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AMC PAMPHLET AMCP 706-327
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ENGINEERING DESIGN
HANDBOOK
FIRE CONTROL SERIES
SECTION 1
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REDSTONE SCIENTIFIC INFORMATION CENTER
FIRE CONTROL ■■■■■
SYSTEMS —GENERAL
FOR RSERENCt ONLY'
HEADQUARTERS, U.S. ARMY MATERIEL COMMAND JANUARY 1968
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HEADQUARTERS
UNITED STATES ARMY MATERIEL COMMAND
WASHINGTON, D.O. 20315
AMC PAMPHLET 23 January 1968
No. 706-327
ENGINEERING DESIGN HANDBOOK
FIRE CONTROL SERIES
SECTION 1, FIRE CONTROL SYSTEMS--GENERAL
This pamphlet is published for the information and guidance of all
concerned.
(AMCRD-R)
FOR THE COMMANDER:
OFFICIAL: CLARENCE J. LANG
Major General, USA
Chief of Staff
Colonel, GS
Chief, Administrative Office
DISTRIBUTION
Special
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AMCP 70G-327
FOREWORD
INTRODUCTION An additional handbook of the Fire Control
Series is AMC Pamphlet AMCP 706-331,
The Fire Control Series forms part of the Compensating Elements. The following para-
Engineering Design Handbook Series which graphs summarizethe content of each of these
presents engineering information and quanti- five handbooks.
tative data for thedesign and construction of Section 1 introduces the subject of fire
Army equipment. In particular, the hand- control systems, discloses the basic fire con-
books of the Fire Control Series have been trol problem and its solution (in functional
prepared to aid the designers of Army fire terms), delineates system-design philosophy,
control equipment and systems, and to serve and discusses the application of maintenance
as a reference guide for all military and ci- and human engineering principles and stan-
vilian personnel who may be interested in the dard design practices to fire control system
design aspects of such material. design.
The handbooks of the Fire Control Series Section 2 is devoted tothe first aspect of
are based on the fundamental parameters of fire control, i.e., gathering intelligence on
the fire control problem and its solutiQn. In target position and motion.
all problems of control over the accuracy of Section 3, because of the complexity of
weapon fire, some method or system of fire the subject of computing systems, is divided
control is employed that derives its intelli- into three parts that are preceded by an in-
gence from the acquisition and tracking of a troductory discussion of the roles of comput-
target; evaluates this system-input intelli- ing systems in Army fire control and by a
gence by computation; and, finally, applies description of specific roles played in parti-
the output information to the positioning of a cular fire-control applications. Part I dis-
weapon along the line of fire. Primary em- cusses the first step in system design, i.e.,
phasis is laid on the systematic approach re- the establishment of a mathematical model
quired in the design of present-day fire con- for the solution of a fire control problem.
trol equipment and systems. This approach Emphasis is given to the basis, derivation,
involves (1) thorough analysis of the particu- and manipulation of mathematical models.
lar fire control problem at hand, (2) establish- Part II discusses the various computing de-
ment ofthemost suitablemathematical mod- vices that perform useful functions in fire
el, and (3)mechanization of this mathematical control computing systems. The discussion
model. ranges from simple mechanical linkages to
complex digital computers. Types of devices
ORGANIZATIONAL BREAKDOWN in each classification are briefly described;
external sources are referenced for detailed
Toaccomplish the aforenoted objectives, information where practical. Part III dis-
the Fire Control Series will consist primarily cusses the various ways in which the comput-
of the following four main sections, eachpub- ing devices described in Part II can be applied
lished as a separate handbook: to the mechanization of the mathematical
models described in Part I., It stresses that
a. Section 1, Fire Control Systems - a fire control computing system designer
General (AMCP 706-327) needs to apply his talents in three special
b. Section 2, Acquisition and Tracking ways: (l)to improvise and innovate asneeded
Systems (AMCP 706-328) to meet particular problems that may arise,
c. Section 3, Fire Control Computing (2) to use ingenuity in obtaining the simplest
Systems (AMCP 706-329) and most economical devices for the particu-
d. Section 4, Weapon-Pointing Systems lar requirement at hand, and (3)to master the
(AMCP 706-330) many problems that result from intrasystem
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AMCP 706-327
interactions when individually satisfactory PREPARATION
components are combined in complex com-
puting systems. Examples culled from actual
fire-control-system design work illustrate The handbooks of the F ire Control Series
the concepts given. have been prepared under the direction of the
Section4 of the Fire Control Seriesdis- Engineering Handbook Office, Duke Univer-
cusses weapon-pointing systems with respect sity, under contract to the Army Research
to (1) input intelligence and its derivation, (2) Office-Durham. With the exception of the
the means of implementing weapon-pointing handbook titled Compensating Elements, the
for the two basic types of weapon-pointing material for the Fire Control Series was pre-
systemsfromthe standpoint of systemstabil- pared by the Jackson & Moreland Division
ity, (3) general design considerations, and of United Engineers and Constructors Inc.,
(4) the integration of components that form Boston, Massachusetts under subcontract
a complete fire control system. to the Engineering Handbook Office. The
AMCP 706-331 presents information on: Jackson & Moreland Divisionwas assisted in
(1) the effects of out-of-level conditions and its work by consultants who are recognized
a displacement between a weapon and its aim- authorities invarious aspectsof fire control.
