Morris R. DrielsU.S. Naval Postgraduate SchoolMonterey California

Second Edition

Weaponeering:Conventional WeaponSystem Effectiveness

AIAA EDUCATION SERIES

Joseph A. Schetz, Editor-in-ChiefVirginia Polytechnic Institute and State UniversityBlacksburg, Virginia

Published by theAmerican Institute of Aeronautics and Astronautics, Inc.1801 Alexander Bell Drive, Reston, Virginia 20191-4344

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CONTENTS

Preface xxiii

Acknowledgments xxix

Nomenclature xxxi

PART 1 BASIC TOOLS AND METHODS

Chapter 1 Overview of Weaponeering and Weapon Effectiveness 1

1.1 Definitions 11.2 Example of a Weaponeering Outcome: Air Tasking Order 11.3 Weaponeering—Part of a Larger Planning Cycle 21.4 An Example of a Weaponeering Tool 61.5 Basic Components Needed to Compute Effectiveness 81.6 Effectiveness Calculation Methodology 251.7 Implementing a Methodology into a Model 26

Chapter 2 Introduction to Statistical Methods 29

2.1 Why Are Statistics Needed? 292.2 Population and Sample 302.3 Univariate Distribution 302.4 Univariate Normal Distribution 332.5 Bivariate Normal Distribution 402.6 Probability 422.7 Circular Normal and Rayleigh Distributions 452.8 Uniform Distribution 492.9 Binomial Distribution 512.10 Mott and Weibull Distributions 552.11 Poisson Distribution 572.12 Testing Data for a Particular Distribution 582.13 Functions of Random Variables 602.14 Mathematical Expectation 602.15 Monte Carlo Simulations 64

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2.16 Generating Random Numbers from the CumulativeDistribution Function 65

2.17 Confidence Levels, Limits, and Intervals 662.18 Required Number of Monte Carlo Iterations 71

Chapter 3 Weapon Trajectory 75

3.1 Introduction 753.2 Initial Release or Firing Velocities 763.3 Zero-Drag, Point Mass Model 773.4 Characterization of Air Resistance 813.5 Trajectory in a Standard Atmosphere 853.6 Linear Drag, Point Mass Model 873.7 High-Fidelity Point Mass Model 913.8 General Stability of Projectiles 953.9 Spin-Stabilized Projectiles—Gyroscopic Effects 973.10 Other Characteristics of Spinning Projectiles 1013.11 Effects of Wind on Ballistic Trajectory 1033.12 Modified Point Mass Model 1083.13 Using Trajectory Models in Fire Control Systems (FCS) 1093.14 Artillery Firing Tables 1103.15 Trajectory for Guided Weapons and Munitions 1123.16 Ballistic Partial/Unit Effects from Trajectory Programs 1143.17 Air-Launched Loft and Dive Toss Deliveries 1173.18 Fuze Models 120

Chapter 4 Delivery Accuracy—Overview 127

4.1 Introduction 1274.2 General Measures of Accuracy 1344.3 Vertical Errors 1394.4 Commonly Used Equations Based on Normal Data 1394.5 Noncircular Distributions 1424.6 Accuracy Measures Including a Bias 1434.7 Accuracy in the Normal Plane 1454.8 Definitions of the Angular Mil 1474.9 Converting Between Ground and Normal Plane

Accuracy Values 1474.10 Treatment of Precision Errors in the Normal Plane 1504.11 Accuracy of Air-Launched Unguided Weapons 1514.12 Accuracy of Air-Launched Guided Weapons 1514.13 Bivariate Analysis of Air-Launched Guided

Weapon Data 157

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4.14 CEP for Nonnormal Miss Distance Distributions 1594.15 Generating Random Miss Distances for PHIT/PNM

Distributions 1624.16 Accuracy Mixture Models 1624.17 Accuracy of Surface-Launched, Unguided Weapons 1664.18 Accuracy of Surface-Launched Guided Weapons 1684.19 General Approach to Accuracy Modeling—

