Baixe (MIL-HDBK-762) Design of Aerodynamically Stabilized Free Rockets - DoD e outras Manuais, Projetos, Pesquisas em PDF para Engenharia Aeroespacial, somente na Docsity! AMSC N/A MIL-HDBK-762(MI) 17 July 1990 MILITARY HANDBOOK DESIGN OF AERODYNAMICALLY STABILIZED FREE ROCKETS AREA GDRQ DISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited. MIL-HDBK-762(MI) F O R E W O R D 1. This military handbook is approved for use by the US Army Missile Command, Department of the Army, and is available for use by all Departments and Agencies of the Department of Defense. 2. Beneficaial comments (recoomendations, additions, deletions) and any pertinent data that may be of use in improving this document should be addressed to: Commander, US Army Missile Command, ATTN: AMSMI- RD-SE-TD-ST Redstone Arsenal, AL 35809, by using the self-addressed Standardization Document Improvement Proposal (DD Form 1426) appearing at the end of this document or by letter. 3. This handbook was developed under the auspices of the US Army Materiel Command's Engineering Design Handbook Program, which is under the direction of the US Army Management Engineering College. Research Triangle Institute was the prime contractor for the preparation of this handbook, which was prepared under Contract No. DAAG34-73-C-0051. ii MIL-HDBK-762(MI) CONTENTS (cont’d) Paragraph Page 2-5.1.3 Fabrication Drawings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-24 2-5.1.4 Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5.2 TESTING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-25 2-5.2.1 Types of Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5.2.2 Test Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-27 2-5.3 SYSTEM INTEGRATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-28 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..... 2-24 2-25 2-28 CHAPTER 3 PERFORMANCE 3-0 3-1 3-2 3-3 3-4 3-5 3-6 3-7 3-8 3-9 LIST OF SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PERFORMANCE PARAMETERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2.1 PERFORMANCE FACTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2.2 PROPULSION SYSTEM FACTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2.3 AERODYNAMIC CONSIDERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . APPROXIMATION TECHNIQUES AND APPLICABLE EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3.1 ESTIMATION OF VELOCITY REQUIREMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3.1.1 Indirect Fire Rockets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3.1.2 Direct Fire Rockets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3.1.3 Sounding Rockets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3.1.4 Surface-To-Air Rockets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3.1.5 Air-To-Surface Rockets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3.2 ESTIMATION OF ROCKET MOTOR REQUIREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3.3 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... PARAMETRIC PERFORMANCE DATA FOR INDIRECT FIRE SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-4.1 DELIVERY TECHNIQUES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-4.2 PARAMETRIC PERFORMANCE DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PARAMETRIC PERFORMANCE DATA FOR DIRECT-FIRE SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-5.1 DELIVERY TECHNIQUES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-5.2 PARAMETRIC PERFORMANCE DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PARAMETRIC PERFORMANCE DATA FOR SOUNDING ROCKETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6.1 DELIVERY TECHNIQUES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6.2 PARAMETRIC PERFORMANCE DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. PARAMETRIC PERFORMANCE DATA FOR SURFACE-TO-AIR ROCKETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-7.1 DELIVERY TECHNIQUES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-7.2 PARAMETRIC PERFORMANCE DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PARAMETRIC PERFORMANCE DATA FOR AIR-TO-GROUND ROCKETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-8.1 DELIVERY TECHNIQUES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-8.2 PARAMETRIC PERFORMANCE DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NUMERICAL EXAMPLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1 3-3 3-4 3-4 3-4 3-5 3-5 3-5 3-6 3-10 3-12 3-13 3-13 3-15 3-19 3-20 3-20 3-21 3-26 3-26 3-26 3-32 3-32 3-32 3-33 3-33 3-35 3-37 3-37 3-37 3-40 3-46 3-46 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... CHAPTER 4 ACCURACY 4-0 LIST OF SYMBOLS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1 4-4 v MIL-HDBK-762(MI) CONTENTS (cont’d) Paragraph Page 4-2 4-3 4-4 4-5 4-36 4-41 4-45 4-45 vi ERROR SOURCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-5 4-2.1 GENERAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-5 4-2.2 PRELAUNCH PHASE ERRORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-6 4-2.3 LAUNCH PHASE ERRORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2.4 BOOST PHASE ERRORS 4-7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-9 4-2.5 BALLISTIC PHASE ERRORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-11 EFFECTS OF ERROR SOURCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-14 4-3.1 GENERAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-14 4-3.2 PRELAUNCH PHASE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-17 4-3.3 LAUNCH PHASE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-17 4-3.4 BOOST PHASE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-22 4-3.5 BALLISTIC PHASE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-22 DISPERSION REDUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-24 4-4.1 GENERAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-24 4-4.2 THE EFFECT OF SPIN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-27 4-4.2.1 Constant Spin Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-31 4-4.2.2 Constant Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-34 4-4.2.3 Constant Deceleration —Slowly Uniformly Decreasing Spin (SUDS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-4.2.4 Spin-Buck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-38 4-4.2.5 Very High Spin Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-38 4-4.2-6 Spin Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-40 4-4.2.6.1 Helical Rails . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-40 4-4.2.6.2 Spin-on-Straight-Rail (SOSR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-40 4-4.2.6.3 Spin Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-40 4-4.2.6.4 Jet Vanes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-41 4-4.2.6.5 Canted Fins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-41 4-4.2.6.6 Spin Power Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-41 4-4.2.6.7 Prespin Automatic Dynamic Alignment (PADA). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-4.2.6.8 Autospin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-41 4-4.3 THE EFFECT OF ACCELERATION LEVEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-41 4-4.4 THE EFFECT OF AERODYNAMIC STABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-43 4-4.5 THE EFFECT OF LAUNCHER GUIDANCE LENGTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-4.6 PRELALINCH-PHASE DISPERSION REDUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-4.6.1 Launcher Location and Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-45 4-4.6.2 Target Location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-45 4-4.6.3 External Error Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-46 4-4.7 LAUNCH-PHASE DISPERSION REDUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-46 4-4.8 BOOST-PHASE DISPERSION REDUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-46 4-4.9 BALLISTIC-PHASE DISPERSION REDUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-47 ACCURACY COMPUTATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-48 4-5.1 GENERAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-48 4-5.2 SIX-DEGREE-OF-FREEDOM EQUATIONS OF MOTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-49 4-5.3 REDUCED DEGREE-OF-FREEDOM EQUATIONS OF MOTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-564-5.4 STATISTICAL METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5.4.1 Measures of Central Tendency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-56 4-5.4.2 Measures of Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-56 4-5.4.3 Measures of Dispersion for Several Error Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-58 4-5.4.4 Range and Deflection Probable Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-60 4-5.4.5 Probability of Hit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-61 4-5.5 ERROR BUDGET AND SAMPLE CALCULATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-62 4-5.5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-62 4-5.5.2 Example Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-62 4-49 MIL-HDBK-762(MI) CONTENTS (cont’d) Paragraph Page 4-5.5.2.1 Prelaunch Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5.5.2.2 Launch Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5.5.2.3 Boost Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5.5.2.4 Ballistic Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5.5.2.5 Additional Unit Effect Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5.5.2.6 Example Range Error Probable (REP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5.5.2.7 Example Deflection Error Probable (DEP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5.5.2.8 Example Circular Error Probable (CEP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5.5.2.9 Example Probability of Hit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-63 4-64 4-68 4-74 4-84 4-84 4-84 4-124 4-124 4-124 4-125 CHAPTER 5 AERODYNAMICS 5-0 LIST OF SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-2 GENERAL DESIGN CONSIDERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3 STATIC STABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3.1 BODIES OF REVOLUTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3.1.1 Nose-Cylinder Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3.1.2 Boattail Afterbody Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3.1.3 Oversized-Head Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3.1.4 Necked-Down Centerbody . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3.1.5 High-Fineness Ratio Body Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3.2 STABILIZING DEVICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3.2.1 Fins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3.2.1.1 Coplanar Fins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3.2.1.2 Wraparound Fins and Tangent Fins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3.2.1.3 Fin Roll Effectiveness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , 5-3.2.2 Flare-Type Afterbody . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3.3 RINGTAILS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3.4 STATIC STABILITY OF COMPLETE CONFIGURATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3.4.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3.4.2 Fin-Body Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3.4.3 Fin-Fin Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3.4.4 Stability Tailoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3.4.5 Sample Calculation Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3.5 ROCKET PLUME INTERACTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3.5.1 Definition of Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3.5.2 Effects on Aerodynamic Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1 5-7 5-7 5-9 5-10 5-11 5-12 5-13 5-13 5-13 5-14 5-14 5-14 5-16 5-17 5-17 5-18 5-19 5-19 5-22 5-24 5-26 5-28 5-28 5-28 5-38 5-39 5-40 5-41 5-41 5-42 5-43 5-43 5-43 5-43 5-44 5-3.5.3 Plume Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3.6 NONLINEAR AERODYNAMICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-4 DYNAMIC STABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-4.1 LONGITUDINAL DYNAMIC STABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-4.2 ROLL DYNAMICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-4.3 SIDE FORCES AND MOMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-4.3.1 Magnus Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-4.3.2 Other Side Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-5 DRAG COEFFICIENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 5-5.1 WAVE DRAG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii MIL-HDBK-762(MI) P a g e Paragraph 7-0 7-1 7-2 7-3 7-4 CONTENTS (cont’d) CHAPTER 7 STRUCTURES LIST OF SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..GENERAL MASS AND BALANCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-2.1 MASS AND CENTER-OF-GRAVITY ESTIMATION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-2.2 TRANSVERSE MOMENT OF INERTIA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-2.3 ROLL MOMENT OF INERTIA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LOAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-3.1 TRANSPORTATION AND HANDLING LOADS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-3.2 LAUNCH LOADS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-3.3 FLIGHT LOADS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . STRUCTURAL DESIGN ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.1 CONCEPTUAL DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2 PRELIMINARY DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.1 Structural Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.1.1 Motor Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.1.2 Nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.1.3 Propellant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.1.4 Payload . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.1.5 Payload Nose Fairing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.1.6 Fins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.2 Preliminary Load Estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.2.1 Mass Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.2.2 Moment of Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.2.3 Airloads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.2.2.4 Shear Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.2.5 Bending Moment Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.2.6 Axial Load Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.3 Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 7-7 7-7 7-9 7-9 7 - 2 2 7 - 2 2 7 - 2 2 7 - 2 5 7 - 2 5 7 - 2 5 7 - 2 9 7 - 2 9 7 - 2 9 7 - 2 9 7 - 2 9 7 - 3 1 7 - 3 2 7 - 3 6 7 - 3 6 7 - 3 7 7 - 3 8 7 - 3 9 7 - 3 9 7 - 4 2 7 - 4 6 7 - 4 7 7 - 4 8 7 - 4 8 7 - 4 9 7 - 5 3 7 - 5 3 7 - 5 6 7 - 5 6 7 - 5 9 7 - 5 9 7 - 6 0 7 - 6 1 7 - 6 2 7 - 6 4 7 - 6 6 7 - 6 8 7 - 7 0 7 - 7 0 7 - 7 2 7 - 7 2 7 - 7 3 7 - 7 7 7 - 7 7 7 - 7 7 7-4.2.3.1 7-4.2.3.2 7-4.2.3.3 7-4.2.3.4 7-4.2.3.5 7-4.2.3.6 Motor Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . End Closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Payload . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Propellant Grain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.4 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.4.1 Structural Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.4.2 Physical Properties of Structural Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.4.3 Manufacturing Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.4.4 Mass-Per-Cost Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.4.5 Propellants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.5 Safety Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.6 Mass and Size Estimating Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.6.1 Payload . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.6.2 Propellant Mass Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.6.3 Motor Sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.6.4 Motor Inert Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.2.6.5 System Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.3 STRUCTURAL MODELING FOR SYSTEM ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . .. . . 7-4.3.1 Load Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x MIL-HDBK-762(MI) CONTENTS (cont’d) Paragraph 7-4.3.2 Structural Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.3.2.1 Lumped Parameter Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4.3.2.2 Finite Element Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-5 DYNAMIC ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-6 AEROELASTICITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7 HEAT TRANSFER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7.2 THE ROLE OF HEAT TRANSFER ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7.3 PHYSICAL SITUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7.3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7.3.2 External Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7.3.3 Internal Heating (Case and Nozzle) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7.3.4 Exhaust Plume Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7.3.5 Propellant Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7.3.6 Heating Interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7.4 MECHANISMS OF THERMAL PROTECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7.5 MATERIALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7.5.1 Case Insulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7.5.2 Nozzle Insulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7.6 DESIGN REQUIREMENTS AND CONSTRAINTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7.7 APPROACH TO THERMAL ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7.8 ANALYTICAL TECHNIQUES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7.8.