ing device, and (2) the instrumentation neces- Specific authorship is indicated where appro-
sary to correct theresulting errors. It also priate. Overall technical guidance and as-
presents general reference information on sistance were rendered by Frankford Arse-
compensating elements that pertains to ac- nal; coordination and direction of this effort
curacy considerations, standarddesignprac- were provided by Mr. Leon G. Pancoast of
tices; and considerations of general design, the Fire Control Development & Engineering
manufacture, field use, maintenance, and Laboratories at Frankford Arsenal.
storage.
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AMCP 706-327
PREFACE
The Engineering Design Handbook Series velopment of Army materiel so that it will
of the Army Materiel Command is a coordi- meet the tactical and the technical needs of
nated series of handbooks containing basic the Armed Forces.
information and fundamental data useful in the Comments and suggestions on this hand-
design and development of Army materiel and book are welcome and should be addressed to
systems. The handbooks are authoritative Army Research Office-Durham, Box CM,
reference books of practical information and Uuke Station, Durham, North Carolina 27706,
quantitative facts helpful inthe design and de-
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AMCP 706-327
TABLE OF CONTENTS
Paragraph Page
FOREWORD i
PREFACE iii
LIST OF ILLUSTRATIONS xii
LIST OF TABLES xix
CHAPTER 1. INTRODUCTION TO FIRE CONTROL SYSTEMS
1-1 DEFINITION AND NATURE OF FIRE CONTROL 1-1
1-1.1 GENERAL. 1-1
1-1.2 DEFINITION AND GOALS OF FIRE CONTROL 1-1
1-1.3 SUMMARY OF FIRE CONTROL METHODS 1-2
1-1.3.1 Direct Fire Control 1-3
1-1.3.2 Indirect Fire Control 1-3
1-1.3.3 Geometry of a Typical Fire Control Problem 1-3
1-1.4 CLASSIFICATIONS OF FIRE CONTROL EQUIPMENT 1-5
1-1.5 APPLICATIONS OF MODERN FIRE CONTROL SYSTEMS ........ 1-5
1-1.5.1 Surface-to-Surface With Guns 1-6
1-1.5.2 Surface-to-Surface With Rockets 1-6
1-1.5.3 Surface-to-Air With Guns 1-7
1-1.5.4 Surface-to-Air With Rockets 1-7
1-1.5.5 Air-to-Surface With Guns 1-7
1-1.5.6 Air-to-Surface With Rockets 1-7
1-1.5.7 Air-to-Air With Guns 1-7
1-1.5.8 Air-to-Air With Rockets 1-7
1-1.6 THE INPUT-OUTPUT CONCEPT 1-7
1-1.6.1 Primary Factors in Establishing Input-Output Relationships .... 1-8
1-1.6.1.1 Factors Affecting the Projectile Path. 1-8
1-1.6.1.2 Target Motion With Respect to the Weapon . ...... ... .... 1-8
1-1.6.2 Secondary Factors in Establishing Input-Output Relationships .. . 1-8
1-2 CHRONOLOGICAL DEVELOPMENT OF ARMY FIRE-CONTROL
EQUIPMENTS ....................................... 1-9
1-2.1 INTRODUCTION. 1-9
1-2.2 PRE-19th CENTURY FIRE CONTROL 1-9
1-2.2.1 A Word on Nomenclature 1-9
1-2.2.2 Control of Weapons PriortoFirearms 1-9
1-2.2.3 Development and Control of Early Firearms. .............. 1-9
1-2.3 DEVELOPMENTS IN THE 19th CENTURY 1-11
1-2.3.1 Improvements in Weapons 1-11
1-2.3.2 Improvements in Fire Control 1-11
1-2.4 DEVELOPMENTS IN THE 20th CENTURY THROUGH WORLD WAR
II 1-12
1-2.4.1 Introduction. 1-12
1-2.4.2 Weapon-Laying Devices. 1-12
1-2.4.2.1 The Gunner's Quadrant 1-12