Error Budgets 1714.20 Treatment of Vertical Errors 1734.21 Spherical Errors (SEP) 176

Chapter 5 Accuracy of Air-Launched Unguided Weapons 179

5.1 Introduction 1795.2 Mechanization 1795.3 Sign Conventions and Definitions 1805.4 CCRP Mechanization 1825.5 CCRP Modes 1855.6 Computation of Miss Distances for CCRP

Mechanization 1875.7 Accumulation of Individual Miss Distances for CCRP 1955.8 CCIP Mechanization 1985.9 CCIP Modes 2015.10 Computation of Miss Distances for CCIP 2015.11 Bombing on Coordinates Mechanization 2065.12 Summary 209

Chapter 6 Accuracy of Surface-Launched Unguided Munitions 211

6.1 Introduction 2116.2 Meterological (MET) Messages 2166.3 Precision Error Model 2176.4 MPI Error Model 2196.5 MPI Errors for Observer Adjusted Fire 2226.6 MPI Errors for Predicted Fire 2226.7 MPI Errors for Registration/Transfer Adjusted Fire 2256.8 MPI Errors for METþ VE Adjusted Fire 2276.9 MPI Error for Range K Adjusted Fire 2326.10 Example 243

Chapter 7 Accuracy of GPS/INS Guided Munitions 249

7.1 Overview of the Global Positioning System 2497.2 Determining Position with No Errors Present 250

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7.3 Pseudorange and Clock Errors 2517.4 User Position from Four Satellite Pseudoranges 2527.5 User Position from More Than Four Satellites 2547.6 User Position in Geodetic and Local Coordinates 2547.7 Accuracy of GPS Measured Locations 2587.8 GPS Error Budgets 2617.9 Differential GPS 2627.10 GPS/INS Guided Munitions 2657.11 Combining Vertical Errors into Equivalent Ground

Plane Errors 2687.12 Targeting Modes 2697.13 INS Only Guidance—GPS Jamming 2747.14 Low-Level Wind (LLW) Effects 2767.15 Nonplanar Trajectories 2787.16 Spreadsheets to Compute GPS Accuracy 280

Chapter 8 Vulnerability Assessment—Introductory Methods 283

8.1 Introduction 2838.2 Introduction to Effectiveness Indices 2838.3 Requirements for the Computation of

Effectiveness Indices 2848.4 Collecting and Characterizing Warhead

Fragment Data 2868.5 Compartment vs Component Vulnerability 2938.6 Vulnerability Assessment for Fragmentation

Warheads 2938.7 Vulnerable Area 2968.8 Critical and Noncritical Components 2978.9 Redundant and Nonredundant Critical Components 2978.10 Target Vulnerability to Single Fragments 2988.11 CASE a: Target Composed of Nonredundant Critical

Components with No Overlap 2998.12 CASE b: Target Composed of Nonredundant Critical

Components That Overlap 3018.13 CASE c: Target Composed of Some Redundant

Critical Components with No Overlap 3038.14 CASE d: Target Composed of Some Redundant

Critical Components That Overlap 3058.15 Multiple Hit Vulnerability 3068.16 Effectiveness Assessment for a Specific Weapon 3078.17 Centroid of Vulnerability and Different

Fragment Weights 311

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8.18 Damage Matrix and Lethal Area 3138.19 Vulnerability Assessment for Blast Warheads 316

Chapter 9 Vulnerability Assessment—Advanced Methods 317

9.1 Introduction 3179.2 Computation of Vulnerable Areas (COVART) 3189.3 Shotline Anaysis 3209.4 Penetration Equations 3219.5 Calculating the Shotline Pk/sh 3259.6 COVART Computational Model for Calculating

Vulnerable Areas 3279.7 Advanced Joint Effectiveness Model (AJEM) 3299.8 Modular UNIX Based Vulnerability Suite (MUVES) 3319.9 Effectiveness Assessment: Computing the

