 

lead/lag logic is illustrated in Figures 6-8 and 6-9 (Case 2). 

The X-Y traces are dramatically different. However, there is less 

difference than anticipated in the PI plots. it will 

be observed that the "diving overshoot" results in a 5700 foot 

altitude drop for QcB". the 

In Case 1, 

"B"'s velocity decreases in spite of 

6-11 
altitude drop and full afterburner setting. It can also be 

observed from Figure 6-6 that a large portion of the altitude 

drop occurs after the "diving overshoot commandIt (which is 

indicated on the figure as ltDOVSgl) is replaced by the 

conventional pursuit (indicated as after t = 3 seconds. 

The maneuver is terminated when the range rate increases. 

However, an examination of case 1 suggests that the maneuver 

might instead be terminated earlier to avoid the altitude drop. 

For example, a criterion for maneuver termination might be when 

I1Bv1 has crossed rlA1f I s projected track. 

6-12 
/ t 

0 

C 

W 

hl i” 

A / 

I I I I 

0 0 

0 0 

0 

U 

0 

0 

0, 

6-13 

0 

0 

4) 

0 

0 

0 

In 

0 

0 

0 

U 

0 

0 

0 

m 

0 

0 

0 

hl 

0 

0 

0 

4 

0 

0 

0 

0 

4 

0 

0 

0 

r4 

I 

0 

0 

0 

m 

I 

0 

0 

0 

U 

I 

n 

e, 

PI 

PI 

u 

W 

* 

dr 

II 

ax 

-1 e 
n 

W 

a 

x 

w 

0 

u 

z 

f a 

8 

5 

[1 

90 - 

80 - 

Figure 6-7 Diving Overshoot 

PI Plot 

6-14 
U 

.d U 

1u 

e,1 e, P) t-lw 

14 

e,d 

0 0 

0 0 

n 0 zz 

P) 

x2 W 

3 

3 

3 

.f 

0 

0 

0 

Pl 

0 

0 

0 

rJ 

0 

0 

0 

rl 

0 

0 

0 

0 

rl 

I 

0 

0 

1 

0 

0 

0 

cc) 

I 

0 

0 

0 

I 

0 

0 

0 

m 

I 

m cl 

6-15 
90 - 

80 - 

3 70 

X 

W 

D 60 z 

W LI 3U ' E 40 

w a 30 

a 

20 

10 

0 

E 

(TIME SEC) 

a PIA + IPlA 

Figure 6-9 LeadILag 

Overshoot PI Plot 

6-16 
6.3 PULL-UP OVERSHOOT 

In section 5, some conditions under which scissors maneuvers 

are generated in forward passes were described. Reference 19 

(page 6-28) describes a counter to that maneuver which consists 

initially of a pull-up with the intent of an overshoot. In order 

for this maneuver to work, the IIBIl aircraft needs a velocity 

excess which it can convert into an altitude advantage. This 

maneuver will be referred to here as a tlpull-up overshoot". 

A sample case is shown in Figure 6-10 and 6-11. These are 

neutral initial angular conditions, with the llBll aircraft having 

a speed advantage over the @#Att aircraft (M.74 vs M.46). The 

initial conditions are similar to Case 4 of Section 5 shown in 

Figure 5-8. 

The maneuver consists of a wings-level high-G (95% of 

maximum G) pull-up for a specified number of seconds (in this 

case 5 seconds.) Following the pull-up, control is reverted to 

the lead-lag logic to finalize the angular conversion with more 

favorable parameters. The wings-level pull-up causes the F-4 to 

Separate angularly from the F-15. Because of the relative 

position at t= 5 sec (the time the F-4 stops climbing), the next 

maneuver was a tail-chase evasion (indicated in the figure as 

ltTCEt@), followed finally by a pursuit ( indicated as IIPlt). As 

shown in Figure 6-11, the trend indicated by the performance 

index is that IIB" is gaining an angular advantage. This would 

indicate that the maneuver has proven succesful in breaking the 

stalemate of the scissors in rqB1@ts advantage. 

6-17 
5,500 

X (feet) 

5,000 

I I t * \I I 

-2,000 -1,500 -1,000 -500 10 \SO0 1,000 1,500 

4,500 

4.000 

3 I 500 

3,000 

2.500 

2,000 

PUOV: Pull-up 

Overshoot 

TCE: Tail Chase 1s500 

Evasion 

P: Pursuit 

LGP: Lag Pursuit 1,000 

500 

A "B" (F-4) 

Time marks in secondr 

~ach No./ALtitudc 

(in boxes) 

0 

$353 

$: 

4 

3 

- 

LGP 

10.10 a a I 

Y 

Figure 6-10 Pull-up Overshoot 

Case 1 X-Y Trace 

(feet) 

6-18 
Figure 6-11 Pull-up Overshoot 

Case 1 PI Plot 

6-19 
7. CONCLUSIONS AND RECOMMENDATIONS 

In the almost twenty years since work on the adaptive 

maneuvering logic started, the AML programs have been 

continuously, little by little, improved. The AML version, which 

was distributed around 1978 by COSMIC had severe deficiencies, 

mostly in the attitude dynamics. It was unfortunately this 

versions (or derivatives thereof) which were installed in a 

number of US Navy and Air Force flight simulators. 

Todays state of AML is that the motion of the AML driven 

aircraft is quite realistic and AML's tactical behavior is most 

of the time sound. 

In the course of this long development period, we have 

learned a few basic and important lessons for the simulation of 

close-in air-to-air combat and for missile evasion: 

- realistic aircraft motion, specifically the 

rotational dynamics, is of greatest importance for 

pilot acceptance. 

- accurate roll and pitch dynamics are crucial when 

developing evasive maneuvers against surface-to-air 

or air-to-air missiles. 

- improving the tactical behavior of AML is very timeconsuming and tedious. 

- the performance of any air-to-air combat program can 

only be evaluated statistically. Well over 100 

different initial conditions must be exercised to 

7-1 
arrive at valid statistics. 

- both methodologies, trial maneuver and IF => THEN, 

show promise. 

- an analysis of the performance of an air-to-air 

combat program can not be made by analysis of nonreal time, batch processing runs alone. An 

interaction with highly skilled human pilots is 

absolutely required. 

- real-life air-to-air combat is extremly complex. 

The original idea of this contract was to prepare a realtime base-line version of AML which could be used by the Flight 

Research Center to play the role as a @@flight-director'@ 

controlling an actual airborne aircraft. By uplink telemetry, 

maneuver commands are issued to the aircraft and by down-link 

telemetrty, aircraft status is received. Thus, the entire 

computational effort can be performed on ground. The complexity 

of such a project precluded implementation under this contract. 

We did, provide the Flight Research Center with an IF 

=> THEN version of AML, running in real time in conjunction with 

an existing flight simulation. Due to lack of adequate real time 

display facilities, this air-combat simulation was not used much 

by the Flight Research Center. 

however, 

We also recognize, at this point, that a number of problems 

in the simulation of one-versus-one combat still require 

additional studies and analyses. To name just a few: 

7-2 
- How can we prevent, early enough, the AML driven 

aircraft's energy to deteriorate to a very low value? 

- If the AML driven aircraft "fliestt against a dissimilar 

aircraft, how do we make best use in performance 

differences between the two aircraft? 

- Is it possible to build an AML where all the IF => THEN 

production rules are formulated in plain English, so 

that a fighter pilot can change them at his will and 

investigate the effects of the change? 

