Louisiana State University LSU Digital Commons LSU Historical Dissertations and Theses Graduate School 1972 Air Armament Planning and Design Through Systems Analysis. John H. Arnold Louisiana State University and Agricultural & Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_disstheses Recommended Citation Arnold, John H., "Air Armament Planning and Design Through Systems Analysis." (1972). LSU Historical Dissertations and Theses. 2192. https://digitalcommons.lsu.edu/gradschool_disstheses/2192 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Historical Dissertations and Theses by an authorized administrator of LSU Digital Commons. For more information, please contact [email protected]. 72-28,326 ARNOLD, John H., 1938- AIR ARMAMENT PLANNING AND DESIGN THROUGH SYSTEMS ANALYSIS. The Louisiana State University and Agricultural and Mechanical College, Ph.D., 1972 Engineering, general University Microfilms, A XEROX Company, Ann Arbor, Michigan AIR ARMAMENT PLANNING AND DESIGN THROUGH SYSTEMS ANALYSIS A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Department of Mechanical, Aerospace and Industrial Engineering by John H. Arnold A.B., Mercer University, 1963 M.S.A.E., University of Notre Dame, 1966 May 1972 PLEASE NOTE: Some pages may have indistinct print. Filmed as received. University Microfilms, A Xerox Education Company ACKNOWLEDGEMENT The author would like to express his sincere appreciation to the Department of Mechanical, Aerospace and Industrial Engineering and to the Graduate School for their latitude in permitting the explora­ tion of a topic of interest to my employer, The United States Air Force Armament Laboratory. In particular, I owe my deepest gratitude to Dr. Robert W. Courter, without whose patience and awareness of relevance, the research could not have been accomplished; and to Dr. Phillip Bryant for his critical review of the statistical concepts and their applications to the physical problem. Also, the author wishes to thank Mr. T. P. Christie and William V. Chase of the Analysis Division, Air Force Armament Laboratory, Eglin Air Force Base, Florida for providing the empirical data used in developing the mathe­ matical models and, the numerically integrated solutions used for comparison to the closed form approximations developed during the course of these investigations. 11 TABLE OF CONTENTS Page ACKNOWLEDGEMENT..........................................11 LIST OF FIGURES............... .......................... vi LIST OF TABLES......................................... x ABSTRACT................................................ xi NOMENCLATURE............. .............................. xiii CHAPTERS I. INTRODUCTION TO THE PROBLEM OF PLANNING AND DESIGNING AIR ARMAMENT...................................... 1 A. Introductory Remarks........................... ^ B. Pattern of Employment of Tactical Air Forces...... 5 C. Target Vulnerability........................... 6 D. Concepts from Weapons Systems Analysis............ 7 1. Damage and Casualty Criteria................ 7 2. Mean Area of Effectiveness................... 10 3. Delivery Accuracy.......................... 10 4. Damage Probability...........................13 E. Concepts from Statistics.........................13 1. Poisson Distribution........................ 13 2. Bivariate Normal Distribution................ 14 3. Equivalent Circular Probable Error............ 16 II. OPTIMAL DAMAGE PROBABILITY AGAINST POINT TARGETS....... 20 A. Singly Delivered Weapons Against a Point Target.... 20 1. The Probability of Coverage, Conditional Damage and Probability of Damage Fuctions for Area Weapons............................ 20 ill Page 2. The Probability of Damage Function for Unitary Weapons............................. 3. Maximization of the Damage Functions......... 25 4. Optimum Cluster Weapons Versus Optimum Unitary Weapons............................. 29 B. Multiply Delivered Weapons Against a Point Target......................................... 35 1. The Probability of Coverage, Conditional Damage and Probability of Damage Functions for Multiply Delivered Area Weapons........... 35 2. The Probability of Coverage, Conditional Damage and Probability of Damage Functions for Multiply Delivered Unitary Weapons........ 39 3. Maximization of the Damage Functions..........39 4. Optimum Cluster Weapons Versus Optimum Unitary Weapons............................. 41 C. Single Massive Clusters Versus Multiply Delivered Small Clusters.■ 44 III. OPTIMUM DAMAGE PROBABILITY AGAINST AREA TARGETS....... 47 A. Singly Delivered Weapon Against an Area Target...... 