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 7-7.8.2 Nozzle Thermal Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7.8.3 Complex Analytical Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7.9 SAMPLE THERMAL DESIGN PROBLEM FOR AERODYNAMIC HEATING . . . . . . . . . . . . . . . . . . . . . . 7-7.9.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7.9.2 Aerodynamic Heating Calculations . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-8 STRUCTURAL TESTING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-9 OTHER STRUCTURAL CONSIDERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 7-77 7-77 7-82 7-84 7-84 7-86 7-86 7-86 7-87 7-87 7-87 7-87 7-93 7-93 7-94 7-94 7-94 7-95 7-95 7-96 7-97 7-98 7-98 7-98 7-99 7-99 7-99 7-102 7-106 7-108 7-108 CHAPTER 8 LAUNCHER CONSIDERATIONS 8-1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2 GENERAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2.1 LAUNCHER FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2.1.1 Environmental Protection and Conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2.1.2 Test and Checkout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2.1.3 Transportation . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2.1.4 Aiming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2.1.5 Ignition, Fuze Setting, and Arming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2.1.6 Initial Guidance and Spin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2.2 SYSTEM CONSTRAINTS ON LAUNCHER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2.3 LAUNCHER CONFIGURATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2.3.1 Tactical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2.3.2 Control of Aiming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2.3.3 Research Launchers . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2.3.4 Tip-Off vs Nontip-Off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2.3.5 Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-1 8-1 8-1 8-2 8-2 8-2 8-2 8-3 8-3 8-3 8-3 8-4 8-4 8-4 8-5 8-5 xi MIL-HDBK-762(MI) CONTENTS (cont’d) Paragraph 8-2.3.6 Types of Launchers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 8-2.3.7 Air-to-Ground Launchers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . 8-2.4 LAUNCHER ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 8-3 INTERFACE CONSIDERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-3.1 MECHANICAL INTERFACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-3.2 ELECTRICAL INTERFACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-3.3 CONTAINER LAUNCHERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . 8-3.4 ROCKET EXHAUST IMPINGEMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-3.4.1 Internal Exhaust Impingement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-3.4.2 External Exhaust Impingement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-3.5 ROCKET SPIN TECHNIQUES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-3.6 LAUNCHER GUIDANCE SCHEMES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-3.7 ROCKET FIN CONSIDERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-4 LAUNCH ACCURACY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . 8-4.1 MAJOR FACTORS AFFECTING LAUNCH ACCURACY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.2 LAUNCH ACCURACY ESTIMATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-4.3 MEASUREMENT OF LAUNCH ACCURACY 8-4.4 FLEXIBLE ROCKET EFFECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P a g e 8-5 8-10 8-10 8-13 8-13 8-14 8-15 8-16 8-16 8-17 8-17 8-18 8-18 8-20 8-20 8-20 8-21 8-22 8-23 8-24 APPENDIX A ATMOSPHERIC DATA A-0 LIST OF SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-2 ATMOSPHERIC PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-2.1 BASIC RELATIONSHIPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-2.2 SOURCES OF THERMODYNAMIC DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-2.2.1 US Standard Atmosphere, 1976 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-2.2.2 US Standard Atmosphere Supplements. 1966 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-2.2.3 Range Reference Atmosphere Documents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-2.2.4 Military Standard Climatic Extremes, MIL-STD-210 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-2.2.5 The NASA/MSFC Global Reference Atmoshere Model-Mod 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-2.2.6 Other Regional-Seasonal Atmospheric Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-3 WIND. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-3.1 WIND SPEED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-3.1.1 The Surface Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-3.1.2 The Boundary Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-3.1.3 The In-Flight Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-3.2 SOURCES OF WIND SPEED DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-3.3 WIND SHEAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-3.4 TURBULANCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-4 ENVIRONMENT TEST METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-1 A-2 A-2 A-2 A-3 A-3 A-4 A-4 A-5 A-5 A-7 A-7 A-7 A-7 A-8 A-8 A-8 A-8 A-9 A-9 A-9 APPENDIX B COMPUTER PROGRAMS B-1 DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B - 1 B-2 PROGRAMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B - 1 xii MIL-HDBK-762(MI) LIST OF ILLUSTRATIONS Figure No. Title Page 1-1 1-2 1-3 1-4 2-1 2-2 2-3 2-4 3-1 3-2 3-3 3-4 3-5 3-6 3-7 3-8 3-9 3-10 3-11 3-12 3-13 3-14 3-15 3-16 3-17 3-18 3-19 3-20 3-21 3-22 3-23 3-24 3-25 3-26 3-27 3-28 3-29 3-30 3-31 3-32 3-33 3-34 3-35 3-36 3-37 3-38 3-39 Examples of Midsize Free Flight Rockets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Examples of Small Free Flight Rockets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Examples of Large Free Flight Rockets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Typical Free Flight Rocket Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . System Design Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concept Selection Phase Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preliminary Design Phase Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . System Validation Phase Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Burnout Ballistic Coefficient and Burnout Velocity on Range—133-mm Rocket . . . Effect of Burnout Ballistic Coefficient and Burnout Velocity on Range—762-mm Rocket . . . Effect of Burnout Ballistic Coefficient and Burnout Velocity on Range—321-mm Rocket . . . Drag Coefficient vs Mach Number—130-mm Rocket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Drag Coefficient vs Mach Number—762-mm Rocket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Drag Coefficient vs Mach Number—321-mm Rocket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coast Drag Velocity Loss—130-mm Indirect Fire Rocket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Boost Drag Velocity Loss—Indirect Fire Rocket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Boost Drag Velocity Loss—Direct Fire Rocket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coast Drag Velocity Loss—Sounding Rocket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Boost Drag Velocity Loss—Sounding Rocket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coast Drag Velocity Loss—Surface-to-Air Rocket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Boost Drag Velocity Loss—Surface-to-Air Rocket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Ideal Burnout Velocity on Booster-Mass Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Growth Factor on Ideal Burnout Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Indirect Fire—Boost; Effect of Initial Acceleration Level on Optimum Launch Quadrant Elevation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Indirect Fire—Boost/Sustain; Effect of Impulse Ratio on Optimum Launch Quadrant Elevation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Indirect Fire—Boost; Effect of Range on Growth Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Boost/Sustain Engine; Variation of Specific Impulse with Thrust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Indirect Fire—Boost/Sustain; Effect of Range on Impulse Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Indirect Fire—Boost/Sustain; Effect of Range on Growth Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Indirect Fire—Boost; Effect of Propellant Mass Fraction on Growth Factor . . . . . . . . . . . . . . . . . . . . . . . . . . Indirect Fire—Boost; Effect of Ballistic Coefficient on Growth Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Direct Fire—Boost/Sustain; Effect of Impulse Ratio on Time to Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Direct Fire—Boost; Effect of Growth Factor on Time to Target for Various G Values . . . . . . . . Direct Fire—Boost; Effect of Ballistic Coefficient on Growth Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Direct Fire—Boost; Effect of Propellant Mass Fraction on Growth Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Burnout Ballistic Coefficient and Burnout Velocity on Summit Altitude-133-mm Rocket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sounding Rocket—Boost; Effect of Growth Factor on Summit Altitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sounding Rocket—Boost; Effect of Propellant Mass Fraction on Growth Factor- . . . . . . . . . . . . . . . . Sounding Rocket- Boost; Effect of Ballistic Coefficient on Growth Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . Surface to Air—Boost; Effect of Time to Altitude on Growth Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Surface to Air—Boost: Effect of Propellant Mass Fraction on Growth Factor . . . . . . . . . . . . . . . . . . . . . . . Surface to Air—Boost; Effect of Ballistic Coefficient on Growth Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Altitude and Flight Path Angle on Maximum Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Maximum Range on Growth Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Release Altitude and Flight Path Angle on Air-to-Ground Trajectory . . . . . . . . . . . . . . . . . . . . Air to Ground-Boost\ Sustain; Effect of Impulse Ratio on Time to Target . . . . . . . . . . . . . . . . . . . . . . . . . Air to Ground-Boost; Effect of Growth Factor on Time to Target for Various G Values . . . xv 1-2 1-3 1-5 1-6 2-2 2-4 2-8 2-23 3-6 3-6 3-7 3-8 3-9 3-10 3-11 3-12 3-13 3-14 3-15 3-16 3-17 3-18 3-20 3 - 2 2 3 - 2 2 3 - 2 3 3 - 2 3 3 - 2 4 3 - 2 4 3 - 2 5 3 - 2 5 3 - 2 7 3-28 3 - 3 1 3 - 3 1 3 - 3 2 3 - 3 3 3 - 3 4 3 - 3 4 3 - 3 5 3 - 3 6 3 - 3 6 3 - 3 7 3 - 3 8 3 - 3 9 3 - 4 0 3 - 4 1 MIL-HDBK-762(MI) DOD-HDBK-762(Ml) LIST OF ILLUSTRATIONS (cont’d) Figure No. Title Page 3-40 3-41 3-42 4-1 4-2 4-3 4-4 4-5 4-6 4-7 4-8 4-9 4-10 4-11 4-12 4-13 4-14 4-15 4-16 4-17 4-18 4-19 4-20 4-21 4-22 4-23 4-24 4-25 4-26 4-27 4-28 4-29 4-30 4-31 4-32 4-33 4-34 4-35 4-36 4-37 4-38 4-39 4-40 4-41 4-42 4-43 4-44 4-45 4-46 4-47 4-48 xvi Air to Ground-Boost; Effect of Ballistic Coefficient on Growth Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Air to Ground-Boost; Effect of Propellant Mass Fraction on Growth Factor . . . . . . . . . . . . . . . . . . . . . . Flow Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aiming Errors .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thrust Misalignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Static and Dynamic Imbalance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Thrust Misalignment on an Aerodynamically Stable Rocket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Wind on an Aerodynamically Stable Rocket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Static Margin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variation of Angular Dispersion and Wavelength of Yaw During Flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Wind on a Ballistic Free Rocket (After Burnout) (Top View) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definitions of Sign Conventions for Dispersion Equations of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Angular Dispersion Due to Initial Angular Rate for Various P Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Angular Dispersion Due to Initial Translational Velocity for Various P Values . . . . . . . . . . . . . . . . . Angular Dispersion Due to Wind for Various P Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Angular Dispersion Due to Thrust Misalignment for Various P Values—Zero Spin . . . . . . . . . . Optimum Wavelength of Yaw for Minimum Total Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Growth of Angular Dispersion For A Rocket With A Thrust Misalignment and No Spin . . . Growth of Angular Dispersion For A Rocket With A Thrust Misalignment and Slow Spin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Spin on Buildup of Angular Dispersion Due to Thrust Misalignment . . . . . . . . . . . . . . . . . Effect of Constant Spin on Dispersion Reduction Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Constant Spin Rate; Various P Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Constant Spin Acceleration; Various P Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Slowly Uniformly Decreasing Spin (SUDS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Wavelength of Yaw on Buck Distance for Zero Angular Dispersion . . . . . . . . . . . . . . . . . . . . . . . . Effect of Buck Distance on Dispersion Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Static Margin on A Rocket With Thrust Misalignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Static Margin on Wind Disturbance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Inertial Coordinate System and Body-Centered Coordinate System for a Free Rocket . . . Positive Sign Conventions of the Six-DOF-Equations of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ratio of CEP to óy/óx for Elliptical Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ratio of CEP to óx for Elliptical Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variation of Range Error Probable With Range-Impact Fuze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variation of Deflection Error Probable With Range-Impact Fuze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variation of CEP With Range-Impact Fuze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Initial Velocity vs Maximum Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit Effect, Range/Departure Angle vs R/Rmax for Various B Values-Impact Fuze . . . . . . . . . . . . Unit Effect, Range Velocity vs R/Rmax, for Various B Values-Impact Fuze . . . . . . . . . . . . . . . . . . . . . . . . . . Unit Effect, Range, Density vs R/Rmax for Various B Values-Impact Fuze . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit Effect, Range/Wind vs R\Rmax for Various B Values-Impact Fuze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit Effect, Deflection/Wind vs R/Rmax for Various B Values-Impact Fuze . . . . . . . . . . . . . . . . . . . . . . . . QE vs R/Rmax for Various B Values-Impact Fuze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Time of Flight vs R/Rmax for Various B Values-Impact Fuze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . QE vs R/Rmax for Various B Values-Time Fuze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Time of Flight vs R/Rmax for Various B Values—Time Fuze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit Effect, Range/Density vs R/Rmax for Various B Values-Time Fuze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit Effect, Range Velocity vs R/Rmax for Various B Values-Time Fuze . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit Effect, Range/Wind vs R/Rmax, for Various B Values-Time Fuze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit Effect, Range/Departure Angle vs R/Rmax for Various B Values—Time Fuze . . . . . . . . . . . . . Unit Effect, Deflection/Wind vs R/Rmax for Various B Values—Time Fuze . . . . . . . . . . . . . . . . . . . . . . . . . . Unit Effect, Altitude/Density vs R/Rmax for Various B Values—Time Fuze . . . . . . . . . . . . . . . . 3 - 4 2 3 - 4 2 3 - 4 4 4-6 4-8 4-8 4-9 4 - 1 0 4 - 1 1 4 - 1 2 4 - 1 3 4 - 1 5 4 - 1 8 4 - 2 0 4 - 2 3 4 - 2 6 4 - 2 8 4 - 2 8 4 - 2 8 4 - 2 9 4 - 3 1 4 - 3 2 4 - 3 5 4 - 3 7 4 - 3 9 4 - 3 9 4 - 4 4 4 - 4 4 4 - 5 0 4 - 5 0 4 - 5 9 4 - 6 0 4 - 6 1 4 - 6 1 4 - 6 4 4 - 6 5 4 - 7 1 4 - 7 5 4 - 7 8 4 - 8 1 4 - 8 5 4 - 8 8 4 - 9 1 4 - 9 4 4 - 9 7 4 - 1 0 0 4 - 1 0 3 4 - 1 0 6 4 - 1 0 9 4 - 1 1 2 MIL-HDBK-762(MI) LIST OF ILLUSTRATIONS (cont’d) Figure No. Title Page 4-49 4-50 4-51 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 5-15 5-16 5-17 5-18 5-19 5-20 5-21 5-22 5-23 5-24 5-25 5-26 5-27 5-28 5-29 5-30 5-31 5-32 5-33 5-34 C N, Cm a n d vs Total Fineness Ratio Afterbody Lengths . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit Effect, Altitude/Velocity vs R/Rmax for Various B Values—Time Fuze . . . . . . . . . . . . . . . . . . . . . . . . . Unit Effect, Range/Time vs R/Rmax for Various B Values—Time Fuze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit Effect, Altitude/Time vs R/Rmax for Various B Values—Time Fuze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rocket Axes—Showing Direction and Sense of Forces, Moments, and Angular Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Normal Force Coefficient Gradient for Tangent Ogive-Cylinder Configurations . . . . . . . . . . . . . . .. Center of Pressure for Tangent Ogive-Cylinder Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Normal Force Coefficient Gradient for Cone-Cylinder Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Center of Pressure for Cone-Cylinder Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Normal Force Coefficient Gradient and Center of Pressure—4-cal Tangent Ogive With Varying Afterbody Lengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Normal Force Coefficient Gradient and Center of Pressure—7.125-deg Cone With Varying Afterbody Lengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Normal Force Coefficient Gradient and Center of Pressure—l/2-Power Nose With Varying Normal Force Coefficient Gradient and Center of Pressure—Varying Tangent Ogive Nose Lengths With Constant Afterbody Length of 6 cal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Normal Force Coefficient Gradient and Center of Pressure—Varying Conical Nose Angle With Constant Afterbody Length of 6 cal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Normal Force Coefficient Gradient and Center of Pressure—Varying n-Power Nose Shape With Constant Afterbody Length of 6 cal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variation of Normal Force Coefficient Gradient and Center of Pressure vs Mach Number for 2-cal Ogive Cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variation of Normal Force Curve Gradient and Center of Pressure vs Mach Number for 3- cal Ogive Cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Nose Blunting of a 4-cal Ogive on Normal Force Coefficient Gradient and Center of Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Some Aerodynamic Characteristics of a Spike-Nosed Rocket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Boattail Normal Force Correlation Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ratio of Boattail Center of Pressure to Boattail Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Afterbody Diameter to Head Diameter Ratio on Aerodynamic Parameters . . . . . . . . . . . . . Normal Force Coefficient Gradient vs Boattail Length to Afterbody Diameter Ratio at 2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Center of Pressure vs Boattail Length to Afterbody Diameter Ratio at 2.2 . . . . . . . . . Rocket With Necked-Down Center Body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aerodynamic Characteristics of Necked-Down Center Body With and Without Shroud . . . . . . Normal Force Coefficient Gradient and Center of Pressure Over Rocket Diameter Ratio vs Mach Number for Family of Nose-Cylinder Configurations—4-cal Nose . . . . . . . . . . . . . . . . . . . . . . . . . . . . Normal Force Coefficient Gradient and Center of Pressure Over Rocket Diameter vs Mach Number for Family of Nose Cylinder Configurations-3-cal Tangent Ogive Nose . . . . . . . . . . . . Typical Free Rocket Stabilizing Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nomenclature of Some Typical Rocket Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Illustration of Exposed Fin-Body and Isolated Wing Geometry, and Accompanying Nota- tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Subsonic Fin Normal Force Coefficient Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary Curves of the Generalized Normal Force Gradient for Electangular Fins at Tran- sonic Speeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Center of Pressure for Rectangular Fins at Transonic Speeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Linear Theory Normal Force Gradient of Rectangular Fins vs Mach Number . . . . . . . . . . . . . . . . . . . . . Linear Theory Normal Force Gradient of Delta Fins vs Mach Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-115 4-118 4-121 5-81 5-81 5-82 5-82 5-83 5-83 5-84 5-85 5-86 5-87 5-88 5-89 5-90 5-91 5-92 5-93 5-94 5-95 5-96 5-97 5-98 5-98 5-99 5-99 5-100 5-101 5-101 5-103 5-103 5-104 5-104 5-105 5-105 5-106 xvii MIL-HDBK-762(MI) DOD-HDBK-762(MI) LIST OF ILLUSTRATIONS (cont’d) Figure No. Title Page 5-113 5-114 5-115 5-116 5-117 5-118 5-119 5-120 5-121 5-122 5-123 5-124 5-125 5-126 5-127 5-128 5-129 5-130 5-131 5-132 5-133 5-134 5-135 5-136 5-137 5-138 5-139 5-140 5-141 5-142 5-143 5-144 5-145 5-146 5-147 5-148 5-149 5-150 5-151 5-152 xx Wave-Drag Coefficient of Slender Ogives at Transonic Speeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wave-Drag Coefficient of Cones and Ogives at Supersonic Speeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sketch Depicting Development of Tangent Ogive (2 cal in this case) and “Given” Ogive . . . . Profiles of Nose Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wave Drag of Secant Ogives in Terms of Ogive Radius for Several Mach Numbers and Nose Fineness Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Percent Change in Drag Coefficient vs Me’plat Diameter (Flat unless otherwise indicated) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zero Lift Dragon Three Special Nose Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variance of Boattail Base Diameter on Total Drag vs for Complete Body Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Subsonic/Transonic Boattail Wave Drag vs Mach Number for Various Length-to-Diameter Ratios . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wave-Drag Coefficient of Conical Boattails at Supersonic Speeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wave-Drag Coefficient of Parabolic Boattails at Supersonic Speeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wave-Drag Coefficient of Conical Flare at Various Mach Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Drag of Slender Conical Afterbodies or Forebodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sketch Showing Diameters to be Used in Eq. 5-39. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison of Drag of Flare, Split Flare, and Split Flare With Shroud . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wave-Drag Coefficient of Fins at Supersonic Speeds for Parabolic Arc and Double-Wedge Shapes for Various ct/cr Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wave-Drag Coefficient of Fins of Various Sectional Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wave-Drag Coefficient of Rectangular Fins at Subsonic and Transonic Speeds . . . . . . . . . . . . . . . . Wave-Drag Coefficient of Delta Fins at Subsonic and Transonic Speeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wave-Drag Coefficient of a Double-Wedge Fin at Transonic Speeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Internal Expansion Angle and Longitudinal Positioning E/d on Ringtail Drag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flat Plate Average Skin-Friction Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reynolds Number as a Function of Flight Mach Number and Altitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Typical Variation of Base Pressure With Thrust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Base Flow Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measured and Correlated Base Pressure for Several Configurations, = 1.5 and 2.0, Turbulent Boundary Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Base Pressure Coefficient for Finless Bodies of Revolution in Terms of Local Pressure and Local Mach Number Ahead of Base, Effects of Mach Number and Reynolds Number on Base Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cylinder to Boattail Base Pressure Ratio as a Function of Base Area Ratio (Power-Off) . . . . . Effect of Boattailed and Flared Afterbodies on Jet-Off Pressures (Flare data were obtained at free-stream Mach numbers of 1.65 and 2.21. ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plume-Off Boattail and Flare Base Pressure Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variation of Conical Boattail Wave and Base Drag With Base Diameter to Cylinder Diameter Ratio . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Base Pressure for Various Split Petal Configurations (Jet-Off) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Rocket Jet Plume on Base Pressure at = 2.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . Base Pressure Variation With Jet Momentum Flux Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Conical Afterbody Geometry on Base Pressure Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effects of Nozzle Position on Base Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Base Pressure Variation With Thrust for Cylindrical Afterbody With Nozzle Flush With . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Multiple Nozzles on Base Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison of Two-Dimensional Base Pressures From Upper Vertical Fin of X-15 Airplane With Theory . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 - 1 7 9 5 - 1 8 0 5 - 1 8 1 5 - 1 8 2 5 - 1 8 2 5 - 1 8 3 5 - 1 8 4 5 - 1 8 5 5 - 1 8 6 5 - 1 8 7 5 - 1 8 7 5 - 1 8 8 5 - 1 9 1 5 - 1 9 1 5 - 1 9 2 5 - 1 9 3 5 - 2 0 1 5 - 2 0 2 5 - 2 0 2 5 - 2 0 3 5 - 2 0 4 5 - 2 0 5 5 - 2 0 5 5 - 2 0 6 5 - 2 0 6 5 - 2 0 7 5 - 2 0 8 5 - 2 0 9 5 - 2 1 0 5 - 2 1 0 5 - 2 1 1 5 - 2 1 2 5 - 2 1 3 5 - 2 1 4 5 - 2 1 4 5 - 2 1 5 5 - 2 1 7 5 - 2 1 8 5 - 2 1 9 5 - 2 2 0 MIL-HDBK-762(MI) LIST OF ILLUSTRATIONS (cont’d) Figure No. 5-153 5-154 5-155 5-156 5-157 With Cylindrical Afterbody at 5-158 5-159 5-160 5-161 5-162 5-163 5-164 5-165 6-1 6-2 6-3 6-4 6-5 Page 5 - 2 2 1 5 - 2 2 2 5 - 2 2 3 5 - 2 2 5 5 - 2 2 6 5 - 2 2 7 5 - 2 2 8 5 - 2 2 9 5 - 2 3 0 5 - 2 3 0 5 - 2 3 1 5 - 2 3 2 5 - 2 3 2 6-7 6 - 1 4 6 - 1 6 6 - 1 8 6 - 2 0 6 - 2 1 6 - 2 1 6 - 2 2 6 - 2 2 6 - 2 7 6 - 2 9 6 - 3 0 6 - 3 1 6 - 3 3 6 - 3 7 6 - 4 0 6 - 4 1 7-8 7 - 1 2 7 - 1 5 7 - 1 6 7 - 1 7 7 - 1 8 7 - 1 9 7 - 2 0 7 - 2 1 7 - 2 3 7 - 2 4 6-6 6-7 6-8 6-9 6-10 6-11 6-12 Comparison ol Lengths ov Various Types of Nozzle for 6-13 6-14 6-15 6-16 6-17 7-1 7-2 7-3 7-4 7-5 7-6 7-7 7-8 7-9 7-10 7-11 Title Base Pressure Coefficient of Fins at Transonic Speeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Ringtail Longitudinal Location on Base Pressure Characteristics of Body Revolution Having a dj/d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Configuration and Design Parameters for Sample Drag Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sample Total and Component Drag Coefficients vs Mach Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Local Normal Force Coefficient Gradient Ratio Distribution for Tangent Ogive = 2.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Distributed Normal Force Coefficient Gradient on Cone-Cylinder, Cone- Cylinder-Boattail, and Cone-Cylinder-Flare Configurations at = 2.0 . . . . . . . . . . . . . Distribution of Local Axial Force Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Distribution of Local Pressure Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Axial Force Distributions on Conical Flare and Boattail Following a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison of Test Results on Full-Size and Scale Model Artillery Rocket . . . . . . . . . . . . . . . . . . . . . . . . . . Relationship Between Maximum Allowable Model Dimensions and Test Section Dimension in Tunnel A and 12X12-in. Tunnel at Von Karman Gas Dynamics Facility at Arnold Engineering Center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aerodynamic Force Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Typical Normal Jet Plume Simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Case Bonded Solid Propellant Rocket Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Motor Performance and Temperature Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two Basic Types of Nozzles Employed in Rocket Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Area Ratio Ax/A* for Complete Expansion as a Function of the Nozzle Pressure Ratio pc/px for Different Values of = cp/cv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pressure Distributions in a Converging-Diverging Nozzle Under Different Operating Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design Thrust Ratio as Function of Nozzle Divergence Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic Cross Sections of Plug and Expansion-Deflection Nozzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Off-Design Thrust Coefficients of Conventional and Plug Nozzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Grain Asymmetries Considered . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flow Chart of Motor Design Sequence Showing Major Iteration Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Specific Impulse Parameter as a Function of Pressure Ratio for Different Specific Heat Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Typical Characteristic Curves for a Solid Propellant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Influence of Pressure and Gas Flow Velocity on Burning Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Typical Variation of Erosive Constant With Burning Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Illustration of Basic Nozzle Configurations and Nozzle Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nozzle for PERSHING First Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Analysis Cycle for Free Flight Rockets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Illustration of Symbols Used in Nose Shape Defining Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Volume of Nose Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ratio of Secant Ogive Volumes to Cone Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ratio of Ogival Volumes to Cone Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Surface Area of Nose Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ratio of Secant Ogive Surface Areas to Cone Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ratio of Ogival Surface Areas to Cone Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CG Location of Ogival Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Secant Ogive Pitch Inertia vs Fineness Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Secant Ogive Roll Inertia vs Fineness Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi MIL-HDBK-762(MI) Page Figure No. 7-12 7-13 7-14 7-15 7-16 7-17 7-18 7-19 7-20 7-21 7-22 7-23 7-24 7-25 7-26 7-27 7-28 7-29 7-30 7-31 7-32 7-33 7-34 7-35 7-36 7-37 7-38 7-39 7-40 7-41 7-42 7-43 7-44 7-45 7-46 7-47 7-48 7-49 7-50 7-51 7-52 7-53 7-54 7-55 7-56 7-57 7-58 7-59 7-60 LIST OF ILLUSTRATIONS (cont’d) Title Axial Loads on Free Flight Rocket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Circumferential Loads on Motor Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concentrated Loads on Free Flight Rockets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nozzle Structural Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Representative Solid Propellant Grain Geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Payload Structure Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Payload Nose Fairing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thin-Plate Fin Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Superposed Shear Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Methods of Mass Distribution Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coordinates for Moment-of-Inertia CalCulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lumped Mass Model of a Typical Rocket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Compontents of Total Normal Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example Problem to Illustrate Shears and Bending Moments on a Typical Rocket . . . . . . . . . . . . Shear Load Diagram for Inertial Load Sample Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bending Moment Diagram for Inertial Load Sample Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Typical Axial Load Diagram During Powered Flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Motor Case Discontinuity Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Motor Case Thermally Induced Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Filament Wound Motor Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Modeling Y-Ring Structure by Shell Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Geometry of Plane-Strain Analysis Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fin and Airload .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fin Shear Carrying Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Equivalent Two-Flange Beam Fin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Relative Motor Case Cost vs Case Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Relaxation Modulus Spectrum for a Typical Double-Base Propellant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Probability of Kill vs Warhead Diameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Propellant Volumetric Loading Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Propellant Mass vs Motor Case Fineness Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rocket Sizing Trade-Off Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Degrees of Freedom in Local Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two-Mass Rocket Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Beam Displacement Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finite Element Mode] of a Typical Nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnified (50X) Deformed Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Maximum Shear Stress Contours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hoop Stress Contours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Maximum Principal Stress Contours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Minimum Principal Stress Contours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Typical Motor Case Wall Heating Before and After Propellant Is Consumed Adjacent to Case Wall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Physical Situation for Sacrificial Ablative Insulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Motor Case Internal Heat Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nozzle Internal Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Analysis Procedure Flowchart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sketch of a Hypothetical Free Flight Rocket Showing Geometry Pertinent to External Heating . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ballistic Trajectory Input for Aerodynamic Heating Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Heat Transfer Output From Aerodynamic Heating Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hot Wall Heat Flux and Motor Case Temperature Calculated From Aerodynamic Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 - 2 6 7 - 2 7 7 - 2 8 7 - 3 1 7 - 3 2 7 - 3 6 7 - 3 7 7 - 3 7 7 - 3 9 7 - 4 0 7 - 4 1 7 - 4 1 7 - 4 3 7 - 4 5 7 - 4 7 7 - 4 8 7 - 4 9 7 - 5 0 7 - 5 2 7 - 5 2 7 - 5 3 7 - 5 5 7 - 5 7 7 - 5 8 7 - 5 8 7 - 6 5 7 - 6 7 7 - 7 1 7 - 7 2 7 - 7 4 7 - 7 5 7 - 7 8 7 - 7 9 7 - 7 9 7 - 8 3 7 - 8 3 7 - 8 5 7 - 8 5 7 - 8 5 7 - 8 5 7 - 8 8 7 - 8 9 7 - 9 0 7 - 9 1 7 - 1 0 0 7 - 1 0 1 7 - 1 0 3 7 - 1 0 4 7 - 1 0 5 xxii 0938-9, RTI, File 0938-01B, Disk 838, A-Times Roman, C-Times Roman Math, JHP MIL-HDBK-762(MI) LIST OF ABBREVIATIONS AND ACRONYMS AFRPL = Air Force Rocket Propulsion Laboratory AP = ammonium perchlorate ARDC = Air Research and Development Command BF = biaxial improvement factors c a l = c a l i b e r s CEP = circular error probable CG = center of gravity CI = configuration item COESA = Committee on Extension of the Standard Atmosphere COSPAR = Committee on Space Research CP = center of pressure = circular port CTPB = carboxy terminated polybutadiene DEP = deflection error probable DoD = Department of Defense DOF = degrees of freedom FAMAS = Field Artillery Meteorological Acquisition System FE = finite element FS = factor of safety HEAT = high explosive antitank HTPB = hydroxyl-terminated polybutadiene IR = in f rared IRIG = Inter-Range Instrumentation Group JMSNS = Justification of Major System New Starts KP = potassium perchlorate LOA = Letter of Agreement MEOP = maximum expected operational pressure MHX = cyclotetramethylene tetranitramine MIL-STD = Military Standard MLRS = Multiple Launch Rocket System MOC = method of characteristics MS = margin of safety MSFC = Marshall Space Flight Center NASA = National Aeronautics and Space Administration NC = cellulose hexanitrate NG = glycerol trinitrate PADA = prespin automatic dynamic alignment PBAA = butadiene acrylic acid copolymers PE = probable error QE = quadrant elevation RDX = cyclotrimethylene trinitramine REP = range error probable ROC = Required Operational Capability rps = revolutions per second SOSR = spin on straight rail SUDS = slowly uniformly decreasing spin TE = trailing edge TMO = transition metal oxide WAF = wraparound fins xxv MIL-HDBK-762(MI) C H A P T E R 1 I N T R O D U C T I O N This chapter introduces the handbook. Rocket systems are presented in two broad classes: military rocket systems and research rocket systems. Military rocket systems are discussed in terms of their application in a battle environment. Research rocket systems are discussed in terms of the application to provide the means of placing data gathering equipment into a desired environment. Operational modes for the rocket systems are described. Finally, brief descriptions of the remaining chapters and the appendices are given. 1 - 1 P U R P O S E O F H A N D B O O K Aerodynamically stabilized free rockets offer relatively simple, reliable, small, low-cost means for delivering payloads and, when great accuracy is not required, are often the optimum systems. This handbook provides engineering design information and data for such rockets. Primarily, this hand- book is intended to cover the conceptual and preliminary design phases; however, reference is made to the technical approaches and computer programs required for the system development phase. The material includes operational and interface requirements as they influence the design of the total wea- pon system. The handbook provides 1. The preliminary design engineer with specific design information and data useful in the rapid response situations required of preliminary design activities 2. The specialist in each technical area an introduction to the other disciplines in terms of data requirements and trade-off studies that must be performed. Free flight rockets are those rockets that do not have an in-flight guidance system; they are aimed, guided, or directed by the launching device. These launchers usually have a launching rail or tube to provide initial direction to the rocket. Free flight rockets are of two basic kinds—spin stabilized and aerodynamically stabilized. The spin stabilized rocket, as the name implies, depends upon a high rate of spin and resulting gyroscopic moments to oppose disturbances. The aerodynamically stabilized rocket depends upon aerodynamic forces on the body and fins to oppose disturbing forces. The aero- dynamically stabilized rocket generally employs some spin to minimize dispersion caused by nonsym- metrical body characteristics (body asymmetries, fin misalignment, thrust misalignment, etc.). The data and concepts presented in this handbook are limited to aerodynamically stabilized free flight rockets. 1 - 2 C L A S S E S O F F R E E F L I G H T R O C K E T S For the purposes of this handbook, rockets are discussed as either military rocket systems or research rocket systems. 1-2 .1 MILITARY ROCKET SYSTEMS 1-2.1.1 General In general, military rockets are used to deliver some form of destructive warhead or other military payload such as smoke canisters or electronic beacons to a target. There are some exceptions, which will be discussed as logistic rockets. The types of military rockets most frequently used are described in the paragraphs that follow. 1-2.1.2 Field Artillery Field artillery rocket systems are used in the same manner as artillery gun systems. They have 1-1 MIL-HDBK-762(MI) 1 - 2 . 2 R E S E A R C H R O C K E T S Y S T E M S 1 - 2 . 2 . 1 G e n e r a l Research rockets have the same general group of components as military rocket systems; the notable difference is the payload. Research rockets usually are designed to accomplish a mission from which technical data will be obtained. The purpose of the data is to further the understanding of some scientific discipline or phenomena. In this role, the payload becomes a device to gather data. Evalua- tion of the gathered data is often done at a later date. It may be necessary to recover the payload, thereby making a recovery system necessary. Means to prevent payload damage or destruction must be designed into the rocket system. 1-2.2.2 Meteorological Aerodynamically stabilized free flight rocket systems are used to place sensing devices at various altitudes. Data providing information about the air, winds, temperature, radiation, and atmospheric moisture content of the Earth and other phenomena are obtained for use by the researcher. An example of a meteorological rocket is the WASP shown in Fig. 1-1. 1-2.2.3 High-Altitude Sounding High-altitude sounding rockets are used to obtain specific information at altitudes ranging to several hundred miles above the surface of the Earth. These rocket systems and most meteorological rocket systems fly near vertical trajectories. The principal design goal for this type rocket is efficient attain- ment of altitude. The BLUE SCOUT JR. rocket shown in Fig. 1-3 is an example of a high-altitude sounding rocket. 1-2.2 .4 Satell i tes Aerodynamically stabilized free flight rockets may be- used to place a payload into Earth orbit. Rocket systems capable of placing a payload in orbit are usually multistage. Design and analysis of multistage rocket systems are not addressed in this handbook. The first stage and perhaps the second stage operate as unguided free rockets. The later stages are guided to permit maneuvering to attain the desired orbital path. The unguided phase of flight places the vehicle at some altitude from which the orbital phase can be initiated. The use of unguided rocket systems for the lower phases of flight can result in considerable savings in guidance hardware when very precise positioning is not required. The SCOUT shown in Fig. 1-3 is an example of a rocket capable of placing a satellite into orbit. 1-2.2.5 Dispensing Dispensing rocket systems dispense materials—either for research or military purposes-at some point in the trajectory of the rocket. Examples are chaff-dispensing rockets, leaflet-dispensing rockets, smoke-dispensing rockets, and rockets to disseminate crystals of various substances for cloud seeding to induce rain. The chaff dispensers are used to put large quantities of very small metallic wires or strips in an area at some height above the ground. Leaflet rockets are used to deliver propaganda leaflets to areas not accessible from the ground. Although not in general use, cloud seeding rockets have been proposed, e.g., a rocket to dispense small pellets of dry ice into fog banks for fog removal over airports and similar areas. The rocket offers the advantage of delivering materials quickly, and its intrusion cannot be easily detected. The LOBBER shown in Fig. 1-1 can be used as a dispensing rocket. 1 - 3 O P E R A T I O N A L M O D E S 1 - 3 . 1 G E N E R A L Aerodynamically stabilized free flight rockets may be designed for use in a number of ways. It is not the purpose of this handbook to discuss all the uses of rockets, but to present the most common uses of military systems. Accordingly, the paragraphs that follow will briefly describe the modes normally used for military rocket systems. Classification by operational mode is normal military practice and also provides a useful alternative and supplement to the classifications used in par. 1-2. 1-4 MIL-HDBK-762(MI) Figure l-3. Examples of Large Free Flight Rockets 1 - 3 . 2 S U R F A C E T O S U R F A C E Surface-to-surface aerodynamically stabilized free flight rockets are launched from a point on the surface of the Earth to a target also on the surface. Most artillery, infantry, and armor rocket systems are used in this mode. They can range from small shoulder-fired rocket systems to large rockets fired from launchers requiring heavy transport equipment. 1 - 3 . 3 S U R F A C E T O A I R Surface-to-air rockets are usually employed in the defense of ground troops or equipment. The rocket is launched from the surface against an airborne target—e.g., a manned aircraft, an unmanned drone, another rocket or missile, or simply a point in space. Air defense, meteorological, high-altitude sounding, and dispensing rocket systems operate in this mode. 1 - 3 . 4 A I R T O S U R F A C E Air-to-surface rocket systems are used for suppressive fire over areas and to deny the enemy a specific position. Air-to-surface rockets are fired from fixed-wing or rotary-wing aircraft, usually from low altitudes because of accuracy limitations, and usually are relatively short range. 1 - 3 . 5 U N D E R W A T E R L A U N C H Rocket systems have been built to be fired from beneath the water and to continue flight after emerging into the atmosphere. The design considerations after entry into the atmosphere are similar to any other atmospheric rocket. This handbook will only address the atmospheric phase of rocket flight. 1 - 5 MIL-HDBK-762(MI) 1 -3 .6 SURFACE OR AIR TO UNDERWATER These systems are fired from the air or surface, experience a phase of atmospheric flight, enter the – water, and continue through the water to the target. A rocket of this type must be designed for travel through the atmosphere and through the water. This handbook will only address design considera- tions for the atmospheric phase of flight. 1 - 4 G E N E R A L R O C K E T S Y S T E M D E S C R I P T I O N A rocket system is made up of a number of subsystems, or elements, each of which performs a function necessary to the successful performance of the system. In general, the system is composed of three main elements—i.e., rocket, launcher, and fire control equipment. Each of these elements is, in turn, composed of subelements or components. This handbook will discuss the rocket in considerable detail and will discuss the other elements only insofar as they interact with the rocket. The reader should consult other handbooks for the details of the other system elements. The basic components of an aerodynamically stabilized free flight rocket area are a payload or war- head, a propulsion motor, and an airframe. The airframe provides structural rigidity and the physical envelope for the internal components. The airframe shape is also important in determining the flight dynamic characteristic of the rocket. A typical rocket configuration and its components are shown in Fig. 1-4. The functions and major characteristics of each component will be discussed in Chapter 2. F i g u r e 1 - 4 . T y p i c a l F r e e F l i g h t R o c k e t C o n f i g u r a t i o n 1 - 5 O V E R V I E W O F C O N T E N T O F T H E H A N D B O O K The applications of this handbook are limited to atmospheric flight of aerodynamically stabilized free flight rockets employing solid propellant motors. The handbook is organized into chapters subse- quently described, that are each self-contained and applicable to a particular technical area. Concep- tual and system design phases of development are discussed in some detail, but the primary emphasis is on the preliminary design phase. The technical areas are System Design, Performance, Accuracy, Aero- dynamics, Propulsion, Structures, Heat Transfer, Launcher Considerations, Atmospheric Considera- tions, and Computer Programs. A synopsis of these chapters follows: 1. Chapter 2, “System Design”, introduces the system design process and illustrates the type of data inputs and outputs for each of the engineering disciplines. 2. Chapter 3, “Performance”, presents data describing the performance of various design concepts. Material is provided which will permit consideration of trade-offs to maximize range for a given mass or optimize mass for a given range. 3. Chapter 4, “Accuracy”, presents data pertinent to estimating the accuracy of a given concept. Launch, powered flight, and ballistic phase errors are considered. The effects that errors during each of the flight phases have on impact dispersion are presented. 1-6 MIL-HDBK-762(MI) C H A P T E R 2 S Y S T E M D E S I G N This chapter- describes the process of designing an aerodynamically stabilized free rocket. The acqui- sition process for development of a rocket system is discussed briefly. The emphasis is on the concept selection and preliminary design. The system validation phase is discussed since this effort is involved in the testing and verification of hardware through prototype development and testing. Production engineering, manufacturing, and deployment are mentioned briefly. 2 - 1 G E N E R A L This handbook, which is primarily intended for conceptual and preliminary design, divides system design into three phases: (1) concept selection, (2) preliminary design, ant! (3) systems validation. The Department of Defense (DoD) acquisition process for weapon systems, as defined by DoD Directives (Refs. 1 through 4), is essentially the same for all branches of service. In general, this acquisition process involves a conceptual phase, a validation phase, a full-scale development phase, and a produc- tion and deployment phase. The concept selection and preliminary design activities described in this handbook are encompassed by the conceptual phase in the DoD acquisition process; the described system validation phase activi- ties correspond to the validation phase of the DoD acquisition process. However, the full-scale devel- opment phase and the production and deployment phase of the DoD acquisition process are not emphasized. The terminology used is that commonly employed by engineers to define the technical activities involved in a system design. Fig. 2-1 depicts the three phases of activities discussed in this chapter. The feedback shown for each of the three blocks is to emphasize the iterative nature of the technical activities involved in the system design process. Fig. 2-1 is discussed further in the paragraphs that follow. 2 - 1 . 1 C O N C E P T S E L E C T I O N P H A S E The concept selection phase begins with the identification of a needed mission or operational requirement or the identification of new technology; it usually ends with the submission and approval of the Justification of Major System New Starts (JMSNS). The JMSNS is the official document used to describe the mission and to justify the initiation of a new major system acquisition. The major activi- ties of concept selection are studies performed to establish system or component constraints, parametric trade-off studies for selection of candidate integrated systems, and system concept definitions. For example, component constraints may require the rocket to operate with an existing piece of equip- ment, to be man rated and shoulder mounted, or to fit on a specific rocket launcher. The parametric studies may include accuracy requirements for kill, guided versus unguided, warhead lethality versus dispersion, size of warhead, propellant selection, propellant design, operational range, type of target, accuracy, fire control technique selection, etc. The concept selection phase ends 1. When the mission and performance envelopes are adequately defined 2. When the system is deemed to be technically feasible and capable of achieving the stated objec-- tives within reasonable cost and schedule constraints 3. When the military objectives, technical requirements, and economic costs are determined to be sound, reasonable, and well defined 4. When the JMSNS document, to allow the study to progress into preliminary design, is approved. 2-1 MIL-HDBK-762(MI) Figure 2-1. System Design Phases 2 - 1 . 