- How can distributed and parallel processing help to 

overcome some of the limitations imposed presently on 

real-time versions of AML? 

- How can we put AML on-board a remotely piloted aircraft 

and then perform the ultimate ttprooftt for AMLts tactics? 

- How can we incorporate some of the results of 

the theory of differential games into AML? 

If one admits that the decision logic of AML is not yet 

perfect (and the authors of this report certainly admit that), 

then a challenging problem is the following: How can we 

methodically improve AML? There are two aspects: (1) How to make 

changes to the decision logic and (2) How to evaluate the 

effects of these changes. It appears that a solution to this 

problem requires extensive use of a real-time full-dome flight 

simulator and the cooperation of experienced fighter pilots. 

It appears, that after almost twenty years, the challenges 

in building an I1iron-pilot1@ have not become smaller, but have 

grown. 

7-3 
REFERENCES 

1.SLAATS (System Level Air-to-Air Tactical Simulation). 

Presented at the ORSA Conference, San Diego, October 25-27, 1982. 

2. MOSCOW'S Lessons from the 1982 Lebanon - Air War -1 by Benjamin 

S. Lambeth, RAiiiijemirorce, R-3000-AF. 

3.Smart Weapons in Naval Warfare, by Paul F. Walker, Scientific 

American, vol 2481 Number 5 (May 1983) 

4.Computer-Automated Opponent for Manned Air-to-Air Combat 

Simulations, by Walter W. Hankins - 

111, NASA Technical Paper 1518, 

September 1979. 

5.m Adaptive Maneuverinq Logic Computer Program for - the 

Simulation af one-on-one air-to-air combat. Volume I: General 

Description, by George H. Burgin, Lawrence J. Fogel and J. Price 

Phelps. NASA Contractor Report CR-2582, September 1975. 

6.An Adaptive Maneuverinq Logic Computer Program - for - the 

Simulation of one-on-one air-to-air combat. Volume 11: Program 

Description,- by George H. Burgin and A. J. Phelps . NASA 

Contractor Report CR-2583, September 1975. 

7.Advanced Air-to air System Performance Evaluation Model 

(AASPEM) Analyst Manual, E g, Boeing Company Report D180-29122- 

1, November 1985. 

8.PACAM , Volume 11, Analyst' Manual. AFWAL-TR81-3128, November 

1981. 

9.The -- TAC BRAWLER Air - Combat Simulation, User's Manual (Rev 2.0), 

M.S. Carey et al. DSA Report No. 413, June 1982 

10.Fighter Combat Tactics Maneuvering, by Robert L. Shaw, 

Naval Institute Press, Annapolis, Maryland, 1985. 

1l.F-15 Basic Paul R. Stucky, USAF Fighter 

Weapons School Nevada, October 1982. 

12.F-5E Combat Tactics Manual. Part 3 Air-to-air Combat 

Effectiveness, Northrop Corporation, September 1974. 

13.Calculation the Exchange Ratio for the Adaptive Maneuvering 

Logic Program, by Frank Neuman and Heinz Erberger. AIAA paper 85- 

0311. Presented at the 23rd Aerospace Sciences Meeting, January 

14-17, 1985, Reno, Nevada. 

14.1~1 rovements the Adaptive Maneuvering Logic Program, by 

George + H. Burg n, NASA Contractor Report 3985, June 1986. 

15.4 Syllabus of Equations - for Force Effectiveness Analysis, USAF 

Assistant chief of staff for Studies and Analysis, 1 December 

8-1 
1970. 

16.AML/SAM User's Manual, Final Report, by G. H. Burgin, Contract 

F26600-78-C-0100, Tactical Fighter Weapons Center, Nellis Air 

Force Base, September 1979. 

17.Multiple Tactical Aircraft Combat Performance Evaluation 

System, AIM-80-0189, by D. S. Hague 

18.Fighters get a quick -1 draw by Richard DeMeis, Aerospace 

America, September-1986. 

19. Aerial Attack, Vol 1. Canadian Forces Air Combat Manual 2- 

311, 1980. 

20. Design of an All-Attitude Flight Control System to Execute 

Commanded Bank angles - and Angles of Attack, NASA-CR-145004, by 

George H. Burgin and 

- 

David M. Eggleston. 

21. - The Adaptive Maneuverinq Logic Program in support of the 

Pilot's Associate Program: Heuristic Approach to ZssG 

Evasion, AIAA Paper-86-0423, by G.H. Burgin, W.H. Wnliams and 

L.B. Sidor. Presented at the 24th AIM Aerospace Sciences 

Meeting, January 6-9, 1986, Reno, Nevada. 

22 .Evaluation dl Avions en Combat Simule/, Calculateur contre 

Calculateur, ou Calculateur contre Pilote Humain, by J. Pedotti 

and Y. Hignarz in Combat Aircraft Manoeuvrability, AGARD-CP-319, 

October 1981. 

23.Automated Maneuvering Decisions - for Air-to-Air Combat, by Fred 

Austin, Giro Carbone and Michael Lewis, in the Proceedings of the 

Military Computing Conference, Anaheim, California, May 1987. 

24. Modern Air - Combat, by Bill Gunston and Mike Spick, Crescent 

Books, 1983. 

25. Strapdown Seeker Guidance for Air-to-Surface Tactical Weapons 

Report AFATL-TR-78-60 by MGile Systems Division, Rockwell 

International Corporation, Columbus, Ohio May 1978. 

- 

8-2 
APPENDIX 

LISTING OF THE FORTRAN ROUTINES FOR 

"BASIC FIGHTER MANEWERS" 

SUBROUTINE SELCTB 

SUBROUTINE OVRSHT 

SUBROUTINE VTOSH 

SUBROUTINE OPSTRN 

SUBROUTINE CLIMB 

A-1 

A-a 

A-10 

A-12 

A-14 
17-Jul-1987 14:0: 

17-JuI-1987 14:0: 

000 1 

0002 

0003 

0004 

0005 

0006 

0007 

0008 

0009 

0010 

0@11 

001 2 

0013 

0014 

0015 

0016 

0017 

0018 

0019 

0028 

002 1 

0022 

0023 

8Q24 

0cd25 

0026 

0Q27 

0028 

0029 

0930 

003 1 

0C532 

0033 

O034 

0935 

0836 

0037 

0038 

0039 

0040 

004 1 

0042 

0043 

0044 

0045 

0046 

0047 

0048 

0049 

0050 

005 1 

0052 

0953 

0054 

0055 

0056 

0057 

SUBROUTINE SELCTB(XEA*YEA*ZEAvXEDOTA.YEDOTA,ZEDOTAIDMTRXA) 