1-2.4.2.2 The Elevation and Range Quadrants. .................. 1-12
1-2.4.3 Optical Sighting Equipment. .......................... 1-14
1-2.4.3.1 The Straight-Tube Telescope ....................... 1-15
1-2.4.3.2 The Elbow Telescope 1-16
1-2.4.3.3 The Panoramic Telescope 1-16
1-2.4.3.4 The Battery Commander's Telescope. ................. 1-20
iv
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TABLE OF CONTENTS (cont)
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1-2.4.3.5 Sights for Recoilless Rifles and Bazookas 1-21
1-2.4.4 Devices for Night and Extreme Environments 1-22
1-2.4.4.1 Instrument Illumination 1-22
1-2.4.4.2 Light Collimation 1-23
1-2.4.4.3 Antiglare Filters and Protective Lens Coatings 1-23
1-2.4.4.4 Environmental Protection 1-23
1-2.4.4.5 Target Illumination and Sound Location 1-23
1-2.4.5 Optical Range Finders 1-25
1-2.4.5.1 Coincidence Ranger Finder 1-25
1-2.4.5.2 The Stereoscopic Range Finder 1-27
1-2.4.6 Tank Fire Control Equipment 1-29
1-2.4.7 Tank Stabilization Systems 1-30
1-2.4.8 Coast Artillery and Antiaircraft Fire Control Equipment 1-33
1-2.4.8.1 Plotting and Correction Devices 1-34
1-2.4.8.2 Mechanical Computers 1-38
1-2.4.8.3 Early Mechanical Directors 1-39
1-2.4.8.4 Data Transmission 1-49
1-2.4.8.5 Refinements in Mechanical Directors 1-51
1-2.4.8.6 Transition to Electrical Directors 1-52
1-2.4.9 Fire Control System Development During World War II 1-53
1-3 RECENT AND CURRENT DEVELOPMENTS IN ARMY FIRE CONTROL . 1-55
1-3.1 GENERAL 1-55
1-3.2 TANK FIRE CONTROL SYSTEMS 1-56
1-3.3 AA FIRE CONTROL SYSTEMS 1-79
1-3.3.1 Late World War II and Post-War Years 1-80
1-3.3.2 T33/M33. 1-80
1-3.3.3 M38 (Skysweeper) 1-80
1-3.3.4 Porcupine X- 1 1-81
1-3.3.5 Stinger. 1-82
1-3.3.6 T50 Raduster 1-82
1-3.3.7 Vigilante 1-85
1-3.4 ARTILLERY FIRE CONTROL SYSTEMS 1-87
1-3.5 ENVIRONMENTAL PROTECTION 1-89
1-3.5.1 Antiglare Filters and Protective Lens Coatings 1-89
1-3.5.2 Unusual Environments 1-89
1-3.6 CONCLUSIONS. 1-91
REFERENCES. 1-91
GENERAL FIRE CONTROL BIBLIOGRAPHY 1-94
CHAPTER 2 . THEORETICAL ASPECTS OF THE FIRE CONTROL PROBLEM AND ITS SOLUTION
2-1 INTRODUCTION. 2-1
2-2 THE FIRE CONTROLPROBLEM 2-1
2-2.1 STATEMENT OF THE FIRE CONTROL PROBLEM ............ 2-1
2-2.2 GENERALIZED FIRE CONTROL THEORY . 2-1
2-2.2.1 Basic Concepts 2-1
2-2.2.2 The Geometrical Approach 2-2
2-2.2.3 Common Geometrical Factors 2-2
2-2.3 FACTORS AFFECTING THE PROJECTILE PATH 2-3
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2-- 2.3.1 Curvature of the Trajectory 2-5
2-- 2.3.1.1 Gravity 2-5
2-- 2.3.1.2 Air Resistance 2-6
2-- 2.3.1.3 Mathematical Relationships Associated With the Trajectory . . . 2-12
2-- 2.3.2 Effects of Jump 2-14
2-- 2.3.2.1 Vertical Jump 2-14
2-- 2.3.2.2 Lateral Jump 2-14
2-- 2.3.3 Variations from Standard Conditions 2-14
2-- 2.3.3.1 Propellant Characteristics 2-15
2-- 2.3.3.2 Projectile Weight 2-15
2-- 2.3.3.3 Air Density 2-15
2-- 2.3.3.4 Air Temperature 2-15
2-■ 2.3.3.5 Differences in Muzzle Velocity 2-15
2-- 2.3.3.6 Drift 2-16
2-- 2.3.3.7 Wind 2-18
2-- 2.3.3.8 Effects of Rotation of the Earth 2-19
2-- 2.3.3.9 Nonrigidity of the Trajectory 2-19
2-- 2.4 EFFECT OF TARGET MOTION 2-20