Damage Matrix 3339.10 Detailed Description of the General Full Spray

Materiel Model (GFSM) 3399.11 Orientation of Weapon in GFSM Scenario 3419.12 GFSM Target Description 3429.13 GFSM Warhead Description 3429.14 GFSM Fragment Drag Data 3429.15 GFSM Fragmentation Zones 3449.16 Fragment Velocity/Maximum Effective Range 3469.17 GFSM Computation of PK 3479.18 GFSM Calculation of PK(r, gj) 3499.19 Review of Computational Procedure 3509.20 Worked Problem for GFSM Methodology 3529.21 Computation of the PK Matrix 3549.22 Joint Mean Area of Effects Model (JMAE) 3559.23 Simplification of Damage Matrix 3669.24 Conserving Lethality for Different Damage Functions 3719.25 Lethal Area Calculation for Targets Sensitive to Blast 3729.26 Combining Lethal Area Matrices—AVMAT Program 3749.27 Vulnerability Assessment for Shaped Charge and

Penetrating Rod Warheads 378

Chapter 10 Basic Effectiveness Calculations 387

10.1 Introduction 38710.2 Basic Approach to Effectiveness Calculation 38710.3 Interpretation of the Weapon Lethal Area 38810.4 Using Other Damage Functions 392

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10.5 Dependent and Independent Fire 39510.6 Combining Round-to-Round Errors with

Damage Functions 39910.7 Conclusions 404

PART 2 INTRODUCTORY AIR-TO-SURFACEWEAPONEERING

Chapter 11 Single Weapons Against Unitary Targets 405

11.1 Introduction 40511.2 Probability of Damage from One Unguided

Weapon and Unitary Target—PD1 40611.3 PD1 for Single Fragmentation Warhead and

Unitary Target 40811.4 Comparing Expected Value with Monte

Carlo Simulation 40911.5 PD1 for Blast/Rectangular Damage Function

and Unitary Target 41011.6 Some Computational Considerations 41311.7 Force Estimation 41411.8 Simple Spreadsheet Implementation to Compute PD1 41511.9 Template for Implementing Weaponeering Solutions 41711.10 Calculating PD1 for Guided Weapons 42311.11 Bomb Burial 42711.12 Comparison of Analytical Effectiveness

Methodologies 42811.13 Comparing Circular and Rectangular Cookie-Cutter

Damage Functions 432

Chapter 12 Single Weapons Directed Against anArea of Targets 435

12.1 Introduction 43512.2 Measurement of Damage 43512.3 Weapon Represented by Rectangular

Damage Function 43812.4 Effect of Multiple Weapons and Aimpoints 43912.5 Fractional Coverage 44312.6 Spreadsheet to Compute FD1 45012.7 Weaponeering Spreadsheet 45012.8 Calculating FD1 for Guided Weapons 45412.9 Weapon Represented by Carlton Damage Function 455

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Chapter 13 Stick Deliveries 461

13.1 Introduction 46113.2 Determining the Pattern Dimensions 46113.3 Calculating the Stick Width 46313.4 Calculating Stick Length 46513.5 Precision Errors for Stick Deliveries 46713.6 Pattern Dimensions 47013.7 Weapon Sparsity and Overlap in the Pattern 47013.8 Summary of Computing Fractional Damage for Sticks 47413.9 Spreadsheet Implementation 47513.10 Advanced Method for Calculating

Fractional Damage 47513.11 Effect on FD of Different Multiple Weapon

Representations 480

Chapter 14 Projectiles 483

14.1 Introduction 48314.2 Simplified Projectile Methodology 48614.3 Accuracy Considerations 48714.4 Damage Functions 48914.5 Effectiveness Calculations 49014.6 PD When More Than One Round Is