C 

C 

C SUBROUTINE BASED ON REACTB (MAR 1986) TO SELECT AND EXECUTE 

C APPROPRIATE MANEUVERS. WHEN SEVERAL MANEUVERS ARE FEASIBLE, ONE 

C SPECIFIC MANEUVER IS SELECTED USING A RANDOM NUMBER 

C WHEN NO SUCH MANEUVER IS FOUND. THIS SUBROUTINE REVERTS TO THE 

C LEAD/LAG STEERING LAW OF REACTB 

C 

c----------------------------------------------------------------------- 

C 

C +it* COMMON BLOCKS FOR REAL TIME SIMULATION AT NASA DRYDEN 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

COMMON/CNSTNS/DT~TBEGNITNOW.PI .PIDV2.PIDV4.TWOPI vDEGRDvRADDGvG9 

1 VAR(20).IVAR(20)vTEND 

COMMON/CONTRL/MSTOP. IPRINT 

COMMON/COfiNDB/ICMNWBIGLEVLBIROTBlMANVRB 

COMMON/RNDMAN/MLDECS.MA”I, ISLCTR 

COMfiON/DATAlB/XEB.YEB.ZEBIXEDOTB.YEDOTB~ZEDOTB~XEDDTB~YEDDTB~ 

1 ZEDDTB.PSIB.THETAB.PHIB.UBIVB.WB.PB.QBIRB~AlB~A2B~ 

2 A3B 9 A4B. VELB v VHORB 

COMMON/ DATA2B/ ALFAB v BETAB v CBARB ( 3.3 ) 9 CDB v CLALFB 9 DMTRXB ( 3.3) v DRAGB v 

1 LIFTB*LODMXBPLODSTB~MACHB,RHOBISPECEB.SB*THRSTB* 

2 PSUBSBITPOSBI INIZB*VEITB*CSB.CLB.PSIBRB.THETBB. 

3 AN 1 B * AN2B AN3B v MASSB 

REAL LIFTBILODMXB~LODSTB~MACHB.~ASSB 

COMMON/ TBF4EB/CLMAXB ( 14) 9 XTAB 1 ( 14) NX1v 

THRIDB(7.14) .XTAB2(7) vYTAB2(14) vNX2.NY2. 

THRMLB (7.14) v XTAB3 (7) p YTAB3 ( 14) v NX3. NY3. 

THRABB(7.14) .XTAB4(7) .YTAB4(14) .NX4*NY4. 

ALFCLB(16.10)~XTAB5(16)tYTAB5(10)vNX5.”5~ 

CLFALB(~~IL~)~XTAB~(~~)~YTAB~(~~).NX~~N

CDFCLB(16.10) vXTAB7(16) .YTAB7(10) vNX7vNY7, 

CLFCDB(18.1Q).XTAB8(18)~YTAB8(10)vNX8,”8~ 

RECAGB(~~.~~)VXTAB~(~~)~YTAB~(~~)PNX~.N

COMMON/POINTP/XEAIM~YEA~M~ZEAIMIPCOMB.QCOMB~RCOMB~ IPOINT 

D 1 MENS 1 ON CMPL( 3.3) 

COMMON/RELVAR/LOSELA.LOSELB.LOSAZA.LOSAZB~LOSANA~LOSANB~ 

1 LSDOTA.LSDOTB*DEVANA.DEVANBIDVDOTAIDVDOTBv 

2 RANGE, RRATE. XAI NBv YAI NB. ZA I NBv XB I NA. YB I NA. 

3 ZB I NA. ANGOFA. ANGOFB 

REAL LOSELAILOSELB~LOSAZA.LOSAZB~LOSANA~LOSANB~ 

A-1 
SELCTtl 17-Jul-1987 14:0 

17-Jul-1987 14:0 

0058 

0059 

0068 

006 1 

0062 

0063 

0064 

0065 

0066 

8067 

0068 

0069 

0878 

007 1 

0072 

0073 

0074 

0075 

0076 I 0Q77 

0078 

B079 

0088 

008 1 

0082 

0083 

(3084 

0085 

3086 

0087 

0885 

0089 

I 0090 

009 1 

0892 

a093 

0094 

0095 

0096 

(309 7 

0093 

0099 

0180 

0101 

0102 

0103 

0104 

0105 

0106 

0107 

0108 

01 10 

011 1 

8112 

01 13 

01 14 

~ 

I 

, 

I 

I 

1 LSDOTA 9 LSDOTB 

C 

C 

C *** LET THROTTLE ROUTINE KNOW WHEN A/C IS IN DIVE RECOVERY 

C 

C 

C 

COMMON/ D I VEB/ 1 RECVB 

COMMON/PAGECT/ICNT 

DATA IXLl.JYL1. IXL2.JYL2/1vlvl.l/ 

DATA IXL9. JYL9/ 1 v 1/ 

C 

C THE DEFAULT DECISION INTERVAL IS MLDEF. ELSE IT IS SET IN 

C THE INDIVIDUAL MANEUVER ROUTINE 

C 

C 

C 

DATA MLDEF/ 201 9 NEGTVG/ 1 / 

IF (INIZB.EQ.1) THEN 

MLDECS=MLDEF 

I SLCTR=0 

I AECVB=0 

RETURN 

END I F 

C 

c --------_------------------------------------------------------------

C 

C GROUND AVOIDENCE LOGIC. 

C 

c----------------------------------------------------------------------- 

C 

HB=-ZEB 

DIVEAN=-THETBB 

I F( I RECVB. EQ. 1 . AND. D I VEAN. GT. 0.) THEN 

MANVRB= 1 

I CMNWB=l 

ROTB=0. 

I PO I NT=0 

GO TO 998 

END I F 

IF( IRECVB. EQ. 1 .AND. DIVEAN. LE. 0. ) THEN 

ELSE 

I RECVB=0 

IF(HB.LT.20000.) THEN 

FMACHX=MACHB 

I F ( FMACHX. LT. .4) FMACHX=. 4 

HX=HB 

IF(HX.LT.200. )HX=200. 

CALL TLU~(HX.FMACHXPXTAB~.YTAB~.AECAGBINX~.NYS* 

IXLS. JYL9vRECAN. IC) 

ELSE 

END I F 

IF(DIVEAN.GT.RECAN) THEN 

RECAN=PIDV2 

ROTB=O. 

GLEVLB= 1. 

A- 2 
SELCTli 17-Jul-1987 14:0 

17-Jul-1967 14:0 

01 15 

01 16 

01 17 

01 18 

0119 

0120 

0121 

0122 

0123 

0124 

0125 

0126 

0127 

0128 

0129 

0138 

0131 

0132 

0133 

0134 

0135 

013C 

0137 

0138 

0139 

0140 

0141 

0142 

0143 

0144 

0145 

0146 

0147 

0148 

0149 

0150 

0151 

0152 

0153 

0154 

0155 

0156 

0157 

0158 

0159 

0168 

0161 

0162 

0163 

0164 

0165 

0166 

0167 

0168 

0169 

0170 

0171 

I CMNWB= 1 

I PO I NT=0 

I RECVB= 1 

MANVRB=Z 

GO TO 998 

END IF 

END I F 

C 

c----------------------------------------------------------------------- 

C 

c *** END OF GROUND-AVOIDENCE LOGIC 

C 

c----------------------------------------------------------------------- 

C 

C 2222222 START OF SELECTABLE MANEUVERS 22222222222222222222222222: 

C 

IF (MOD(IVAR(l)vnLDEF).EP.8 .AND. ISLCTR .EQ. 0) THEN 

EPSD=ANGOFB+DEGRD 

FLAMBD=LOSANB*DEGRD 

MAN 1 N I=-1 

C 

IF (EPSD . GE. 120. . AND. EPSD . LE. 180. . AND. 

1 FLAMBD.LE. 60. 1 THEN 

ISLCTR-1010 

END I F 

IF (EPSD . GE. 120. .AND. EPSD .LE. 180. . AND. 