2-- 2.5 THE PREDICTION ANGLE. 2-21
2-- 2.6 COORDINATE FRAMES FOR FIRE CONTROL 2-23
2-- 2.6.1 Primary Coordinate Frames of Use for Stating the Fire
Control Problem 2-24
2-- 2.6.2 Coordinate Frames of Use in Data Handling and Computing 2-25
2-- 2.6.3 Effect of the Reference Coordinate Frame on the Prediction
Angle and Its Components 2-28
2-2.7 DIFFERENCES BETWEEN FIRE CONTROL FOR GUNS AND
ROCKETS. 2-30
2-3 SOLUTIONOFTHEFIRE CONTROLPROBLEM 2-30
2-3.1 GENERAL 2-30
2-3.2 SIGHTING AND RANGING 2-31
2-3.2.1 General 2-31
2-3.2.2 Sighting 2-32
2-3.2.3 Ranging 2-33
2-3.3 COMPUTATION OF FIRING DATA 2-33
2-3.3.1 Weapon and Target Both Stationary 2-33
2-3.3.2 Weapon Stationary and Target Moving 2-33
2-3.3.3 Weapon Moving and Target Stationary 2-36
2-3.3.4 Weapon and Target Both Moving 2-37
2-3.4 APPLICATION OF FIRING DATA 2-37
APPENDIX 2-1. Summary of the Mathematics Associated With the
Exterior Ballistics of a Projectile 2-39
REFERENCES. 2-44
CHAPTER 3. FUNCTIONAL ELEMENTS OF FIRE CONTROL EQUIPMENT EMPLOYED
IN THE SOLUTION OF THE FIRE CONTROL PROBLEM
3-1 INTRODUCTION. 3-1
3-2 TYPES OF FUNCTIONAL ELEMENTS EMPLOYED IN FIRE
CONTROL SYSTEMS 3-2
3-2.1 ACQUISITION ELEMENT 3-5
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3-2.2 TRACKINGELEMENT ................ .... 3-5
3-2.3 BALLISTIC-DATA ELEMENT 3-6
3_2.4 PREDICTINGELEMENT. ............................. 3-6
3-2.5 ARBITRARY CORRECTION ELEMENT .................... 3-6
3-2.6 COMPENSATING ELEMENT 3-7
3-2.7 POINTING ELEMENT 3-7
3-2.8 DATA-TRANSMITTING ELEMENTS 3-7
3-2.9 FUZE-SETTING ELEMENT ............................ 3-7
3-2.10 COMMANDELEMENT ............................... 3-7
3-3 FACTORS ASSOCIATED WITH THE INTEGRATION OF FUNCTIONAL
ELEMENTS INTO FIRE CONTROL SYSTEMS. ................. 3-8
3-3.1 THEFACTOROF WEAPONFUNCTION. ................... 3-8
3-3.1.1 Field-Artillery Fire Control System Example. .... ......... 3-8
3-3.1.2 Antiaircraft Fire Control System Example .... . . ....... ... 3-11
3-3.1.3 Comparison of the Selected Examples .... ..... 3-12
3-3.2 THE FACTOR OF KIND AND SIZE OF WEAPON INVOLVED ... ... 3-12
3-3.3 THE EFFECT ON FIRE-CONTROL-SYSTEM DESIGN OF A
MULTIPURPOSE REQUIREMENT OF THE WEAPON SYSTEM ..... 3-12
3_3.4 THE EFFECT ON FIRE-CONTROL-SYSTEM DESIGN OF A
WEAPON-MOBILITY REQUIREMENT . .... ..... ........ ... 3-15
3-3.5 THE EFFECT ON FIRE-CONTROL-SYSTEM DESIGN OF
SPEED AND ACCURACY REQUIREMENTS. ..... 3-15
3-4 COMPATIBILITY PROBLEMS OF VARIOUS TYPES OF OPERATING
ELEMENTS. ........................................ 3-15
3-4.1 GENERALPRINCIPLES 3-15
3-4.2 FACTORS REQUIRING PARTICULAR ATTENTION 3-16
3-4.2.1 Relative Accuracies 3-16
3-4.2.2 Relative Speeds of Operation 3-16
3-4.2.3 Relative Ranges of Operation .... ... . . . . ...... ..... ... 3-16
3-4.2.4 Types of Associated Equipment. . . ........... .......... 3-16
3-4.2.5 Interconnecting Devices. ... ............... ..... ..... 3-16
3-5 EXAMPLES OF FUNCTIONAL ARRANGEMENTS EMPLOYED IN
VARIOUS TYPES OF FIRE CONTROL SYSTEMS . . . . ..... ... .... 3-17
3-5.1 INTRODUCTION. ................................... 3-17
3-5.2 FIRE CONTROL EQUIPMENT FOR ARTILLERY .............. 3-17