Required for a Kill 49114.7 Spreadsheet Implementation 49314.8 Gunnery Model with Correlation–Aimpoint

Wander 49314.9 Round-to-Round Correlation 49614.10 Generating Correlated Impact Points 49914.11 Correlation Coefficients 50014.12 Effectiveness Calculations with Correlation 50014.13 Effectiveness for Penetrating Munitions 500

Chapter 15 Cluster Munitions 505

15.1 Introduction 50515.2 General Analytical Treatment of Cluster Munitions 51115.3 Trajectory Computations 51315.4 Submunition Pattern Dimensions 51515.5 Rectangular Patterns in the Ground Plane 51515.6 Circular Patterns in the Normal Plane 52015.7 Effect of Precision Error 52215.8 Spreadsheet Implementation 522

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Chapter 16 Weaponeering for Specific Targets UsingEffectiveness Indices 527

16.1 Introduction 52716.2 Bridges 53116.3 Effective Miss Distance Damage Function 53516.4 Above Ground Buildings 54216.5 Indirect Aimpoints 54816.6 Summary of Weaponeering Methodologies

and Locator 558

PART 3 INTRODUCTORY SURFACE-TO-SURFACEWEAPONEERING

Chapter 17 Indirect Fire—Artillery and Mortar Systems 561

17.1 Introduction 56117.2 Terminology and Combat Scenarios 56117.3 Aimpoint Selection 56217.4 Weapon Lethal Area 56317.5 Delivery Accuracy 56817.6 Munition Trajectory 57017.7 Naval Gunfire 57017.8 Comparing Sequential Dependent or

Independent Events 57217.9 Methodologies for Surface-to-Surface

Weaponeering Tools 57817.10 Superquickie 2, Unitary Warhead 57917.11 Superquickie 2, Improved Conventional Munition 58617.12 High-Fidelity Model—Matrix Evaluator Program 58817.13 Fractional Damage Calculations for

Multiple Events 59617.14 Improved Conventional Munitions

(ICM) in Matrix Evaluator 59717.15 Matrix Evaluator V2.0 59917.16 ARTQUIK Method 60517.17 Damage Done by a Single Weapon with an

Offset Aimpoint 60617.18 Combining the Damage Function with

Precision Error 60817.19 Defining the Volley Damage Grid 60917.20 ARTQUIK Model for Improved Conventional Munitions 61217.21 Summary of Model Features 614

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Chapter 18 Direct Fire: Infantry, Vehicles, and Small Boats 617

18.1 Introduction 61718.2 Direct Fire Against Personnel Targets (FBAR) 61818.3 Direct Fire Against Vehicles—Passive Vehicle

Target Model (PVTM) 62418.4 Naval Direct Fire Systems (JGEM) 630

Chapter 19 Mines 647

19.1 Introduction 64719.2 Land Mines 64719.3 Land Minefield Specification and Planning 64919.4 Simplified Land Mine Method—Minefield Density 65119.5 Detailed Land Mine Method 65419.6 Sea Mines 65919.7 Shallow Water Sea Mines 66019.8 Deep Water Sea Mines 66119.9 Antisubmarine Mines 666

PART 4 ADVANCED WEAPONEERING

Chapter 20 Historical Review of Weapon Effects Methods 669

20.1 Introduction 66920.2 Review of Weaponeering Methodologies

Prior to WWII 67120.3 Variable Time and Proximity Fuze 67520.4 Review of Weaponeering Methodologies

After WWII 68020.5 Further Work of John Von Neumann 68320.6 Roger Snow (with Ryan, Harris, and Lind) 68620.7 Salvo Formula 69020.8 Fendrikov and Yakovlev 69820.9 U.S. Organizational History 699

Chapter 21 Personnel Targets 703

21.1 Introduction 70321.2 Casualty Criteria 70421.3 Wound Ballistics 70521.4 Computer Man Program 71821.5 Computer Man Injury Assessment 72221.6 Computer Man Shotline Modes 729