C 

1 FLAMBD. GE. 60. . AND. FLAMBD. LE. 120. ) THEN 

C 

C 

C OPTION 1 (DEFENSIVE) FORCE AN OVERSHOOT 

C OPTION 2 (DEFENSIVE-OFFENSIVE) ROLL REVERSAL 

I F(RANGE . LE. 6000. ) I SLCTR=400 

C 1SLCTR=200 

C 

IF (ABS(ZEA-ZEB) .LE. 1000.0) THEN 

ELSEIF (ZEA . LT. ZEB) THEN 

ISLCTR=810 

ELSEIF(2EA .GT. ZEB) THEN 

ISLCTR-910 

END I F 

C 

END IF 

C 

C IF (EPSD .GE. 120. .AND. EPSD .LE. 180. . AND. 

C 1 FLAI'IBD.LE. 60. ) THEN 

C ISLCTR=610 

C END I F 

WRITE(77v491)TNOWv ISLCTRvEPSDvFLAMBDvRANGE 

WRITE(*v491)TNOWv ISLCTRvEPSDvFLAMBDvRANGE 

END I F 

C 

C 

C 

C 

I SLCTR=0 

A- 3 
SELCTEl 17-Jul-1987 14:01 

1 7- J u 1 - 1 987 1 4 : 0 1 

0172 

0173 

0174 

0175 

0 176 

0177 

0178 

0179 

0180 

0181 

0182 

0183 

0 184 

0185 

0186 

0187 

0188 

0189 

0190 

0191 

0192 

0193 

$194 

a195 

0196 

0197 

0 198 

0199 

020n 

(320 1 

0202 

0203 

02@4 

0205 

0206 

13207 

(3208 

0209 

0210 

021 1 

0212 

0213 

0214 

0215 

0216 

0217 

0218 

0219 

022D 

022 1 

0222 

0223 

0224 

0225 

0226 

0227 

0228 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

2222272 EXECUTION PART OF SELECTABLE MANEUVERS 

IF (ISLCTR .NE. 0 .AND. MOD(IVAR(L).MLD~~F).EQ.O) THEN 

IF(1SLCTR .EQ. 400) 

1 CALL. OVRSHT (XEA, YEA. ZEA. XEDOTA. YEIIOTA. ZEDOTA. DMTRXA) 

IF(1SLCTR .EP. 810) 

1 CALL VTOVSH ( XEA 9 YEA t ZEA. XEDOTA. YEIIOTA * ZEDOTA. DMTRXA ) 

IF(1SLCTR .EP. 610) 

1 CALL. OPSTRN (XEA. YEA, ZFA. XEDOTA. YEIIOTA. ZEDOTA. DMTRXA) 

IF( ISLCTR .EQ. 1010) 

1 CALL. CL I MB (XEA. YEA, ZEA. XEDOTA, YEDOTA. ZEDOTA. DMTRXA) 

END IF 

IF (ISLCTR .NE. 0 ) RETURN 

2222222 END OF SELECTABLE MANEUVERS 222222222222222222222222?221 

START OF LEAD/LAG 111111111111111111111111111111111111111111111111. 

MLDECS=200 

I PO I NT=0 

EPSD=ANGOFB*DEGRD 

FLAMBD=LOSANB*DEGRD 

RO'I' P R V = R 0 T B 

IF (MOD(IVAH(l).MLDECS).EQ.B) THEN 

c *** CHI,:CK FIRST IF WE WANT TO INVOKE THE POINTING ALGORITHM 

C 

IF (FLAMBD. LE. 30. . AND. EF'SD. LE. 45. ) 1'HEN 

I PO I NT=1 

XEA I M=XEA 

YEA I M=YEA 

ZEA I M=ZEA 

MANVRB=7 

GO TO 998 

END I F 

C 

c *** LEAD-LAG -PURSUIT DECISION FOLLOWS 

C 

IF (EPSD. LE. 30. . AND. FLAMBD. LE. 30. THEN 

DTPRETI=3. 

MANVRR=3 

DTPHED=0. 

MANVRB=4 

DTPREW-3. 

MANVRB=5 

DTPREU=0. 

ELSE IF (FLAMBD.LE. (90.-EPSD)) THEN 

ELSE IF(FLAMBD.LE. (180.-EPSD)) THEN 

ELSE 

A-4 
SELCTB 17-Jul-1987 14:0: 

17- JU 1 - 1987 14 : 0: 

0229 

0230 

023 1 

0232 

0233 

0234 

0235 

(a236 

0237 

0238 

0239 

0240 

024 1 

0242 

0243 

0244 

0245 

0246 

0247 

0248 

0249 

0259 

025 1 

0252 

0253 

0254 

0255 

0256 

0257 

0258 

0259 

0269 

026 1 

0262 

0263 

0264 

0265 

0266 

0267 

0268 

0269 

0270 

027 1 

0272 

0273 

0274 

0275 

0276 

0277 

0278 

0279 

0289 

028 1 

0282 

0283 

0284 

0285 

C 

c *** 

C 

C 

C 

c *** 

C 

MANVRR=9 

EN11 I F 

XEXA=XEA+DTPRED*XEDOTA 

YEXA=YEA+DTPRED*YEDOTA 

ZEXA=ZEA+DTPRED*ZEDOTA 

TAXEzXEXA-XEB 

TAYE=YRXA-YEB 

T A 7. E =Z EX A- ZE B 

VHOR2=XEDOTB**2+YEDOTB**2 

VHORB=SQRT(VHOR2) 

VEL.2=VHOR2+ZEDOTB * *2 

VEI .B=SQRT (VEL2) 

DZr (XEDOTB*ZEDOTB*TAXE+YFDOTB+ZEDOTB*ZEDOTB~TAYE-VHORB**2*TAZE)/V~LH 

DY=-YEDOTB*TAXE+XEDOTB*TAYE 

I F (DZ. EP. 0. . AND. DY. EQ. 0. ) THEN 

ROTB=0. 

ELSE IF (DY.EQ.0.) THEN 

IF(DZ.GT.0.) ROTB=0. 

IF(DZ.LT.0.) ROTB=PI 

ELSE 

EN11 I F 

ROTB=ATAN2(DY,DZ) 

SELECI’ THE. POSITIVE G-LEVEL DEPENDING ON B’S VELOCITY 

IF(VELR.GT.400.)THEN 

ELSE 

EN11 IF 

GLVPOS=(LODSTB+LODMXB)/ (2.*LODMXB) 

GLVPOS=LODSTB/LODMXB 

TAS=VELB*0. 5925 

CAS=TAS*SPRT(RHOB/0.0023768) 

IF(CAS.GT.1.2*330.)GLVPOS=(LODSTB~LODMXB)/(2.*LODMXB) 

I CMNWB=l 

CALCUI.ATE INTERCEPT TRAJECTORY G-LEVEL 

I f; (FLAMBD. LT. 60. ) THEN 

CALI. D I RCOS (PSI BRB t THETBB v ROTB 7 CMI’L ) 

DIST2=TAXE**2+TAYE**2+TAZE**2 

RADISrDIST2/(2.*ZMT) 

ZMT=TAXE*CMPL(3*l)+TAYE*CMPL(3*2)+TAZE*CMPL(3*3) 

GL~=(ABS((VELB**~)/RADIS)/G)+CMPL(~V~) 