3-5.2.1 Observing and Position-Finding Equipment. ...... ..... .... 3-17
3-5.2.1.1 Optical Equipment ........................... ... 3-17
3-5.2.1.2 Radar Equipment. .......... .................... 3-19
3-5.2.1.3 Sound and Flash Equipment 3-20
3-5.2.2 Firing-Data Computation Equipment ........ 3-20
3-5.2.2.1 Human Data Computation. .... ..... . . ....... ... .... 3-22
3-5.2.2.2 Mechanical, Electrical and Electronic Data Computation. .... 3-22
3-5.2.3 Equipment for the Application of Firing Data. . .... . . ....... 3-23
3-5.2.3.1 Optical Equipment . 3-24
3-5.2.3.2 Mechanical Equipment 3-25
3-5.2.3.3 Automatic and/or Remote-Control Equipment 3-25
3-5.3 FIRE CONTROL EQUIPMENT FOR TANKS. . ......... ....... 3-26
REFERENCES 3-28
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TABLE OF CONTENTS (cont)
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CHAPTER 4. DESIGN PHILOSOPHY
4-1 INTRODUCTION. 4-1
4-2 MODELS. . ....." 4-5
4-3 DEVELOPMENT OF MATHEMATICAL MODELS 4-7
4-3.1 GENERALCONSIDERATIONS. 4-7
4-3.2 MODELS FOR IDEALIZED SYSTEMS. 4-8
4-3.3 MODELS FOR OPTIMUM SYSTEMS . 4-8
4-3.4 APPLICATION OF COMPUTERS TO THE STUDY OF
MATHEMATICAL MODELS 4-9
4-3.4.1 Information To Be Computed 4-9
4-3.4.2 Degree of Sophistication Necessary 4-10
4-3.4.3 Accuracy Required 4-10
4-3.4.4 Solution Time 4-11
4-3.4.5 Choice of Parameter Ranges 4-11
4-3.5 MODELS FOR PRACTICAL SYSTEMS 4-11
4-3.6 CONCLUSIONS 4-12
4-4 SYSTEM AND SUBSYSTEM ACCURACY CONSIDERATIONS. ... ..... 4-12
4-4.1 INTRODUCTION. 4-13
4-4.1.1 Systematic and Random Errors 4-14
4-4.1.2 Engagement Hit Probability 4-14
4-4.1.3 An Outline of the Procedure for Designing a Fire Control
System of Prescribed Accuracy 4-15
4-4.2 BASIC CONCEPTS OF PROBABILITY THEORY. 4-19
4-4.2.1 Probability Applied to Discrete Events 4-20
4-4.2.2 Continuous Functions of a Random Variable . .... .... . . ... . 4-23
4-4.2.3 Averages of Random Variables 4-29
4-4.2.4 Gaussian Distribution 4-33
4-4.2.5 The Bivariate Normal Distribution 4-36
4-4.3 HIT AND KILL PROBABILITY THEORY 4-37
4-4.3.1 The Probability of Kill and the Diffuse Target 4-39
4-4.3.2 Single-Shot Kill Probability 4-40
4-4.3.3 Single-Shot Hit Probability 4-42
4-4.3.4 Engagement Hit Probability 4-46
4-4.4 ERROR ANALYSIS DM FIRE CONTROL SYSTEMS. ... ..... . . ... 4-53
4-4.4.1 Introduction. .................................... 4-53
4-4.4.2 Analysis of Error Propagation in Systems Describable by
Equations Other Than Differential Equations 4-55
4-4.4.3 Analysis of Error Propagation in Systems Describable by
Differential Equations . . 4-75
4-4.4.3.1 Use of the Impulse-Response Approach 4-76
4-4.4.3.2 Use of the Transfer-Function Approach 4-82
4-4.4.4 Illustrative Example of an Error Analysis for a System
Describable by Differential Equations . ...... 4-94
4-4.5 WEAPON-SYSTEM ERRORS THAT ARE BEYOND THE CONTROL
OF THE FIRE CONTROL SYSTEM DESIGNER. 4-114
4-4.5.1 Introduction. .................................... 4-114
4-4.5.2 Errors Associated With the Input Portion of a Weapon System . . . 4-115
4-4.5.2.1 Radar Glint Noise. 4-116
4-4.5.2.2 Amplitude Noise 4-119
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