2 P R E L I M I N A R Y D E S I G N P H A S E Preliminary design phase activities begin with the output of the concept selection phse and end with the creation of fuctional baseline specifications. All interfaces between the rocket and other equipment should have been defined at the end of preliminary design. The advanced development studies begin during the preliminary design phase. Activities in this phase include trade-off studies and breadboarding for key subsystems and components to show feasibility and to demonstrate capability. For systems exceeding spedified levels of development cost, an official required document called Letter of Agreement (LOA) is prepared by the combat developer, corrdinated with the material developer, and submitted through official channels to support further development work. The preliminary design phase is a highly iterative process with activities performed either simultaneously or sequentially. This phase requires a continuous system integration effort to provide updated requirements and data inter- faces to all technical disciplines and design efforts involved. The preliminary design system integration effort compares and makes trade-offs between the known altermatives, determines the status of technol- ogy for each alternative, evaluates the environmental impact of each alternative, and recommends specific actions that should be followed to meet the required capablity. Usually, the task of exploring and identifying alternative system concepts is made into a competitive activity to facilitate the selection of the best possible solutions from industry, the academic community, and Government sources, including foreign developments. The validation and updating of the JMSNS includes initiating and conduction studies that involve system analysis trade-offs, cost-effectiveness, and evaluation of techni- cal approaches. A primary objective of the preliminary design effort is to compare alternative system design approaches before selection of the single approach that best meets the need. The preliminary design data are basic to the accomplishment of parallel support studies such as risk assessment, cost estimates, utility analysis, and energy effictiveness studies. Government sources usually are involved in the technical and cost risk assessment and trade-off analysis studies as state-of-the-art experts. Part of the preliminary design activities usually are performed as parallel advanced development efforts by competing industrial and Government sources. Major design or technological uncertainties are identified during preliminary design for further investigation during the system design (validation) phase. Planning for testing to eliminate these uncertainties begins during preliminary design. Estimated test costs, schedules, and facility support requirements are also and output of the preliminary design phase. Production feasibility assessments, producibility problems, production processes, tolling develop- ments, production tests, and demonstrations identified during preliminary design are evaluated to determine overall production risk, production cost, and schedule impacts. This assessment is used to identify prototype tests and demonstrations that must be performed in the system development phase. The functional baseline (program baseline requirement) is established by the end of the preliminary design phase and includes broad system performance objectives and operational concept, a logistic concept, and cost estimates. The system specification defines the technical portion of the baseline. 2 - 1 . 3 S Y S T E M V A L I D A T I O N Activities performed in the system validation phase include a definition of the program charac- teristics—i.e., performance, cost, and schedule. These parameters are validated and refined through extensive study and analysis, hardware development, or prototype testing. The quantity and level of prototype and hardware validation depend on the nature of the program and the risks and trade-offs involved. 2-2 MIL-HDBK-762(MI) The end objective of the system validation phase is to determine whether to proceed with full-scale development. The ultimate goal of the system development phase, in which the development is to be performed (usually by a contractor), is to establish firm and realistic equipment performance specifica- tions that meet the operational and support requirements. The test hardware produced during this phase is usually produced by other than production methods and probably is a prototype in form. Although qualification testing is performed in the full-scale development phase, the testing performed at this point should be conducted to check the design for functional performance. Development, test, and evaluation of training simulators, test equipment, tools, and other support equipment parallel the development of system prototypes. The baseline design requirement is established during the system development phase and is the basis for detailed design and development of the system during the full-scale development phase. This base- line incorporates the technological approaches developed to satisfy the objectives in the functional baseline (program requirements). During the system development phase, these objectives are translated into system segment, subsystem, and configuration items (CIs) performance requirements and decision constraints. The system validation phase should produce a more precise and detailed definition of the systtvn as the functional baseline grows into the design requirements baseline. Documentation resulting from the system development phase should include the following technical reports: 1. System engineering studies and analysis information 2. Updated system specification 3. Detailed specifications for prime item equipment, real property facility items, computer pro- grams, and critical identifiable engineering components 4. Data requirements or recommendations. System end-items or components requiring hardware proofing are identified in the system develop- ment phase. Prototypes of systems or components requiring hardware proofing also are produced and tested in the system development phase. Development prototypes produced will vary from a breadboard of a system or subsystem to complete flying prototypes. A major effort in the system validation phase is performing trade-off studies to ensure that a config- uration being defined for full-scale development addresses tactical needs and is the best possible bal- ance among total costs, schedule, and operational effectiveness. A document called the Required Operational Capability (ROC) is written during the system valida- tion phase. The ROC is the requirement document that supports the work to be undertaken in the full-scale engineering development effort. The remainder of this chapter addresses the various techni- cal activities, data requirements, and data interfaces involved in the system design of an aerodynami- cally stabilized free rocket. 2 - 2 R E Q U I R E M E N T S The development of any new rocket system begins with a specific requirement the user believes must be met, i.e., requirements start with the definition of some mission objective by the user. Mission objectives can be stated in a wide variety of terms and even in very broad terms, For example, a need may start simply as the desire to provide the infantry with some defense against armor. The statement of this mission objective could be very broad—provide a weapon that is transportable by an infantry- man and capable of destroying armor at a particular range. The ability to place a particular payload at a point at specified ranges within certain accuracy requirements is another example of a broad mission objective. The general requirements to meet some particular need establish broad requirements on the rocket system. The broad requirements then are the genesis of more detailed requirements, i.e., 1. Operational requirements to meet a broad mission objective usually hav the effect of placing more detailed requirements on the system. 2. Compatibility with other systems and subsystems places additional restraints on a system. 3. Weight and size usually are physical constraints imposed upon a system. 4. Performance objectives place certain requirements on a system that are incompatible with the 2-3 MIL-HDBK-762(MI) parameters to determine, in an iterative manner, the rocket performance and propulsion requirements. Chapter 3 presents data that can be used to provide estimates of propulsion system sizing. The parameters that are sized or considered in the performance trade-off studies involve aerodynamic and propulsion considerations as well as performance interactions. The perfomrance type parameters that are determined in these studies are payload mass, burnout velocity, range, time of flight, and launch angle. Determination of these performance patameters requires knowledge of aerodynamic characteristics, primarily drag, as a function of length, diameter, nose shape, and stabilizing surfaces. Propulsion-type parameters identified in the performance calculations are specific impulse, motor propellant mass fraction, total impulse, burning time, and thrust to initial rocket mass ratio. The aerodynamic design of a rocket involves trade-off studies of small variation in component per- formance for different candidate comfigurations. The aerodynamic design goal is to select an integrated rocket configuration that provides tailored aerodynamic stability and lowest drag consistent with other design constraints to achieve minimum dispersion and maximum range performance. To estimate the aerodynamic stability characteristic for different configurations, it is necessary to know the aerody- namic coefficients of each major rocket component and interference relationships between the compo- nents. The aerodynamic trade-off studies are defined in detail in Chapter 5. The aerodynamicist must know how to combine these component coefficients to arrive at values for the complete configurations. 2 - 3 . 2 . 2 M o t o r s The primary function of the rocket motor is to accelerate the rocket with its payload to the required velocity to achieve the desired flight range. In the conceptual phase, the initial effort to define the rocket motor is directed toward establishing nominal values—those which meet the user and opera- tional requirements and restraints—for all essential parameters. For instance, if limitations are given for impulse, chamber pressure, burning time, size, and mass, then a set of advantage values can be derived for motor physical design characteristics, propellant ballistic mass flow, and other properties. Often in the comceptual phase the performance characteristics of solid propellant rocket motors are scaled from motors with similar characteristics. The parameters suitable for scaling or simple calcula- tions are rocket thrust, nozzle throat or exit area, motor mass, specific impulse, total impulse, chamber pressure, burning rate, and burn duration. 2 - 3 . 2 . 3 W a r h e a d s Warhead trade-off studies involve many factors and considerstions. For example, there are trade-offs between warhead weight and overall rocket weight, and trade-offs between warhead types for various target mixes. Reload and or resupply situations also will influence the types of launchers and person- nel handling requirements in warhead trade-off studies. Other trade-offs will address the problem of packaging various available ordnance into allowable physical dimensions to establish the most effec- tive configuration from a target kell probability point of view. These studies consider rocket delivery accuracy, warhead lethality, and target vulnerability to determine the size, number, and type of war- head required. The specific type of warheads wused in the trade-off studies will depend on the target characteristics and the kill effectiveness of the various warheads against the targets. The types of warheads that would be considered are blast fragmentation, kinetic energy peretrators, shaped charge, self-forging grag- ments, and duel purpose. Each type of submunition can be considered as a warhead and trade-offs made to determine the type required. 2-3.2.4 Error Sources Accurate free flight rocket systems are achieved by either reducing the magnitude of the error source or the sensitivity of the rocket to the error. The most significant error sources influencing the accuracy of free flight rockets are malaim, mallaunch, total impulse reproducibility, thrust misalignment, dynamic unbalance, surface wind, ballistic coefficient, air density, and ballistic wind. The dispersions for these error sources are calculated using a 6-degree-of-freedom (DOF) and a point- mass trajectory program. After error free baseline trajectory is established, each error source is usually 2-6 MIL-HDBK-762(MI) considered independently in preliminary design studies to determine the contribution to dispersion due to that error. The dispersions for the various error sources are then root sum squared, and the circular error probable (CEP) is calculated for a particular rocket design. It should be recognized that in some cases error sources are interdependent and cannot be root sum squared. The error source trade-off studies will show the relative merit of competing aerodynamic tailoring techniques for reduc- tion of dispersion during the burn phase. The accuracy studies will also identify the important error sources. The error analysis trade-off studies coupled with warhead lethality studies can provide data for use in the cost-effectiveness studies. The dispersion sensitivities to error sources determined in the error analysis studies also provide input to the design of a rocket system. Monte Carlo methods can be used to provide data for system accuracy analysis and are often used when the assumptions for calculating miss by applying the root-sum-squared method to individual errors are invalid. 2 - 3 . 3 S Y S T E M S E L E C T I O N The system selection process consists of applying the given requirements and constraints (boundary conditions) to the parametric trade-off studies and selecting the concept(s) that best meets the user and operational requirements. The concept selection process will include all technical disciplines necessary to establish the interac- tion between rocket components, and the interaction between rocket components and the environment to ascertain that rocket user and operational requirements are met. The rocket system selection process begins with performance parametric trade-off studies. These studies establish the interaction-with certain rocket aerodynamic factors and propulsion parameters—of payload mass, burnout velocity, range, time of flight, and launch angle. The parametric studies provide information for the selection of the proper aerodynamic shape, thrust energy management, total impulse, warhead type(s), and fin deployment. The class of rocket needed and its operational mode are primarily determined by user needs and mission objectives. The parametric trade-off studies will determine whether accuracy requirements are comparable with a free rocket. Launcher considerations are influenced by the rocket class, accuracy requirements, and opera- tional mode. The launcher, in turn, initially influences the rocket drag because of shoes, sabots, spin lugs, umbilical, etc. Operational environments also place constraints on the launcher type considered for the system. The system selection process should result in the definition of a rocket system concept(s) that has a high probability of meeting the mission objectives and operational effectiveness criteria. New technol- ogy development requirements are identified, and the time frame for meeting the development requirements is established. Estimates of system development costs and life cycle costs also are made. Finally, system effectiveness studies are made to determine the overall cost-effectiveness of the selected concept(s). Data of the type described in this paragraph are used in deciding whether to proceed into the pre- liminary design phase. 2 - 4 P R E L I M I N A R Y D E S I G N The development of a new rocket system proposed in the conceptual design phase reaches a formal status with the start of the preliminary design phase. The JMSNS has now been prepared and received appropriate approval. The output of the conceptual design phase is available to start the preliminary design. The mission objectives and requirements developed in the conceptual design phase provide the basis for starting the preliminary design, and the concept(s) selected for further analysis is refined and analyzed in the preliminary design phase. All information and data developed in the conceptual design phase are input data to the preliminary design phase. Fig. 2-3 depicts the technical activities that take place in the preliminary design phase. Subsystems are designed and optimized in an iterative fashion. The results of the parametric studies and trade-offs are used in the subsystem design and, in conjunction with the mission objectives, are amalgamated into an overall system design. The system design is then translated into a set of specifications, interface 2-7 MIL-HDBK-762(MI) Figure 2-3. Preliminary Design Phase Activities control documents, and design drawings from which the prototype or engineering development can proceed. Fig. 2-3 illustrates a system integration function that accepts inputs and provides feedback to all the other activities. The system integration function is illustrated this way to stress the importance of information exchange among the activities, and it is assigned this strong role to stress the impor- tance of maintaining balance and a single sense of purpose for the other activities. System integration also provides the interface with other activities involved in the development of auxiliary devices. The preliminary design phase explores alternative system concepts to evaluate the effects of various trade-offs in minimizing the major design and technological uncertainties. A test and evaluation plan is developed at the end of the preliminary design phase for use during the system design phase. Testing is pm-formed during the system validation phase to verify that all major uncertainties identified during the preliminary design phase have been eliminated. The preliminary design phase concept selection process is an iterative process. Further detail on each of the preliminary design activities is provided in the paragraphs that follow. 2 . 