47 1. The Probability of Fractional Coverage, Conditional Damage and Fractional Damage Functions for Area Weapons................... 47 2. The Probability of Fractional Coverage, Conditional Damage and Fractional Damage Functions for Unitary Weapons.................50 3. Maximization of the Damage Functions.......... 51 4. Optimum Cluster Weapons Versus Optimum Unitary Weapons............................. 54 B. Multiply Delivered Weapons Against an Area Target......................................... 55 1. The Probability of Fractional Coverage, Conditional Damage and Probability of Fractional Damage Functions for Area Weapons.................................... 55 iv Page 2. The Probability of Fractional Coverage, Conditional Damage and Probability of Fractional Damage Functions for Unitary Weapons ............................... 57 3. Maximization of the Damage Functions.......... 58 4. Optimum Cluster Weapons Versus Optimum Unitary Weapons............................. 61 IV. OPTIMUM DAMAGE PROBABILITY AGAINST TARGETS WITH LOCATION UNCERTAINTY............................... 64 V. SYSTEMS ANALYSIS AND DESIGN APPLICATIONS............. 66 A. Representative Systems and Targets............... 66 1. Systems Considered in the Analysis........... 66 2. Targets Considered in the Analysis............67 B. Point Targets Analyses.......................... 72 1. Area Weapons Analysis....................... 72 2. Unitary Weapons Analysis.................... 73 3. Cluster Weapons Versus Unitary Weapons........ 73 4. Weapons Design Characteristics and Employ­ ment Parametric 75 5. Multiple Weapons Employment.................. 94 C. Area Target Analyses............................ 118 VI. CONCLUSIONS AND RECOMMENDATIONS..................... 128 A. Conclusions.................................... 128 B. Recommendations................................ 132 SELECTED BIBLIOGRAPHY.................................... 134 APPENDIX: ANNULAR PATTERN METHODOLOGY.....................136 VITA ...................................................138 v LIST OF FIGURES Figure Page I-I Equivalent Circular Error Probable..............18 1-2 Parameters of the Circular Normal Distribution .. .19 2-1 Conditional Damage for a Single Area Munition ....23 2-2 Unitary M A E .................................. 33 2-3 Conditional Damage for Multiple Area Munitions... .37 3-1 Single Area or Single Unitary Munition Cover Function.....................................48 3-2 Multiple Area or Multiple Unitary Munition 59 Cover Function............................... 59 5-1 Single Weapon Probability of Damage - Weapon 1 vs Target 1................................. 76 5-2 Single Weapon Probability of Damage - Weapon 2 vs Target 1 ................................ 77 5-3 Single Weapon Probability of Damage - Weapon 4 vs Target 1 ................................ 78 5-4 Single Weapon Optimum Pattern Radii - Weapons 1, 2 and 4 vs Target 1 ........................ 79 5-5 Weapon Preference Parametric - Weapon 1 vs Group 1 vs Target 1 ........................... 80 5-6 Weapon Preference Parametric - Weapon 2 vs Group 1 vs Target 1............................81 5-7 Weapon Preference Parametric - Weapon 4 vs Group 1 vs Target 1............................82 5-8 Single Weapon Probability of Damage - Weapons 6,7, 8 and 9 vs Target 1............... 83 5-9 Single Weapon Probability of Damage - Weapon 1 vs Target 2...........................84 5-10 Single Weapon Probability of Damage - Weapon 2 vs Target 2........................... 85 5-11 Single Weapon Probability of Damage - Weapon 3 vs Target 2 .......................... 86 vi fjjure Page 5-12 Single Weapons Optimum Pattern Radii - Weapons 1, 2 and 3 vs Target 2..................87 5-13 Weapon Preference Parametric - Weapon 1 vs Group 1 vs Target 2 ........................ 88 5-14 Weapon Preference Parametric - Weapon 3 vs Group 1 vs Target 2 ........................ 89 5-15 Single Weapon Probability of Damage - Weapons 6, 7, 8 and 9 vs Target 2............... 90 5-16 Submunitions Parametric - Weapon 3 vs Target 2 .....................................91 5-17 Weapons Parametric - Weapon 3 vs Target 2 ...... 92 5-18 Weapons Parametric - Weapon 7 vs Target 2 ...... 93 5-19 Multiple Weapon Probability of Damage - Current vs Optimum - Weapons 6 and 9 vs Target 2 (4 Weapons in Pairs).................. 97 5-20a Multiple Weapon Probability of Damage - Weapons 6, 7, 8 and 9 vs Target 2 (4 Weapons in pairs)............................. 98 5-20b Multiple Weapon Probability of Damage - Weapons 6, 7, 8 and 9 vs Target 2 (4 Weapons in Salvo)............................. 99 5-21 Multiple Weapon Optimum Pattern Radii - Weapons