GL3=ABS(CMPL(2.3) 1 

GLEVRR=SQRT(GL2**2+GL3**2)/LODMXB 

I F ( GLEVRB. LT. GLVPOS ) THEN 

ENDIF 

GLVPOS=GLEVRB 

________-------------------------------------------------- 21 APRIL 

CALCULATE INTERCEPT TRAJECTORY FOR NEGATIVE G’S 

IF(R0TB .LE. 0. )THEN 

A-5 
SELCTB 

0286 

0287 

0288 

0289 

0290 

029 1 

0292 

0293 

0294 

0295 

0296 

0297 

a298 

(a299 

030Q 

030 1 

0302 

0303 

d304 

0305 

(6306 

0307 

0308 

0309 

0310 

031 1 

0312 

0313 

0314 

(3315 

33 16 

(33 17 

13318 

0319 

0320 

032 1 

0322 

(6323 

0324 

0325 

0326 

0327 

0328 

0329 

0339) 

033 1 

0332 

0333 

0334 

0335 

0336 

0337 

0338 

0339 

(6340 

034 1 

0342 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

17-Jul-1987 14: 01 

17-Jul-1987 14:01 

ROTBNG=PI+ROTB 

ROTBNGz-PI+ROTB 

ELSE 

END IF 

CALL DIRCOS(PSIBRB.THETBBIROTBNG.CMPL) 

ZMT=TAXE*CMPL(3,1)+TAYE*CMPL(3*2)+TAZE*CMPL(3s3) 

RAD IS: D I ST21 (2. *ZMT) 

GLZ=(ABS((VELB**2)/RADIS)/G)+CMPL(3s3) 

GL3-ABS(CMPL(2.3) 1 

GLEVRB=SPRT(GL2**2+GL3**2)/LODMXB 

GLVNEG=2.0/ LODMXB 

I F ( GLEVRB . LT. 2.01 LODMXB ) THEN 

GI .VNEG=GLEVHB 

END IF 

DETERMINE IF NEGATIVE G’S ARE ALLOWED, INCLUDING WHETHER GLVNEG EXCE 

ALLOWAfILE LEVEL (PRESENTLY SET TO -2 G) 

CONDITIONS FOR USING NEGATIVE G’S: 

1. B’S AIRSPEED MUST BE LOWF:R THAN A’S 

2- A MUST BE IN B’S FORWARD QUARTER AND LOW (FLAHRD (60 DEG. 

LOSELA < -5 DEG) 

ROI .L I NG I NVERTED 

3. B’C; ROLL ANGLE MUST NOT EXCEED 30 DEGREES- ELSE: HE IS BETTER OFF 

THE OHJECTIVE OF NEGATIVE G’S IS TO BRING B’S NOSE ON A WITIIOUT 

PULL I NG H I GI1 G’ S (HENCE LOS I NG A I RSPEED ) 

(A FUNCTION HAVING SIMILARITIES WITH THE POINTING ALGORITHM) 

IN GENERAL.. NEGATIVE G’S WOULD BE USED TO UNLOAD THE AIRPLANE IN 

ORDER TO GAINIREGAIN AIRSPEED, E.G. TO GAIN SEPARATION 

NEGGEI?= 1 

I f: ( LOSELB . GT. -5.01 DEGRD) NEGGEE=@ 

I F‘ ( PH I B . LE. -30.01 DEGRD . OR. PH I B . GE. 30.01 DEGRD ) NEGGEE=0 

SI1EEDA=SQRT(XEDOTA**2+YED0TA**2+ZEDOTA**2) 

IF (VELB .GT. .90*SPEEDA) NEGGEE=@ 

--SELECT THE MANEUVER WHICH YIELDS THE SMAL.LEST VARIATION IN ROTB 

IF( ARS(R0TBNG-ROTPRV) .LT. ABS(R0TB-ROTPRV) 

1 .AND. NEGGEE .EQ. 1) THEN 

GLEVLB= -GLVNEG 

ROTB=ROTBNG 

MANVRB=ll 

GOT0 998 

GLEVLB=GLVPOS 

MANVRB=6 

GOT0 998 

ELSE 

END IF 

END IF 
i SELCTB 1 7-JU 1-1987 1 4: 0 

17-Jul-1987 14:0 

(3343 

0344 

0345 

0346 

0347 

0348 

0349 

0350 

(335 1 

a352 

"a353 

0354 

w355 

'6356 

0357 

0358 

0359 

0360 

D36l 

0362 

0363 

0364 

0365 

0366 

8367 

0368 

0369 

0370 

837 1 

0372 

0373 

(3374 

8375 

0376 

0377 

0378 

0379 

a380 

IFCEPSD. GT. 120. .AND. FLAMBD. GT. 120. ) THEN 

GLEVLB=0.9 

IF(CAS.GT.330.) GLEVLB=l. 

ROTB=ROTB-PIDV2 

MANVRB=8 

END I F 

C 

998 CONTINUE 

WRITE(*v491)TNOW.MANVRB.ROTBwDEGRD.GLEVLBvRANGE 

C 

C 

C 

C 

C *** END OF REGULAR DECISION MAKING PART 

C 

WRITE(~~P~~~)TNOW*HANVRBIROTB+DEGRD,GLEVLB~RANGE 

491 FORMAT ( ' SELCTB S DECISION' F15.2. 15. F10.2. Fl0.2. F12.1 / / ) 

ICNT=ICNT+3 

CALL THRTLB 

END I F 

C 

C END OF LEADILAG IF 1111111111111111111111111111111111111111111111. 

C 

C 

c----------------------------------- 

C 

C MANVRB= 1 DIVE RECOVERY ACTIVE 

C MANVRB=2 DIVE RECOVERY INITIATED 

C MANVRB=3 LEAD PURSUIT 

C MANVRB=4 PURSUIT (FLAMBD= TO :EPSD= TO ) 

C MANVRB=5 LAG PURSUIT 

C MANVRB=6 I NTERCEPT TRAJECTORY 

C MANVRB=7 POINTING ALGORITHM 

C MANVRB=8 TAIL-CHASE EVASION 

C MANVRB=9 PURSUIT (FLAMBD= TO :EPSD= TO ) 

C MANVRB= 1 1 NEGATIVE G'S 

999 RETURN 

MANEUVER CODES ------------ 

END 

A- 7 
17-Jul-1987 14:0

17-Jul-1987 14:0

800 1 

m002 

0003 

D004 

@a05 

0B06 

0007 

@0@8 

OW9 

0018 

a011 

0012 

0013 

0014 

0015 

%a16 

rd017 

0018 

0819 

032 1 

2022 

m023 

@a24 

8'325 

r3326 

C'027 

3828 

*3;?a29 

033B 

@a3 1 

1;) 3 3 2 

0833 

0034 

,2035 

8936 

0037 

GU38 

a039 

L!04(3 

004 I 

C042 

3043 

e844 

0045 

0046 

0347 

(5048 

OB49 

3050 

005 1 

DO52 

0053 

a854 

€4855 

0a56 

0857 

0820 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

SUBROUTINE OVRSHT(XEA*YEA.ZEA.XEDOTA.YEDOTA.ZEDOTAvZEDOTAvDMTRXA) 

COMMONIRNDMANI MLDECSvMANINI. ISLCTR 

COMMON/CNSTNS/DT. TBEGN, TNOW v P I 9 P I DV2. P I DV41 TWOP I * DEGRD. RADDG. Gs 

1 VAR(20),1VAR(20).TEND 

COMMON/CONTRL/MSTOP. IPRINT 

COHMON/DATAlB/XEB~YEBIZEBIXEDOTB~XEDOTB~YEDOTB~ZEDOTB~XEDDTB~YEDDTB

1 

2 A~B.A~B.VELBVVHORB 

ZEDDTB. PS I B v THETAB, PH I B v UB v VB 9 WB. PB, QB 9 RB v A 1 B v A2B v 

COMMON/DATA2B/ALFAB.BETAB.CBARBo.CDB~CLALFB~DMTRXB(3~3) VDRAGB. 