4 - 1 P A Y L O A D The class of rocket and the operational mode largely determine the type payload required for an aerodynamically stabilized free rocket. The payload for most military rockets is a warhead. A general description of a warhead was presented in par. 1-4.2 and will not be repeated here. This paragraph briefly defines the engineering analyses and trade-off studies involved in the preliminary design of a warhead. The detailed mission objectives will define the function of the warhead. Questions to be resolved before detailed warhead design begins include type of target(s), hardness of target(s), rocket accuracy, and number of rockets expendable per target. Probability of kill for a particular target is a consideration in establishing the requirements for the warhead. Probability of kill analysis involves target vulnerability studies and detailed information on the destructive effects of the warheads. Proba- 2-8 MIL-HDBK-762(MI) management techniques are used in most military aerodynamicaly stabilized free flight rockets. Sour-ding rockets sometimes use the staged boost method of energy management. Aerodynamically stabilized free rockets require high thrust and high acceleration during the boost phase to minimize dispersion. Plumes from underexpanded motor exhausts induce boundary layer separation; the net effect on aerodynamic characteristics is a reduction in the static stability margin. Considerate ion should be given to plume effects on the aerodynamic characteristics in order to prevent instabilities. However, the desirable situation to reduce sensitivity to wind is to have a rocket very near to neutral stability. The results published in Ref. 22 show how plume effects call be beneficially used to tailor static margin. A boost-sustain configuration can reduce dispersion due to all ballistic phase error sources if the sustainer thrust matches the ballistic drag variation. The maximum to minimum thrust ratio required to reproduce this thrust variation is on the order of 10 or more. This variation in thrust is not within the present state of the art of solid rocket motors without significant system level trade-offs. This energy management technique loses its potential advantage in accuracy over a boost-only configura- tion because of this constraint, and the added error sources of sustainer total impulse, thrust level variation, and increased base drag during sustainer operation. Based on Ref. 23, the boost-sustain configuration does not reduce dispersion over that for a boost-only configuration due to state-of-the-art performance constraints placed on the boost-sustain motor. 2-4.2 .2 Motor Design 2-4.2.2.1 Motor Physical Characteristics A solid propellant rocket is made up of two major components-a loaded motor case assembly and a nozzle assembly. The motor case assembly consists of a head closure, cylinder, propellant, liner or inhibitor, insulation, aft closure, slivers, and igniter. A nozzle normally is composed of a convergent section, a throat, and an expansion section. Nozzles are designed to provide the proper expansion ratio depending upon the flight regime of operation (see Ref. 21). Nozzles for operation at sea level are different from nozzles for high altitude operation. If the rocket is to operate over a mixed flight regime (sea level and high altitude), the nozzle is designed to obtain the best compromise in overall performance. Motor cases may be made of a medium alloy steel, a hardened alloy steel, a maraging steel, titanium, aluminum, or composites. Life cycle costs are important considerations in the choice of a motor case. Chapter 6 provides more detail of the physical characteristics of a rocket motor. 2-4.2.2.2 Performance Characteristics The rocket performance characteristics are determined primarily by the motor performance, specifi- cally by the propellant performance characteristics. For an acrodynamically stabilized free rocket to function properly it is important that the motor performance be predictable and repeatable. Minimiz- ing variations in total impulse (the integral of the thrust with respect to time) and specific impulse (the impulse developed in burning one unit of propellant mass) are of fundamental importance in most rocket motor applications. Variation in impulse is typically the second or third largest source of range dispersion error in free flight rockets. Sources that contribute to impulse variation are burning rate variation, throat area variation, grain asymmetry, propellant mass variation, grain temperature, sur- face area variations, etc. (Ref. 24). A rocket motor preliminary designer’s usual goal, which is to select a propellant with the highest value of specific impulse and specific mass, is not as important for free flight rockets as obtaining a formulation that provides reproducibility of specefic impulse and specific mass. The major source of specific impulse variation can be reduced by reducing burning rate variations. It is shown in Ref. 25 that the composite propellant burning rate reproducibility was far superior to the other propellant families. Care should be taken in the preliminary design to select propellants that have burning rates as consistent as possible for the expected operational environment. Motor case, propellant grain, and nozzle variations produce variations in nozzle performance, propellant symmetry (thrust misalign- 2-11 MIL-HDBK-762(MI) ment), or propellant surface area (combustion pressure)—all of which also affect overall propulsion reproducibility. 2 - 4 . 2 . 2 . 3 P r o p e l l a n t s Two types of propellants have been used in solid propellant rockets—double base propellants and heterogeneous composite propellants. Recent propellant technology development incorporates aspects of these two propellant types into a new heterogeneous propellant that employs an energetic binder. A double base propellant is a homogeneous, plastic, solid monopropellant comprised of three principal ingredients—a polymer, an oxidizer-plasticizer, and a fuel plasticizer. The heterogeneous composite propellants also have three principle ingredients—a fuel that is an organic polymer called binder; a finely powdered oxidizer; and additives for catalyzing the combustion process, increasing the density, incrasing the specific impulse, improving physical properties, and increasing storage life. Considera- tions in the coice of type of propellant to use include exhaust plume smoke, impulse reproducibility, type of case insert needed, and cost. Free rockets are usually produced in large quantity; therefore, life cycle costs are an important consideration in the selection of a propellant. 2 - 4 . 3 A E R O D Y N A M I C S The aerodynamic design of a rocket involves the study of the effect of variations in components on the dynamics, accuracy, and performance of the different candidate configurations. The aerodynamic design goal is to select an integrated rocket configuration that provides stable flight with minimum drag while it maintains insensitivity to outside disturbances. To determine the aerodynamic drag and stability characteristics for different configurations, it is necessary to estimate the aerodynamic coeffi- cients of each major rocket component and each interference between components. The aerodynamicist must know how to combine these component coefficients to arrive at values for the complete configu- ration. The remainder of this paragraph will discuss methodology for estimating drag, calculating stability, and determining the effects of nonlinear aerodynamics. Each of these subjects will be dis- cussed in general terms. The reader should refer to Chapter 5, “Aerodynamics”, and Ref. 26 for more detailed discussions. 2 - 4 . 3 . 1 D r a g Drag forces on an aerodynamic surface are fundamentally the result of the horizontal components of the normal and tangential forces transitted from the air to the body. Estimation of drag for free rockets can be restricted to zero-lift because the rocket follows a ballistic path. The total drag on the rocket is the summation of wave drag, skin-fiction drag, and base drag. Wave drag is the result of pressure forces acting normal to all surfaces except teh base. Skin-friction drag is the result of viscous forces acting tangential to the surfaces. Base drag is produced by pressure forces acting normal to the base. Each drag force is discussed in teh paragraphs that follow. The aerodynamic drag of the complete rocket is the most important foactor affecting accuracy and performance during the sustain the ballistic flight phases. Minimizing drag, for example, is more important for an indirect fire rocket since the sustain and or ballistic flight times are much greater than those of the boost phase. 2 - 4 . 3 . 1 . 1 W a v e D r a g Wave drag is present on the rocket nose, the afterbody (boattail or flare), and the fins or other stabilizing surfaces. Nose wave-drag is influences primarily by the fineness ratio, nose shape, and Mach number. For preliminary design estimates, the family of nose shapes-of-interest for free rocket is bounded by cones and ogives. Data on these basic shapes are given in Chapter 5 and 7. Various techiques can be used to reduce the drag on a rocket vehicle in flight. For example, if the exit diameter of the rocket nozzle is smaller than the body-cylinder diameter, the afterbody of the rocket may be tapered to form a boattail to reduce the base drag. This technique, however, increases the wave drag on the configuration. Therefore, an optimum boattail configuration results from balancing the increase in wave drag with the reduction of base drag. Flared afterbodies are used sometimes to provide inherent restoring moments for which precise sta- 2-12 MIL-HDBK-762(MI) bility margin control is required. The drag on flares, however, is higher than the drag on fins giving equivalent stabilization. The wave drag on fins is slight compared to the total rocket drag, and it is influenced strongly by the thickness-to-chord ratio and sectional shape. 2-4.3.1.2 Skin-Friction Drag Friction drag results from the boundary layer airflow over the rocket surface. Shear stress is imposed on the external surface of rockets due to the velocity gradient in the boundary layer. The magnitude of this shear stress is a function of the position of transition from laminar to turbulent flow, and, there- fore, it is Reynolds number and Mach number dependent. Correlation of experimental data and analyt- ical techniques has shown that the skin-friction coefficient for bodies of revolution is approximately 73% higher for laminar flow and 17% higher for turbulent flow than that on a flat plate (Ref. 27). The aerodynamicist must make appropriate transformations to available data to account for body shape. 2-4.3.1.3 Base Drag The base drag is caused by the pressure forces resulting from airflow separation at rearward-facing steps such as body bases and fin trailing edges. The geometry of the rearward-facing step and the properties of the boundary layer approaching the step affect the drag. 2-4.3 .2 Stabili ty Static stability is defined as the condition in which a disturbance of the system creates forces or restoring moments in the proper sense to drive the system toward equilibrium at zero angle of attack. If the subsequent motion finally restores the equilibrium, the system is termed dynamically stable. How- ever, if the motion —although starting the system brick toward the initial equilibrium, never restores equilibrium-the system is termed dynamically unstable. The natural frequency of the system is pro- portional to the restoring moments anti inversely proportional to the inertia. For a rocket to possess flight stability, a restoring moment must be produced when the longitudinal axis of the rocket is rotated away from the flight direction, i.e., when an angle of attack exists. This flight stability is achieved in aerodynamically stabilized free rockets by designing the external con- figuration so that the center of pressure of aerodynamicaatvx)(i}mamic forces acting normal to the longitudinal axis is located aft of the center of gravity. When the center of pressure is aft of the center of gravity, the rocket is said to be statically stable. The degre of aerodynamic stability, or the static margin requirement, varies with the desired accu- racy of each rocket and the design approach. For example, a rocket designed for minimum dispersion during powered free flight requires special tailoring of the static margin over the expected Mach number regime; however, a high-acceleration rocket, which achieves most of its velocity prior to release from the launcher, only has a requirment that the stability margin remains within certain upper and lower bounds. The width of this stability band is governed primarily by the requirement to maintain a suitable spread between roll and pitch-yaw frequencies. 2-4.3 .3 Nonlinear Aerodynamics The aerodynamicist must consider nonlinear aeridynamic forces and moments under certain situa- tions. The basic aerodynamic coefficients of a free flight rocket design are nonlinear when very high thrust levels exist during boost. The resulting plumes are underexpanded at the nozzle exit and con- tinue to expand until they are 1.5 to 2.0 missile diameters in size. These plumes can cause nonsymmet- rical flow separation that changes the center of pressure location and results in a loss of stability. The degree of nonlinearity is also a function of the angle-of-attack magnitude. Nonlinear aerodynamics can increase the dispersion errors caused by crosswinds. If the nonlinear effects cause side forces and moments greater than those predicted by linearized aerodynamics, the dispersions cause by the cross- wind can be larger than anticipated. Nonlinear normal force and pitching moment test data can be used to provide better estimates of the effects. If computer simulations are used, actual coefficients as functions of angle of attack and Mach number can be input into the simulation. Nonlinear aerodynamics are also introduced if a fin is damaged or torn off during flight. The nonlin- ear aerodynamic coefficients have to be determined from wind-tunnel or free flight testing for each 2-13 MIL-HDBK-762(MI) Manufacturing tolerances should be considered during the preliminary design phase because (1) tolerances that are too tight result in high manufacturing costs, and (2) manufacturing tolerance build- up can create rockets with asymmetries in internal mass distribution and external configuration. Inter-- nal mass distribution asymmetrics produce center-of-gravity offsets, whereas external configuration asymmetries can cause aerodynamic force unbalance. Center-of-gravity offsets and aerodynamic force imbalance both produce moments that cause aerodynamic angle of attack. Rockets flying at angles of attack have higher drag, thus performance losses. The offset center of gravity causes coning in a spin- ning vehicle. Therefore, trade-offs must be made between manufacturing tolerances and manufactur- ing costs. Two of the major contributor-s to artillery-type free flight rocket dispersion are ballistic wind and atmospheric density variations. The errors due to these sources are greatest during ballistic flight. Drag reduction reduces the sensitivity to atmospheric density. Variations, and improved or updated meteoro- logical data can provide information for firing table corrections in the artillery rocket system. The wind sensitivity during the boost phase can be reduced by tailoring the static margin. Wind and den- sity trade-off studies are performed to desensitize the rocket to these effects during launch and ballistic flight. Error budgets are usually established for particular components and system errors. A typical error budget will include one-sigma component error values and burnout angular errors for range and deflection for several error sources. These sources are usually malaim, mallaunch, thrust misalign- ment, surface wind, total impulse, ballistic coefficient, density, and ballistic wind. Based on these data, a CEP in meters and roils is calculated. Table 24, Ref. 23, presents several error budgets for different ranges and different age meteorological data. Table 2-1 is presented to illustrate a typical error budget for an artillery rocket. TABLE 2 -1 . ERROR BUDGET EXAMPLE 2-4.4.2 Dynamic Loads Dynamic loads are the result of accelerations of the rocket, which can arise from a number of exter- nal or internal forces acting upon the vehicle. Some typical acceleration- or disturbance-producing quantities are shock, thrust, acoustics, handling, aerodynamic forces, and launcher-induced accelera- tions. The shock environment may be produced by one or more of the following events: truck transpor- tation; rail transportation; ship transportation; handling during transit, including drops; propulsion unit ignition, boost-sustain transition, and shutdown; fin opening or abrupt stabilizing surface area 2-16 MIL-HDBK-762(MI) change; operation of mechanical or electroexplosive devices; and rail launch tip-off. High-intensity acoustic-producing events occur during free or powered flight and the firing of adjacent rockets. 2-4.4.3 Rocket Vibrational and Bending Considerations Vibration and bending of the rocket may be caused by either external forces and moments or induced by accelerations. Sources of disturbances which can produce bending are transportation by truck, rail, ship, and aircraft; handling or transfer operations; launcher operations; launch-to-target sources such as turbulent boundary layer, propulsion unit, rotating devices; and any unusual protrusion into the airflow. Simplified solutions of the equations of motion are available for the flexible launcher and rocket interaction problem, for example, Ref. 32. Detailed vibration studies often involve finite element modeling and usually are deferred to the advanced development phase. The information needed to develop a finite element model often is not available until the advanced development phase. 2 - 4 . 5 S T R U C T U R E S The rocket structure provides a specific external shape, a protective envelope, and a platform for the delivery of a payload to a target. The structure must be designed with minimum mass and sufficient strength to withstand ground handling, launch, and flight loads. Producibility and aerodynamic heat- ing are also considerations in structural design. The strength of a structure depends upon the physical and mechanical properties of the materials and the geometric configurations of the structural members. The proportional limit, elastic limit, yield point, ultimate strength, modulus of elasticity, ductility, anti hardness are the significant material properties considered in the preliminary design. The physical dimensions, moments of inertia, and cross-sectional area are the significant geometric factors of the structural members. 