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21.7 Sperrazza and Kokinakis Methods (SK) 73021.8 General Full Spray Personnel Model (GFSP) 73421.9 Detailed Description of GFSP 74121.10 Ballistic Limit for Fragments 74721.11 Effect of Terrain on Presented Area 74921.12 Component-Level Personnel Injury Modeling 75221.13 Injury due to Blast 75421.14 Operational Requirement Based Casualty Assessment

(ORCA) 76121.15 Risk Estimates, Collateral Damage, and Minimum Safe

Distances 764

Chapter 22 Advanced Trajectory Methods 767

22.1 Air-to-Surface Trajectory 76722.2 Unguided Weapon Trajectory Software (UWTS) 76722.3 Guided Weapon Trajectory Software (GWTS) 77022.4 GWTS Trajectory Mode 77222.5 GWTS Impact Mode 77522.6 GWTS Implementation in JWS 77722.7 Precision Munition Planning Tool (PMPT) 77722.8 Example Trajectory Model for Guided Weapons 78022.9 Surface-to-Surface Weapon Trajectory 787

Chapter 23 Ground Penetration 791

23.1 Introduction 79123.2 Penetration Modeling Using PC Effects Program 79123.3 Penetration Modeling Using PENCRV3D 79623.4 PENCRV3D Stress Equations 80023.5 Ricochet and Broach 80223.6 Advanced Bomb Burial 806

Chapter 24 Air Blast 811

24.1 Fundamentals of Air Blast 81124.2 Explosion Characteristics 81124.3 Characteristics of Air 81224.4 Shock Front 81324.5 Formation of the Blast Wave 81524.6 Explosive Yield 81624.7 Characteristics of the Blast Wave 81724.8 Shock-Wave Reflection 82424.9 Normal Air Shock-Wave Reflection 825

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24.10 Blast Characteristics—Attenuation with Distance 83024.11 External Blast Loading on Structures 83324.12 Dynamic Response of Structures

and Components 83724.13 Internal Blast Loading on Structures 84024.14 FACEDAP Program 84324.15 Engineering Models for Predicting

Blast Damage 84824.16 Blast Effects Against Materiel Targets 85124.17 Blast Lethal Miss Distance 85324.18 Joint Blast Analysis Methodology (JBAM) 860

Chapter 25 Tunnels 865

25.1 Introduction 86525.2 Overview of JWS Tunnel Weaponeering

Methodology 86525.3 Tunnel Crater Methodology 86825.4 Spall Crater Development 86925.5 Breach Crater Development 87825.6 Combined Spall and Breach Crater Formation 88025.7 Rubble Volume 88425.8 Craters on Nonplanar Surfaces 88625.9 Multiple Craters 88625.10 Air Blast in Tunnels 88725.11 Blast Door Vulnerability Model 88925.12 Damage Criteria for Tunnels 893

Chapter 26 Cratering 895

26.1 Introduction 89526.2 Treatment of Cylindrical Charges 89526.3 Crater Geometry and Definitions 89526.4 Detonations in Soil 89626.5 Surface Craters in Concrete 90026.6 Surface Craters in Concrete over Soil 90126.7 Ejecta 906

Chapter 27 Above-Ground Buildings and Bunkers 915

27.1 Introduction 91527.2 Overview of FIST Functionality 91827.3 Basic Building Structural Models 92027.4 Smart Target Model Generator for Buildings (STMG) 921

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27.5 Weapon Impact, Penetration, and Detonation 92427.6 Internal Detonations—Shock-Wave Path Length 92627.7 Structural Damage for Internal Detonations 92927.8 Flexural Failure due to Shock Loading 93127.9 Breach and Spall 93327.10 Flexural Failure due to Quasi-Static