1 LIFTBvLODMXB~LODSTB,MACHB,RHOB.SPECEB,SB~THRSTBv 

2 PSUBSBvTPOSB. INIZBIWEITB.CSBICLB*PSIBRB.THETBB. 

3 AN 1 B 9 AN2B 9 AN3B 9 MASSB 

REAL LIFTB*LODMXB.LODSTB*MACHB.MASSB 

COMMON/POINTP/XEAIM~YEAIM,ZEAIM.PCOMB,PCOMB~QCOMB~RCOMB~ IPOlNT 

DIMENSION CMPL(3.3) 

COMMON/RELVAR/LOSELAILOSELBILOSELB~LOSAZA~LOSAZB~LOSANA~LOSANB~ 

1 LSDOTA~LSDOTBIDEVANA~DEVANB.DVDOTA,DVDOTA~DVDOTB~ 

2 RANGE~RRATE.XAINBvYAINB.ZAINB.XBINB*XBINAvYBINA* 

3 ZB 1 NA v ANGOFA v ANGOFB 

REAL 

1 

LOSELA.LOSELB.LOSAZA.LOSAZB.LOSAZB*LOSANA~LOSANBv 

LSDOTA v LSDOTB 

THIS SUBROUTINE GENERATES COMMANDS TO THE B AIRCRAFT TO 

FORCE AN OVERSHOOT OF THE A AIRCRAFT . THIS MANEUVER COMBINES ROLL 

IN THE DIRECTION OF A. COMBINED WITH A DIVE 

IF(MANINI.EQ.-l)THEN 

TIMREQ= 15. 

MLDECS= INT(TIMREQ/DT) 

TINIT= TNOW 

TQUIT= TNOW+TIMREQ 

MAN IN I =0 

END I F 

DTPRED=0.0 

XEXA= XEA + DTPRED*XEDOTA 

YEXA= YEA + DTPRED*YEDOTA 

ZEXA= ZEA + 10000. 

TAXE=XEXA-XEB 

A-8 
0 I? R SH 'r 17-Ju1-1987 14:0: 

17-Jul-1987 14:0: 

0058 

0059 

0060 

006 1 

0862 

(3063 

0064 

0965 

QB66 

0,367 

OB68 

05369 

9B7B 

897 1 

OB72 

8073 

0074 

0975 

0076 

0077 

0B78 

OB79 

a5380 

328 1 

0982 

(3983 

05384 

a5385 

OB86 

85187 

0088 

0989 

(sPJ98 

Bd9 1 

3fi92 

TAYE=YEXA-YEB 

TA%E=ZEXA-ZEB 

VHOR2=XEllOTB**2+YEl3OTB**2 

VHORB=SQRT(VHOR2) 

VEI .2=VHOR2+ZEDOTB * *2 

VEI .B=SQRT ( VEL2 ) 

DZ~(XEDOTB*ZEDOTB*TAXE+YEDOTB*ZEDOTB~TAYE-VHORB**2*TAZE)/V~L~ 

DYr-YEDOTB*TAXE+XEDOTB*TAYE 

IF (DZ. EQ. 0. . AND. DY. EQ. 0. ) THEN 

ROTB=0. 

ELSE IF (DY.EQ.0.) THEN 

IF(DZ.GT.0.) ROTB=0. 

IF(DZ.LT.0.) ROTB=PI 

ELSE 

EN11 I F 

ROTB=ATAN2(DYvDZ) 

C 

C SEI.ECT MAXIMUM G TRUN 

C 

GLEVLH=Q. 95 

TPOSB: 2.0 

I CMNWH=l 

C 

C CHECK FOH MANEUVER TERMINATION CONDITIONS 

C 

IF(TN0W .GE. TQU1T)THEN 

END I F 

IF (RRATE . G1'. 0. ) THEN 

END IF 

RETURN 

END 

I SLCTR=0 

I SLCTR=0 

A-9 
17-Jul-1987 14:0 

17-Jul-1987 14: 0 

OQ0 1 

OQ02 

0803 

0004 

~ 0005 

0006 

63007 

C308 

0309 

rdG11Q 

@all 

0Q12 

0013 

CQ14 

0'3 15 

0'3 16 

0'317 

0818 

88 19 

802Q 

OQ2 1 

0'122 

rj323 

3324 

U826 

OG127 

2'328 

1" '3 2 3 

G'33Q 

I '3 0 3 1 

3'332 

"833 

0834 

I 0335 

I OQ36 

I 0037 

e338 

OQ39 

OQ4a 

1284 1 

GG142 

0843 

0344 

a345 

0046 

0047 

0348 

2050 

5985 1 

D852 

a053 

(5054 

oa55 

0056 

0857 

I 

2025 

lai)849 

C 

C 

SUBROUTINE VTOVSH(XEA~YEA*ZEAPXEDOTA.YEDOTA.ZEDOTA~ZEDOTA~DHTRXA) 

COMHON/RNDMAN/ MLDECS. MAN 1 N I 9 I SLCTR 

COMMON/CNSTNS/DT~TBEGN.TNOW.PI.PI~PIDV2~PIDV4~TWOPI~DEGRD~RADD

1 VAR(20).IVAR(20),TEND 

C 

COMMON/CONTRL/MSTOP* IPRINT 

C 

C 

COMMON/COMNDB/ICMNWBIGLEVLB.ROTB.MANVRB 

COMMON/DATAlB/XEB~YEB.ZEBIXEDOTB.YEDOTB~YEDOTB~ZEDOTB~XEDDTB~YEDDTB

1 ZEDDTB.PSIB.THETAB,PHIB.UB.VB,WB.PB.PB,WBPBQBRB.AlB~A2B~ 

2 A3BVA4BvVELBvVHORB 

C 

COMMON/DATA2B/ALFAB.BETAB.CBARB(3.3).CDB~CLALFB~DHTRXB(3~3) VDRAGB. 

1 LIFTBvLODMXB.LODSTB.MACHB.RHOB.SPECEBISB~THRSTB~ 

2 PSUBSBPTPOSB. INIZB,WEITB.CSB,CLB.PSIBRB*THETBBv 

3 AN 1 B v AN2B v AN3B. MASSB 

REAL LIFTB.LODMXB.LODSTBvHACHBvHASSB 

COMMON/POINTP~XEAIM~YEAI~~ZEAIM~PCOMB~QCOMB~RCOMB~ IPOINT 

D I MENS I ON CMPL ( 3.3) 

COMMON/RELVAR/LOSELAILOSELB.LOSELB~LOSAZA~LOSAZB~LOSANA~LOSANB~ 

1 LSDOTA,LSDOTBvDEVANA,DEVANB.DVDOTA,DVDOTA*DVDOTBv 

2 RANGE.RRATE.XAINB.YAINBvZAINBvXBINAvYBINAv 

3 ZB I NA * ANGOFA v ANGOFB 

C 

REAL 

1 

LOSELA t LOSELB 9 LOSAZA 

LSDOTA P LSDOTB 

LOSAZB v LOSANA v LOSANB v 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

THIS SUBROUTINE GENERATES COMMANDS TO THE B AIRCRAFT TO 

CLIMB IN THE VERTICAL PLANE FOR A SPECIFIED TIME. 