2-4.5 .1 Materials The structural engineer must not only be concerned with the elastic constants, yield and breaking strength, and fatigue characteristics but also the temperature, creep and plasticity, notch sensitivity, moisture, and dielectric characteristics of the materials. The compatibility of dissimilar materials that are physically connected must be considered because materials with different coefficients of expansion could produce undesirable stresses; also the problem of gait’anic corrosion of metals exists. Rockets require a broad spectrum of materials ranging from explosives, propellants, metals, to plastics— however, this paragraph will address only the load-carrying, structural materials. The main load- carrying structures for a rocket are the rocket case and motor case. Rocket motor cases frequently have been made of high strength steels. These materials have high yield and ultimate strength, are not notch sensitive, and are elastic. They can be cycled to 75% of full load several times without hoop strength failure, and they have been proven to be safe for man- launched rocket applications. However, steel cases are heavy, and therefore, structural designers also have used aluminum and composites. Several rockets using other materials have been designed; for example, the VIPER motor case is made of a composite material with an 8-mil aluminum liner. The aluminum liner is included to eliminate gas leaks and to provide a moisture barrier for the combustion chamber. The PERSHING II motor case is another example; it is made of Kevlar®. Special aluminum alloys have been developed which have high yield and ultimate strength in the 620 to 685 MPa range. However, these materials are relatively notch sensitive and brittle. The composite motor cases offer high strength to mass properties. However, proof test procedures and environmental protection must be considered before these materials are selected for use in structural components. 2-4.5.2 Structural Sizing The structural designer must develop loads and moment data in order to calculate the stresses and deformations sustained by candidate materials. The equations used for calculating the stresses and deformations of rocket and motor cases are those applicable to unreinforced thin shells. The detailed stress and deformation calculations for rocket structures are provided in Chapter 7. 2-17 MIL-HDBK-762( MI ) DOD-HDBK-762(MI) DOD-HBK-762(MI) 2-4.5.3 Mass and Balance. The mass and balance calculations performed are mass and center-of-gravity estimation, pitch iner- tia, and roll inertia. The equations for evaluating the volumes of typical reccket sections are presented in Chapter 7. The volumes are calculted for homogeneous sections, and the masses are then calculated by multiplying by assumed densities. Equations for calculating the center-of-gravity location also are provided by Chapter 7. For convenience, these locations are identified as rocket station numbers, i.e., distance from the nose tip. The location of the center of gravity of the complete configuration can be estimated by summing moments of the section masses about the nose tip and dividing by the total rocket mass. Thi pitch and roll inertias fo the rocket are calculated by similar methods. 2-4.6 HEAT TRANSFER The depth of heat transfer analysis performed in the preliminary design phase of an aerodynamically stabilized free rocket is highly dependent upon the type of rocket. Some rockets may require consider- able heat transfer analysis, wheras for others extrapolation from similar rocket may suffice. The description of analyses and studies in this paragraph covers those analyses for a completely new rocket vehicle design. Details for carrying out the analysis are described in Chapter 8, “Heat Transfer”. Tra- jectory and configuration data are required to define aerodynamic heating. Velocity, attitude, and altitude data versus time; configuration data; and a selected heating rate option are the usual inputs to an aerodynamic heating rate program such as the one given i nRef. 33. A heating rate indicator pro- gram will calculate the integrated aerodynamic heating rate versus trajectory time for any point on the conceptual body. The integrated heating rates for various designs provide the designer with data to use in the preliminary design process. During the preliminary design phase, system component temperatures are calculated by using closed-form solutions of the general energy equation. The internal heat transfer solutions are obtained by applying the aeroheating boundary conditions to known exponential form Laplace solutions given in Ref. 34 or to temperature response chart solutions given in Ref. 35. The rocket motor case must case must meet structural load requirements while bing heated both internally and externally. Calculation of internal heating requires knowledge of the combustion gaseous equili- brium composition and flow rate for the expected conbustion chamber pressure and termperature con- ditions. The exposed propellant grain surface and downstream flow restriction areas determine the chamber pressure. Propellant composition determines the equilibrium termerature. For the prelimi- nary design phase, chamber conditions can be estimated from previous similar rockets or test pro- grams. Rocket duct and nozzle propellant gas flow solutions to the momentum equation are obtained by useing ideal gas flow relationships. There relationships involve duct area change, energy subtraction from and addition to the flow, momentum loss, mass addition to or subtraction from the flow, or combinations of these changes in the form of influence factors (Ref. 36). Once the combustion chamber pressure and temperature time histories are known, the convection coefficients in the rocket ducting and nozzle can be calculated by using Bartz's relationship given in Ref 37. The heat transfer from the combustion chamber to the rocket skin can be calculated by using relatively simple computer pro- grams, such as the on in Ref. 38, that couple a one-dimensional surface ablator analysis to backup layers of nonablative materials. This analysis accounts for both the ablative heating on the combution chamber side and the aerodynamic heating on the rocket mold line side. Design analysis includes determining the effect of the rocket on the launcher, e.g., is the launcher purely structural or a shoulder-fired weapon. The heat effects of the launcher ususally result from plume impingement. Plume temperature and velocity flow fields must be defined before the plume impingement heating calculations can be performed. Flow field solutions must be provided for both the gaseous and condensed phase. Computer programs are available for calculating the gaseous flow field through the nozzle and into the atmosphere. No simple methods are available for calculating the condensed phase trajectories resulting from a body being submerged in a rocket plume. Convective and radiative heat transfer contributions from both the gaseous and condensed phase must be included in the analysis. The convective heat transfer between the gaseous phase and structure is dependent on the 2-18 MIL-HDBK-762(MI) of the squibs or initiators. The electrical and mechanical blocks often are incorporated into a single mechanism. 2-4.9.4 Fuze Setting Equipment Every rocket warhead has a safe and arm, and fuze setting system. The rocket may be launched by a remote management system that sets the fuze in the warhead and activates the rocket igniters. Fuzes can be super quick, time delay, or proximity. The electronic time fuze is one of the more accurate delay fuzes available; it can be set to initiate the detonation process at any time after a specific event. It can also be designed for remote setting. 2-4.9 .5 Shipping Containers The rocket shipping container must be designed to absorb shock; isolate the rocket from rain, hail, sand, and dust; and insulate the rocket from diurnal temperature variations. Some shipping containers also serve as part of the launch system. See Ref. 39 for information on container design. 2-4.9.6 Other Devices Unique to a Given System Other devices unique to a given system may be a laying and aiming system; target acquisition, discrimination, tracking, and engagement systems; etc. 2 - 4 . 1 0 S Y S T E M I N T E G R A T I O N The preliminary design phase requires continuous system integration effort to provide updated requirements and to maintain interfaces on a daily basis with all technological disciplines and design areas involved. System integration during this phase expedites the exchange of data among the differ- ent disciplines and design areas. This is to insure that all subsystems and components intermesh phys- ically and functionally in an acceptable manner. The system integration process also must consider- component performance, reliability, availability, and maintainability Manufacturing techniques and life cycle costs are also of concern to the engineers involved in system integration. Each of these areas is discussed in the paragraphs that follow. 2 - 4 . 1 0 . 1 P e r f o r m a n c e The system integration process continuously compares the updated performance characteristics and the design requirements of the rocket components to those required to satisfy the mission need. The warhead performance requirement may be antipersonnel and have a specified kill probability within a certain area. Other interfaces could create an updated design requirement that a certain size wire bundle be carried through the warhead section or that the warhead skin carry the structural loads in a certain manner. The propulsion performance requirement may be that the propellant provide a progressive thrust in a manner that minimizes low velocity crosswind-induced dispersions at the warhead delivery point. A design requirement may be that a rocket motor or auxiliary device impart a spin rate to the rocket while it is still on the launcher. Aerodynamic performance often requires that trade-offs be made between the shape of the warhead and drag characteristics. Static margin tailoring and fin design require trade-offs. The types of fins and the launcher sometimes pose compatibility problems. The rocket and launcher interface must be con- sidered when defining the drag. An accuracy performance requirement may be that the CEP of the rocket be no greater than 300 m at a 30-km range. From a total system integration design standpoint, the accuracy of a rocket can be improved by using a better meteorological data sounding system such as FAMAS as is discussed in par. 2-4.9. Thus, the use of the FAMAS system could be an accuracy design requirement. It may be required that the rocket structure be formed to minimize thrust misalignment, i.e., a performance requirement. A design requirement would be the imposed load distribution for handling, launch, and flight. Cost for manufacture must be considered in the structure design. A requirement that impacts on heat transfer studies is the rocket thermal protection system require- ments. A design requirement may be that the motor case structure be maintained below some specified temperature. 2-21 MIL-HDBK-762(MI) The system integration engineer must trade off the individual discipline or subsystem requirements with that of the rocket mission. He nust keep in mind that the important performance requirements are those associated with payload, velocity, range, altitude, time of flight, and launch angle. 2 - 4 . 1 0 . 2 R e l i a b i l i t y A reliability assurance program must be established and maintained in accordance with military standards such as MIL-STD-790 for electronics. The systems engineer must not only be concerned with whether a component will perform satisfactorily but also whether the component has a satisfactory reliability history. A reliability failure analysis must be performed on each component. Government supplied parts, reiability data are beneficial in this analysis. Once component reliability is established, the reliability engineer must determine whether the differnet components of a subsystem are compati- ble. He must determine whether materials are dissimilar, whether stress concentrations are created by different materials having different doefficients of thermal expansion, etc. Once a reliable subsystem has been configured, the reliability engineers must evaluate the interplay amont the different subsys- tems to perform a total system reliability analysis. 2 - 4 . 1 0 . 3 C o s t A life cycle cost-effectiveness analysis models a total weapon system for a specified life cycle in terms of logistics, ammunition, training, personnel, and costs. The total recket system next would be deployed against a specified battle scenario in a computer-simulated battle. Then a quantities of diferent types of rockets and associated equipment are adjusted until the battle is won-i.e., all targets have been attacked or a specified number destroyed. In this manner a parameter can be varied within the weapon system, the system adjucted to be successful, and the total cost determined. This is a life cycle cost analysis that could be applied in preliminary design to a total weapon system; however, all types of cost studies are necessary from the time the component selection process begins, until the total system selection process is completed. Cost and performance versus quality assurance are trade-offs made at each level of weapon system design. These cost studies not only apply to the design of systems but also to the verification of that system through an enviromental quality assurance program. 2 - 4 . 1 0 . 4 A v a i l a b i l i t y D a t a Literature searches must be performed to gather information on the availability of the different types of systems which are bing considered. Contracts made through use of vendors' supplier lists are also good sources of availability data. The system engineer must continue to evaluate his proposed system until he is certain that it will be state of the art and producible within the time frame of his contract. 2 - 4 . 1 0 . 5 M a n u f a c t u r i n g C o n s i d e r a t i o n s The system engineer must consider manufacturing processes from the forming, assembly, and cost- effectiveness standpoints. He may machine, spin, shear, form, stamp, deep draw, tube draw, roll bend, host extrude, cold extrude, hydrostatically extrude, or expand the part in the forming process. He may assemble the parts by using rivets, quick disconnects, or an array of welding and brazing process. Available processes are arc, electron beam, tungsten inert gas, and plasma welding; or vacuum, hydro- gen, inert gas, and retort hydrogen atmosphere brazing. Ref. 40 provides information on producibility From a cost-effectiveness and minimum weight standpoint, the substitution of advanced composite for metals must be considered. This is particularly true for large, nonload-carrying structural members. Generally speaking, epoxy graphite composites, although light in weight and relatively easy to pro- cess, are costly. The system engineer must constantly monitor advancements completed by materials laboratories such as the Air Force Materials Laboratory at Wright Patterson Air Force Base. Refs. 41 through 44 provide useful information on composites. 2 - 4 . 1 1 S P E C I F I C A T I O N S The functional baseline (baseline of program requirements) and interface control specifications are established by the end of the preliminary design phase. The functional baseline includes broad system performace objectives, an operational concept, a logistic concept, and cost estimates. The system 2-22 MIL-HDBK-762(MI) specification defines the technical portion of the baseline program requirements. An interface control specification establishes the physical, functional, safety, inspection, and test interfaces among rocket components, and between the rocket and launcher subsystem. 