Combat Modeling (eBook)

Preface 6
Contents 7
Chapter 1 Generalities and Terminology 9
1.1 Introduction 9
1.2 Classification of Combat Models 10
1.3 Modeling Shortcuts 12
1.3.1 Expected Value Analysis 13
1.3.2 Universal Independence 14
1.3.3 Tuning Parameters 15
1.3.4 The Ostrich Effect 16
1.3.5 Convenient Distributions 17
1.4 Notation and Conventions 18
1.5 Book Overview 19
Chapter 2: Shooting without Feedback 19
Chapter 3: Shooting with Feedback 19
Chapter 4: Target Defense 19
Chapter 5: Attrition Models 19
Chapter 6: Game Theory and Wargames 20
Chapter 7: Search 20
Chapter 8: Mine Warfare 20
Chapter 9: Unmanned Aerial Vehicles 20
Chapter 10: Terror and Insurgency 21
Appendices 21
Chapter 2 Shooting Without Feedback 22
2.1 Introduction 22
2.2 Single-Shot Kill Probability 23
2.2.1 Damage Functions and Lethal Area 23
2.2.2 Cookie-Cutter Damage Function 24
2.2.3 Diffuse Gaussian (DG) Damage Function 27
2.2.4 Other Damage Functions 28
2.3 Multiple-Shot Kill Probability 29
2.3.1 Simultaneous Independent Shots 29
2.3.2 Salvos of Dependent Shots 32
2.3.3 The Diffuse Gaussian Special Case 38
2.3.4 Area Targets and Multiple Error Sources 40
2.4 Multiple Shots, Multiple Targets, One Salvo 42
2.4.1 Identical Shots, Identical Targets, Optimal Shooting 42
2.4.2 Identical Shots, Diverse Targets, Optimal Shooting 43
2.4.3 Diverse Shots, Diverse Targets, Optimal Shooting 44
2.4.4 Identical Shots, Identical Targets, Random Shooting 45
2.5 Further Reading 47
Chapter 3 Shooting with Feedback 53
3.1 Introduction 53
3.2 Feedback on the Status of a Single Target 54
3.3 Feedback on Miss Distances 55
3.4 Shoot Look Shoot with Multiple Targets 58
3.4.1 Identical Shots and Identical Targets with a Time Constraint 58
3.4.2 Variety of Shots and Targets, No Time Constraint 61
3.4.3 Variety of Shots and Targets, Unreliable Feedback 62
3.5 Further Reading 65
Chapter 4 Target Defense 71
4.1 Introduction 71
4.2 Defense of One Target Against Several Identical Attackers 72
4.2.1 Known Attack Size 72
4.2.2 Bayesian Defense 75
4.2.3 The Maximum Cost Defense Against a Shoot-Look-Shoot Attack 76
4.2.4 Prim–Read Defense 78
4.3 Defense of Multiple Targets Against ICBM Attack 79
Chapter 5 Attrition Models 85
5.1 Introduction 85
5.2 Deterministic Lanchester Models 85
5.3 Stochastic Lanchester Models 92
5.4 Data for Lanchester models 98
5.4.1 The Engineering Approach 98
5.4.2 The Statistical Approach 100
5.5 Aggregation and Valuation 104
5.6 The FAst THeater Model (FATHM) 106
5.6.1 FATHM’s Ground Model 107
5.6.2 FATHM’s Air Model 109
5.6.3 Implementation and Usage 110
Chapter 6 Game Theory and Wargames 116
6.1 Introduction 116
6.2 Game Theory 117
6.2.1 Matrix Games and Decision Theory 118
6.2.2 Tree Games and Saddle Points 123
6.2.3 Solvable Games 125
6.2.4 Information and Its Effects on Combat 129
6.3 Wargames 133
Chapter 7 Search 138
7.1 Introduction 138
7.2 Sweep Width 140
7.3 Three “Laws” for Detection Probability 142
7.3.1 Exhaustive Search 143
7.3.2 Random Search 144
7.3.3 The Inverse Cube Law 147
7.4 Barrier Patrol 148
7.5 Optimal Distribution of Effort for Stationary Targets 150
7.5.1 Discrete Effort 151
7.5.2 Continuous Effort 154
7.5.3 Search of a Bivariate Normal Prior 154
7.6 Moving Targets 156
7.6.1 Dynamic Enhancement 156
7.6.2 Markov Motion 158
7.6.3 Evasive Targets 161
7.7 Further Reading 163
Chapter 8 Mine Warfare 166
8.1 Introduction 166
8.2 Simple Minefield Models 167
8.3 The Uncountered Minefield Planning Model (UMPM) 168
8.4 Minefield Clearance 173
8.4.1 Are Clearance Forces Vulnerable? 175
8.4.2 Is Clearance Level a Sufficient Output? 176
8.4.3 Is Clearance a Sequential Process? 176
8.4.4 Are There Multiple Mine Types? 177
8.4.5 Are There Multiple Sweep Types? 177
8.4.6 Still More Questions 178
8.4.7 A Prototype Minesweeping Optimization Model:OptSweep 178
8.5 Mine Games 179
8.5.1 The Analytical Countered Minefield Planning Model (ACMPM) 180
8.5.2 Triangular Sweeping 181
8.5.3 IED Warfare 184
Chapter 9 Unmanned Aerial Vehicles 189
9.1 Introduction 189
9.2 Routing a UAV 190
9.2.1 Intelligence – Investigating an Object 191
9.2.2 Reconnaissance – Detecting a Mobile Target 197
A 198
9.3 Unmanned Combat Aerial Vehicles 202
9.3.1 Disposable UCAV 202
• 203
9.3.2 Retrievable Multiple-Weapon UCAV 208
9.4 Summary, Extensions and Further Reading 212
9.4.1 Optimizing the Employment of UAVs 212
9.4.2 Unmanned Combat Aerial Vehicles 213
Chapter 10 Terror and Insurgency 215
10.1 Introduction 215
10.2 The Effect of Suicide Bombing 216
10.2.1 Dispersion of Fragments 217
10.2.2 Modeling the Arena 219
k 220
10.2.3 The Effect of Crowd Blocking 221
10.2.4 Analysis 223
10.3 Response Policies for Bioterrorism – The Case of Smallpox 225
10.3.1 The Epidemic and Possible Interventions 226
10.3.2 A Model for Mass Vaccination 227
10.3.3 Numerical Example 229
10.4 Counterinsurgency 232
10.4.1 The Model 233
10.4.2 Numerical Example 235
Appendix A Probability – the Mathematics of Uncertainty 240
Appendix B Optimization 259
y = 261
x 261
x - v= 0 261
Appendix C Monte Carlo Simulation 265
Additional Reading 276