THIS CAN BE USED TO FORCE AN OVERSHOOT OF THE A AIRCRAFT 

WHEN IT IS DIVING ONTO B 

IF(MANINI.EQ.-l)THEN 

TIMREQ= 15. 

MLDECS= INT(TIMREQ/DT) 

TINIT= TNOW 

TQIJIT= TNOW+TIMREQ 

MAN IN I =0 

END IF 

C 

ROTB=(d. 

C 

C SELECT LOW G IN ORDER NOT TO LOSE TOO MUCH ENERGY 

A-10 
VTOYSII 

0058 

0059 

0060 

006 1 

0062 

0'163 

0'164 

0065 

0066 

a067 

0068 

0a69 

0370 

007 1 

GO72 

0873 

17-Jul-1987 14:0 

17-Jul-1987 14:0 

C 

GLEVLB= 1.51 LODMXB 

TPOSB= 2.0 

I CMNWB= 1 

C 

C CHECK FOR MANEUVER TERMINATION CONDITIONS 

C 

IF(TN0W .GE. TQU1T)THEN 

END I F 

1 F (RRATE . GT. 0. ) THEN 

END I F 

I SLCTR=0 

I SLCTR=0 

RETURN 

END 

A-11 
800 1 

0002 

0003 

0904 

0005 

05306 

0007 

a008 

8009 

00lQ 

a01 1 

(3%, 12 

0913 

(3%) 14 

8015 

0016 

a217 

0818 

cas 19 

a5328 

(302 1 

OD22 

6023 

0024 

01625 

OD26 

05327 

0828 

01629 

(3030 

093 1 

0032 

8'633 

E7234 

9035 

,3936 

0937 

3938 

0039 

0940 

004 1 

0042 

0043 

e044 

w045 

8046 

0a47 

0'248 

OD49 

0050 

005 1 

13952 

0953 

3054 

0055 

0056 

(3957 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

17-Jul-1987 14:01 

17- Jul - 1987 14 : 01 

SUBROUT I NE OPSTRN ( XEAt YEA. ZEA. XEDOTA. YEIIOTAt ZEDOTA. DMTRXA) 

COMMON/ RNDMAN/ MLDECS. MAN I N I 9 I SLCTR 

COMMON/CNSTNS/DT.TBEGN.TNOW,PI vPIDV2vPIUV4.TWOPI .DEGRD.RADDG.G. 

1 VAR(20). IVAR(P0)vTEND 

COMMON/ CONTHL/ MSTOP t I PR I NT 

COMMON/ COMNL)B/ I CMNWB GLEVLB ROTB 9 MANVRB 

COMMON/DATAlB/XEB.YEB.ZEB.XEDOTB.YEDOTB,ZEDOTB~XE~DTB~YEDDT~* 

1 

2 

ZEDDTBI PS I B t THETAB 9 PH I B v UH 9 VB * WB. PB 

A3B * A4B v VELB v VHORB 

PBv RB 9 A1B v A2B I 

COMMON/DATA2B/ALFAB.BETAB.CBARB(3t3)*CDR*CLALFB,DMTRXB(3,3) .DRAGB. 

1 LIFTB,LODMXB.LODSTBtMACHB~RHOB*SPECEB.SBtTHRSTB* 

3 PSUBSB*TPOSB* INIZB~WEITBtCSB~CLB~PSIBRBtTHETBBt 

:< AN 1 B t AN2B 9 AN3B 9 MASSB 

REAL LIFTB.LODMXB.LODSTB.MACHB.MASSB 

COMMON/POINTP/XEAIM~YEAIM~Z~AIM~PCOMB.PCOMB~RCOMB~ IPOINT 

D1MENC;ION CMPL(3.3) 

COMMON/ RELVARI LOSELA. LOSELB t LOSAZA. LOSAZB LOSANA. LOSANB v 

1 LSDOTA.LSDOTBvDEVANA.DEVANB,DVDOTA.DVDOTAvDVDOTBt 

2 RANGE*RRATE.XAINB.YAINB.ZAINB.XBINB~XBINA*YBINAs 

li ZB I NA I ANGOFA. ANGOFB 

REAL 

1 

LOSELA~LOSELB.LOSAZA~L0SANA.LOSANBt 

LSDOTA t LSDOTB 

THIS C;UBROUI'INE GENERATES COMMANDS TO 1'HE B AIRCRAFT TO 

TURN OPPOSITE TO A FOR A DURATION OF 15 SECONDS 

OR UNl'IL A IS WITHIN A 60 DEG CONE ANGLE: 

IT IS USE11 TO GENERATE A NOSE-TO-NOSE CONVERSION (B CONVERTS 

TO A'S NOSE) 

THIS MANEUVER SHOULD BE INITIATED UNDER THE FOLLOWING CONDITIONS: 

IF(MANINI.EQ.-1)THEN 

TIMREP= 20. 

MLT)ECS= INT(TIMREQ/DT) 

TINIT= TNOW 

TPU I T= TNOW+T I MREQ 

MAN I N I =0 

DTPREL)=0. 0 

XEXA= XEA + DTPRED*XEDOTA 

A-1 2 
~ 

i 

I 

I 

I 1 OPSTRN 

I 

t 11958 

0959 

0060 

0Q6 1 

(2962 

0063 

OD64 

L 0965 

0966 

0067 

0968 

(3969 

0D70 

007 1 

0072 

0073 

(3974 

8975 

3076 

8077 

0978 

0879 

0080 

008 1 

0082 

0083 

0084 

8985 

0086 

0987 

0 288 

9989 

0890 

009 1 

0092 

(3293 

0094 

8995 

0096 

0097 

a298 

0099 

010D 

0101 

0102 

0103 

0104 

0 105 

0106 

0107 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

17-Jul -1987 14 : 0 

17-Jul-1987 14:8 

YEXA= YEA + DTPREDrYEDOTA 

ZEXA= ZEA 

TAXEzXEXA-XEB 

TAYE=-(YEXA-YEB) 

TA%E=ZEXA-ZEB 

VHOR2=XEDOTB**2+YEDOTB**2 

VHORB=SQRT(VHOR2) 

VEI .2=VHOR2+ZEDOTB**2 

VEI.B=SQRT (VEL2 ) 

DZ= (XEDOTB*ZEDOTB*TAXE+YEDOTB*ZEDOTB~TAYE-VHORB**2*TAZE)/VEL€~ 

DY:-YEDOTB*TAXE+XEDOTB*TAYE 

IF1DZ. EQ. 0. .AND. DY. EQ. 0. ) THEN 

ROTB=0. 

ELSE IF (DY.EQ.0.) THEN 

IF(DZ.GT.0.) ROTB=0. 

IF (DZ. LT. 0. ) ROTB=P I 

ELSE 

EN11 I F 

ROTB=ATAN2(DYvDZ) 

END IF 

SEI.ECT MAXIMUM G TURN 

GLEVLn=0. 95 

TPOSB. 2.0 

CAS=Vf-:LB*0. 5925 

CAS=TAS*SQRT(RHOB/0.0023768) 

VCORNI{=339,. 