Pressure (GPRS) 93827.11 Quasi-Static Pressures Outside the Blast Room 93927.12 External Bursts—Ground Shock 94127.13 External Bursts—Cratering and Breach 94227.14 Building Collapse 94527.15 Progressive or Disproportionate Collapse 94727.16 Structural Kill Metrics 94927.17 Functional Kill 95027.18 Equipment Damage 95127.19 Personnel Injury 95427.20 Bunkers and Hardened Targets 957

Chapter 28 Nonhomogeneous Targets 961

28.1 Introduction 96128.2 Target Description 96228.3 Attack Description 96328.4 Weapon–Target Interaction 96428.5 Target Shielding 96528.6 PK Calculations for All Weapon—Target Pairings 96628.7 Combining PD for Multiple Weapons 97128.8 Damage to the Complete Target—Disablement

Diagrams 97128.9 Monte Carlo Structure 97528.10 Summary of Methodology 977

Chapter 29 Bridge Targets 979

29.1 Introduction 97929.2 Bridge Components 98029.3 Bridge Types 98129.4 Damage Requirements for Defeating a Bridge Target 98429.5 Elementary Concepts in Structural Mechanics 98529.6 Bridge Design Codes and Standards 99029.7 Characteristic Dimensions in Structural Design 99229.8 Damage Mechanisms Involved in Collapsing a Span 99229.9 Fragment and Blast Loading of Structural Members 997

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29.10 Characterizing Failure Criteria 100229.11 Weapon Damage Model 100729.12 Overview of Structural Failure Prediction

Methodology 1008

Chapter 30 Collateral Damage Estimation 1011

30.1 Introduction 101130.2 Simple Collateral Damage Methodology 101230.3 Four-Tier Collateral Damage and Casualty Estimation

Methodology 101330.4 Collateral Damage Boundaries and Hazardous Areas 102030.5 Collateral Damage Estimates (CDE) Methodology 1022

Chapter 31 Antiair Weapon Effectiveness 1033

31.1 Introduction 103331.2 Joint Antiair Model (JAAM) 103331.3 General Model Description and Features 103631.4 Missile Model Description 103831.5 Aircraft Model Description 103931.6 Launch Acceptable Region (LAR) Generation 104131.7 Suite of Antiair Kill Chain Models and Data (SAK-MD) 104231.8 Aimpoints 104331.9 Delivery Accuracy 104331.10 Fuze Function 104531.11 Single-Fragment Probability of Kill 104731.12 Damage due to Fragments 105131.13 Damage due to Direct Hit 105531.14 Damage due to Blast 105631.15 Total Damage PK 1056

Chapter 32 Target Acquisition 1059

32.1 Introduction 105932.2 Experimental Contrast Thresholds for the Human Eye 106032.3 Overington Threshold Model 106432.4 Field Tests Detecting Military Targets 106832.5 Johnson’s Frequency–Domain Experiments 106932.6 ACQUIRE Target Acquisition Model 107332.7 Air-to-Surface Target Acquisition 107832.8 Flight Profile and Run–in Effects 107932.9 Terrain Model 108132.10 Detection Range RVIS 1084

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32.11 Conversion of Range to Probability of Launch 108632.12 Target Acquisition Tool 108932.13 Time-Dependent Target Detection—Search 1092

Appendix A Standard Statistical Tables 1095

Appendix B Derivation of Error Equations for Unguided,Surface-Launched Weapons 1099

B.1 Precision Error—PD/Proximity and Altitude Fuze 1099B.2 Precision Error—Time Fuze 1100B.3 MPI Errors for Predicted Fire—PD/Proximity and

Altitude Fuze 1101B.4 MPI Errors for Predicted Fire—Time Fuze 1104B.5 MPI Errors for Registration/Transfer Adjusted

Fire—PD/Proximity and Altitude Fuze 1106B.6 MPI Errors for Registration/Transfer Adjusted

Fire—Time Fuze 1113

Appendix C Weapon Selection Based on Target andDamage Criteria 1121

Index 1147

Supporting Materials 000

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