IF (CAS .GT. VCORNR) GELVLB-LODSTBILODMXB 

ICMNWH=l 

CHECK FOH MANEUVER TERMINATION CONDITIONS 

IF(TN0W .GE. TQU1T)THEN 

END IF 

I SLCTR=0 

FLAMBD=LOSANB *DEGRD 

I F (RRATE . GI'. 0.) THEN 

I SLCTR=Q 

END I F 

RETURN 

END 

A-13 
17-Jul-1987 14:01 

17-Jul-1987 14:01 

000 1 

0002 

0003 

0004 

0005 

0C306 

0007 

0908 

0009 

0010 

0011 

0912 

(32 13 

0914 

0915 

0016 

0017 

a018 

0919 

(2920 

002 1 

8022 

0023 

0024 

GD25 I GD26 

C027 

0028 

32329 

0030 

, 0231 

8332 

535333 

3D34 

0035 

0036 

0937 

31939 

0040 

004 1 

05342 

8943 

01344 

0045 

0046 

0047 

0948 

0049 

0950 

095 1 

(3D52 

0853 

0254 

0055 

0056 

0057 

I 

I 

I 

I 

~ 

I 0038 

SUBROUTINE CLIMB(XEA.YEA.ZEAvXEDOTAIYEDOTA.ZEDOTAvZED0TAvDMTRXA) 

C 

COMMON/RNDMAN/ MLDECSVMANINI. ISLCTR 

C 

COMMON/CNSTNS/DTv TBEGN. TNOW * P I 9 P I DV21 P I UV4r TWOP I 9 DEGRD. RADDG. GI 

1 VAR(20)vIVAR(20).TEND 

C 

COMMON/ CONTRL/ MSTOP v I PR I NT 

C 

COMMON/ COMNDB/ I CMNWB 9 GLEVLB * ROTB v MANVHB 

C 

COMMON/DATAlB/XEB.YEBIZEBIXEDOTB.YEDOTB~YEDOTB~ZEDOTB~XEUDTB*YEDDT~~ 

1 

2 

ZEDDTB. PS I B. T€IETAB, PH I B. UII, VB. WB. PB. PB. RB, A 1B v A2Bw 

A3B v A4B VELB * VHORB 

C 

COMMON/DATA2B/ALFAB.BETABICBARB(3.3).CDB,CLALFB'DMTRXB(3.3) *DHAGBv 

1 

? PSUBSBVTPOSB, INIZBvWEITB*CSB*CLB.PSIBRBITHETBn. 

3 AN 1 B AN2B 9 AN3B 9 MASSB 

L I FTB v LODMXB v LODSTB r MACHB v RHOB 9 SPECEB r SB 9 THRSl'B 9 

REAL LIFTB.LODMXB9LODSTB.MACHB.MASSB 

COMMON/ PO I NI'P/ XEA I M 9 YEA I M * ZEA I M v PCOMB 7 PCOMB r RCOMB I PO I NT 

D IMEN,C; I ON CMPL (39 3) 

COMMON/ RELVAR/ LOSELA. LOSELB * LOSAZAr LOSA7.B * LOSANA. LOSANB r 

1 LSDOTAvLSDOTB.DEVANA.DEVANB.DVDOTA.DVDOTA*DVDOTBr 

3 RANGE.RRATE.XAINB.YAINBvZAINB,XBINA,YBINA*YBINA* 

3 ZB I NA. ANGOFA. ANGOFB 

C 

REAL LOSELA.LOSELB,LOSAZA.LOSAZB.LOSAZBvLOSANAvLOSANB* 

1 LSDOTA LSDOTB 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

C 

THIS SUBROUTINE GENERATES COMMANDS TO THE B AIRCRAFT TO 

CLIMB IN THE VERTICAL PLANE FOR A SPECIFIED TIME. 

THIS CAN BE USED TO FORCE AN OVERSHOOT OF THE A AIRCRAFT 

WHEN IT IS DIVING ONTO B 

IF(MANINI.EQ.-l)THEN 

T I MREQ=5. 

MLI)ECS= I NT (T I MREPIDT) 

TINIT= TNOW 

TQUIT= TNOW+TIMREQ 

MAN I NI =0 

END IF 

C 

ROTB=PI. 

C 

C 

C 

SEI.ECT LOW G IN ORDER NOT TO LOSE TOO MUCH ENERGY 

ELSE SEI.ECT HIGH G IN ORDER TO GAIN ALTITUDE RAPIDLY 

A-14 
17-Jul-1987 14:0 

17-Jul-1987 14: 0 

1 0058 

01359 

0960 

006 1 

01362 

0963 

0@64 

' G065 

0066 

, 0067 

0968 

0069 

C970 

097 1 

(3972 

Q@73 

C 

GLEVLII=O. 95 

TPOSB: 2.0 

I CMNWH= 1 

C 

C 

C 

C 

C 

C 

CHECK FOfl MANEUVER TERMINATION CONDITIONS 

IF(TN0W .GE. TQU1T)THEN 

END I F 

I SLCTR=0 

IF(RHATE .GT.0.) THEN 

END I F' 

I SI .CTR=0 

RETURN 

END 

COKMAND QUALIFIERS 

FORl'RAN/L I S7'/ SHOW: NOMAP APPEND I X 

/CHECK=(NOBOUNDSvOVERFLOW."DERFtOW) 

/DERUC=(NOSYnBOLS.TRACEBACK) 

/STANDARD=(NOSYNTAX,NOSOURCE_FORM) 

/SHOW~~NOPRI~~PROCESSOR~NOINCLUDE~NOMAPrNODICTIONARY~~INGLE~ 

/ WA1;N I NGS= ( GENERAI. * NODECLARAT I ONSI NOULTFl I X) 

/ CONT I NUAT I ONS= 19 / NOCROSS-REFERENCE / NOD-L I NES / NOEXTEND-SOURCE / F./7 

/ NO(i--FLOAT I NG / I 4 / NOMACH I NE-CODE /OPT 1 M I ZE 

COMP I I .AT I ON STAT I ST I CS 

Run Time: 12.01 seconds 

Elapsed Time: 13.04 seconds 

Page Faults: 1071 

Dynamic Memory: 552 pages 

A-15 
Report Documentation Page 

1. Report No. 2. Government Accession No. 

NASA CR-4160 

4. Title and Subtitle 

7. Key Words (Suggested by Author(s11 

Adaptive maneuvering logic 

Air combat maneuvering 

Computer simulation 

Rule-Based Air Combat Simulation 

18. Distribution Statement 

Unclassified-Unlimited 

Subject category 61 

7. Author(s1 

G.H. Burgin and L.B. Sidor 

9. Security Classif. (of this report) 20. Security Classif. (of this page1 21. NO. of pages 

Unclassified Unclassified 136 

9. Performing Organization Name and Addreas 

Titan Systems, Inc. 

P.O. Box 12139 

La Jolla, CA 92037 

22. Price 

A0 7 

12. Sponsoring Agency Name and Addreas 

National Aeronautics and Space Administration 

Washington, D.C. 20546 

5. Supplementary Notes 

3. Recipient'a Catalog No. 

5. Report Date 

September 1988 

6. Performing Organization Code 

8. Performing Organization Report No. 

H-1501 

IO. Work Unit No. 

RTOP 505-66-1 1 

11. Contract or Grant No. 

NAS2- 11990 

13. Type of Report and Period Covered 

Contractor Report-Final 

14. Sponsoring Agency Code 

NASA Technical Monitor: 

Research Facility, Edwards, California 93523-5000. 

Eugene L. Duke, NASA Ames Research Center, Dryden Flight 

6. Abstract 

This report documents an improved version of the Adaptive Maneuvering Logic (AML) 

program for air-combat maneuvering. The document details the modifications and 

improvements incorporated into the AML program. 

NASA-Langley, 1988