2 - 5 S Y S T E M V A L I D A T I O N The system validation phase serves to validate and refine program characteristics through extensive study and analysis, prototype hardware development, and prototypte testing. The objective of this phase is to establish firm and realistic performance specifications that impose the operational and support requirements. Hardware that will meet the functional and performance requirements is defined and designed during this phase. Prototype models are fabricated and tested to verify the ability of the system to meet these requirements. Fig. 2-4 depicts the technical activities that take place in the system validation phase. The prelini- nary design functional requirement baseline is translated into a design requirement baseline during system validation phase. The functional baseline during this phase is redefined in terms of perfor- mance requirements, decision constraints, and physical configurations. The parametric trade-off stud- ies performed during the preliminary design phase are refined further. These studies lead into the demonstration and validation of concept tests and studies. These tests and studies are performed to insure that a configuration being defined for the full-scale development phase meets the updated mis- sion needs and is the best possible balance among the alternatives, considering total cost, schedule, and operational effectiveness. The quantity and level of prototype modeling and hardware validation per-- formed during the validation phase depend on the nature of the program and the risks and trade-offs involved. It must be remembered that the hardware tested in this phase is produced by other than production methods. Testing is performed to determine whether a design is functional and meets performance requirements. Complete qualification testing is performed in the full-scale development phase. Overall program office management activity increases in the system validation phase. Usually at the time of the system validation phase, a somewhat definitive contract has been written. New data, the results of technology studies, test results, or changing needs may alter the functional requirements defined as output of the preliminary design. Any changes in the requirements placed on a weapon supplier must be coordinated through official channels. Thus program office management must coor- dinate its changing requirements through the contract organization. Figure 2-4. System Validation Phase Activities 2-23 MIL-HBDK-762(MI) data and burn time. since all other parameters are known, the variation of the cahracteristic velocity with t ime is obtained. The specif ic impulse is determined by dividing the measured thrust by the calculated average nozzle mass-flow rate. The theoretical rocket thrust, spedifica impulse, and characteristic velocity are calculated. The ratio of the measured values to theoretical values provides the designer with the characterist ic velocity and specific impulse efficiencies. The motor case structuarl tests are performed to demonstrate that a motor case design of minimum dimensions and material strength will carry a specified pressure without yielding and to demonstrate location and type of failure during burst pressure test. Microtensile specimens can be taken from the case failure region for use in further determination of the minimum ultimate strength and minimum yield strength of the case. These determinations are make in the circumferential and longitudinal d i r e c t i o n s . Wind-tunnel tests are perfomed to measure and determine aerodynamic force and moment coeffi- cients, aerodynamic heating parameters, and heat transfer characteristics. The aerodynamic tests mea- sure forces, moments, and pressure loads. The aerodynamic heating tests are conducted to measure heating rates and recovery temperatures. Heat transfer tests are performed to measure ablation rates and temperatures at critical locations throughout the rocket. The aerodynamic force, moment, and derived stability data are used in computer simulations of the boost phase and the coast phase. Wind-tunnel tests are conducted at subsonic, transonic, supersonic, and hypersonic speeds to cover the entire spec- trum of flight velocity. Thus no one tunnel can be expected to cover this range, and it may be necessary to use several tunnels to establish a complete aerodynamic data base. The tunnels should have a high Reynolds number in order to yield reliable data. The models ussed to obtain basic 6-component aerody- namic data are sized by the facility to be used for the test and can range from 5% of full scale to full scale. The model scale must be of sufficient size so that the component parts normally exposed are not submerged in the boundary layer of the test model. Coefficeints for forces along, and moments about, three orthogonal axes are obtained by using a sting- or strut-support internal force balance. Pressure taps can be placed on the model to determine pressures at selected locations. For each Mach number tested, the angle of attack of the model in the vertical plane may be varied. Each model configuration incorportating tai l f ins is tested at various roll angles. The force and moment data are reduced to coefficient form and plotted versus appropriate a ngle of attack. Those parameters showing nonlinear vatiation with angle of attack are noted to further study. The resulting coefficient data are normal force, side force, axial force, pitching moment, yawing moment, and rolling moment. Pressure data are used in aerodynamic load analysis . Flight profiles for some rockets indicate that aerodynamic heating must be considered in the design of the external surfaces. Therefore, erodynamic heating tests are conducted for rockets with f l ight regimes that cause significant aerodynamic heating. Wind-tunnel tests are conducted to measure undis- turbed, interference, and protuberance heating of a rocket. Tests are performed at supersonic and hypersonic Mach numbers, and at Reynolds numbers characterist ic of severe heating f l ight regimes. The undisturbed heating tests use scale models of the clean body configurations of the entire rocket, but interference and protuberance heating tests use scale models of the intire rocket including f ins, bourrelets, etc. The ratio of the heating measured on the interference and protuberance model to that measeured on an undisturbed model, and the calculated clean body heating for the full-scale f l ight rocket are used to calculate total heating rate of the rocket. Heat transfer tests normally are conducted wieh a full-scale model that will have an adiabatic wall and heat transfer convection coefficeint equi- valent to that exist ing on the rocket at some Mach number and Reynolds number during the f l ight time of interest. Thermographic phosphors and external thermocouples are used to show the natural boundary layer transit on these full-scale models. Heat flux gages can be used to verify that the correct surface heat f lux is simulated at a particular location on the rocket, whereas internal thermocouples are used to evaluate system component performance. Flight tests are used to verify component and system performance, aerodynamic stability and drag characteristics, overall accuracy characteristics of the rocket, structural load, moment and vibration 2-26 MIL-HDBK-762(MI) environments, and rocket roll rate. The primary purpose of a flight test program is to obtain engineer- ing data on the rocket during the launch, boost, and ballistic flight phases, and during flight to impact. In addition to evaluating total functional performance of the system, the objective of a flight test program may be to gather specific data on velocity and spin rate profiles, rocket and launcher interaction, tip-off or nontip-off characteristics, rocket stability, structural integrity of the rocket and launcher, detent release, motor performance, fin dynamics, and blast pressure effects of a rocket. Dur- ing these tests, the rockets are ballasted so that their masses and centers of gravity will simulate the tactical weapon. The instrumentation used in flight test programs includes everything described under static tests plus that required to monitor the flight dynamics of the vehicle. The instrumentation to monitor flight dynamics can be an on-board package or a range setup. On-board packages will have inertial instrumentation and either a telemetry system or a recording system. Range instrumentation usually involves a variety of cameras, radars, and other tracking equipment to record the position and orienta- tion of the rocket. The decision to use on-board or range instrumentation, or a combination of both, varies with the types of rockets, range equipment available, and specific data requirements. Flight test programs allow different component configurations to be demonstrated and the best con- figuration to be verified for use in the final configuration selection process. 2-5.2 .2 Test Plan A test—whether a static test, a wind-tunnel test, or a flight-test- should have a specific set of clearly defined objectives. These objectives are best accomplished by a carefully planned test. Testing proce- dures may vary for different types of tests, but the fundamentals of planning, conducting, and analyz- ing the results of any test are similar. Data required to determine whether the test objective is met must be specified. The models or equipment needed to provide test data are then determined, and instrumen- tation required to measure and record data is identified. The method of reducing and analyzing the data is then determined. Once all this information is available, the test plan can be written. The test plan is the documentation to support and define the operations to accomplish the test objectives. The next paragraph describes the essential contents of a test plan. A test plan should include an introduction, a model description, instrumentation requirements, operation requirements, data reduction and presentation requirements, a run schedule, and model drawings. Each element is discussed further: 1. Introduction. Presents information about test location, test date, and the objective of the testing to be performed. It also names the test engineer and delineates distribution of the test data. 2. Model Description. Includes a description of the model construction, a reference to the rocket configuration represented by the model, and a description of the coordinate system used to identify instrumentation. The model description includes dimensional data showing a comparison between full-scale rocket dimensions compared to model dimensions. 3. Instrumentation Description. Delineates the number and types of instrumentation to be used in the test program. The locations of all instrumentation on the model are defined by coordinate location and by sketches of the model. 4. Operations. Required sequence of events to conduct the test and the delineation of responsibili- ties for model preparation, test preparation, instrumentation, test conduction, data reduction, and data analysis. Operations includes specifying which instrumentation fits into which data set and describes the process of conducting the test. The definition of the test conditions and parameters to be measured and recorded is part of operations. Specific data requirements such as photographs are part of the operations portion of the test plan. 5. Data Reduction. Specifics the procedure for transforming the raw instrumentation data into useful engineering parameters. Specific algorithms for transforming data are supplied in the test organization. Data formats for returning test data to the designer or other ultimate user are specified. 6. Run Schedule. Includes model geometry and altitude data, tunnel Mach number and Reynolds number, and instrumentation set to be used for each test run. The run schedule also defines all runs to be performed. 2-27 MIL-HDBK-762(MI) 7. Model Drawing. Provided for use in manufacturing the models. The drawings spedify material requirements, surface finish requirements, machining operations, method of attachment of parts, and instrumentation installation processes. The conduct of a successful test program requires considerable consideration between the requesting organization and the organization conducting the tests. For the user to receive the desired information from a test program, it is necessary for him to know the quantities that can be instrumented, the accuracy of the data that can be obtained, the test conditions available to obtain the data, and what is required of the model or test item. Information exchange or system integration is very important for the conduct of a successful test program. 2 - 5 . 3 S Y S T E M I N T E G R A T I O N System integration is an important function in all phases of the development of a rocket system; it is to assure compatibility of all elements of the system. All the functions performed in the preliminary design phase continue in the system validation phase. Integration and coordination of activities and data increase in importance in the system validation phase. This is the phase during which prototype hardware is fabricated, testing and final system designs are performed, and manufacturing require- ments and field support and training needs are defined. During the system validation phase, the system design becomes sufficiently firm and detailed; accordingly, changes may be difficult and very costly to implement. Simulations are used to aid in the integration of the various system components into an overall functional system. As subsystems are designed and tested, simulations can be updated to reflect actual hardware dynamics and functional responses. The overall system is simulated to assure the ability of the system to meet the requirements. Costing for the overall system is updated. Life cycle costing is performed to provide data for the cost-effectiveness trade-offs performed before commitment to production. Manufacturing processes and availability considerations feed into the design. Materials for the fabrication of particular items are considered. The cost and availability of mate- reals, manufacturing processes, availability of tooling, and reiablility of the finished product all are considerations for system integration in the system validation phase. The reliability of the system, as expected in the field, is determined in the system validation phase. Failure rates for the components, subsystems, and the system are determined and used in life cycle costing and overall system effectiveness studies. Maintainability and logistic requirements for support- ing the system in the field are determined. Training requirements for operation and maintenance are defined and furnish information into the life cycle costing studies. The configuration management aspects of system integration continue in the system validation phase, and additional emphasis is placed on interface and change controls. Any changes to the system must be properly cooridated and evaluated to determine the effect on any and all elements of the system. The impact of the change of performacne, reliability, producibility, maintainability, cost, etc., must be evaluated before any changes can be allowed. In summary, the system integration function is very important in the development, manufacture, and fielding of a cost-effective rocket system. R E F E R E N C E S 1. DoD Directive No. 5000.1, Major System Acquisition, 29 March 1982. 2. DoD Directive No 5000.2, Major System Acquisition Process, 8 March 1983. 3. DoD Directive No. 5000.3, Test and Evaluation, 26 December 1979. 4. DoD Directive No. 5000.4, OSD Cost Analysis Improvement Group, 13 June 1973. 5. DARCOM-P 706-101, Engineering Design Handbook, Army Weapon Systems Analysis, Part One, November 1977. 2-28 MIL-DBK-762(MI) C H A P T E R 3 P E R F O R M A N C E The chapter prevents information for use in determining the free rocket physical characteristics that result from mission range and payload requirements. Idealized velocity requirement estimates are pre- sented in equation form. Also included are equations and figures useful in the estimation of additional velocity requirements resulting from aerodynamic drag and gravitationale effects. Data for several classes of rockets are presented. Figures depicting parametric relationships useful to the performance design function are presented. These parametric data are useful in design trade-offs and in establishing limits on some parameters for several classes of free rockets. A numerical example is presented to illustrate the use of the information and data presented in the chapter. 3 - 0 L I S T O F S Y M B O L S A ref = B = B bo = C D = C D B = C D bO = C D C = ( CD B)bo = d ref = F B = F D = F S = G = g 0 = H = H max = † Isp = I S/ IB = , aerodynamic reference area, m2 m/(CdA ref), ballistic coefficient, kg/m 2 m bo/(CDbOA ref), ballistic coefficient immediately after motor burnout, kg/m 2 FD/(qA ref), aerodynamic drag coefficient, dimensionless instantaneous drag coefficient during rocket flight (boost), dimensionless aerodynamic drag coefficient immediately after rocket motor burnout, dimensionless instantaneous drag coefficient during rocket unpowered flight (coast), dimensionless aerodynamic drag coefficient immediately before rocket motor burnout, dimensionless aerodynamic reference length, m thrust of rocket booster motor, N aerodynamic drag force, N thrust of rocket sustainer motor, N FB/(m0g0), initial acceleration level of rocket, dimensionless 9.80665 m/s2, reference acceleration due to gravity altitude, m maximum altitude of sounding rocket, m FB/(mg0), rocket motor specific impulse, s ratio of sustainer motor total impulse IS to booster motor total impulse IB, dimensionless †In this chapter, the specific impulse is defined in the traditional sense, i.e., ISP = FB/( g0) with units newton/(newton/second) or second. The equations herein use this definition. In Chapter 6, ISP is defined in a manner consistent with the International System of Units (SI). 3-1 MIL-HDBK-762(MI) ( ISP) S/ ( ISP) B = ratio of sustainer motor specific impulse to booster motor specific impulse X 100, % K = a function accounting for variation of CD, mass, and gravity during boost, kg/ mŽs2 M= Mach number, dimensionless m = rocket mass, kg = rocket motor mass flow rate, kg/s m bo = m0 — mp, rocket mass at motor burnout, kg m p = mass of usable propellant, kg m pld = payload mass, includes all mass not associated with the rocket motor, kg (Usually taken to mean all mass forward of the motor.) m 0 = rocket gross mass at ignition, kg P M F = mp/ ( m0 – m pld), propellant mass fraction, the ratio of propellant mass to the mass associated with the motor, dimensionless 3-2 P a = atmospheric pressure, Pa P c = rocket motor chamber pressure, Pa P c/ Pa = ratio of rocket motor chamber pressure to standard atmospheric pressure, dimensionless Q = m0/ mpld, growth factor, the ratio of rocket gross mass to payload mass. dimensionless QE = quadrant elevation angle, measured positive above horizon, deg or rad as noted q = pV2/2, instantaneous dynamic pressure, Pa R = range, m or km R m a x = maximum range, km r b = m0/ ( m0 — m p), booster mass ratio, the ratio of rocket gross mass to burnout mass, dimensionless t = time, s t a l t = time to altitude, s tb = rocket motor burn time, s t b o = time of rocket motor burnout, s t i m p = time of rocket flight termination, s t t = time to target, s t 0 = time of rocket ignition, s V = velocity, m/s V B = estimate of rocket velocity requirement without drag and gravity losses, m/s v bo = burnout ve loc i ty , m/s V ideal = g 0I SPI n ( rb) = rocket velocity determined by the ideal velocity equation, m/s Vp r o p = total rocket motor propulsive velocity requirement including estimates of drag and gravity effects, m/s = estimate of velocity increment lost to drag during powered flight (boost), m/s = estimate of velocity increment lost to drag during unpowered flight (coast), m/s = estimate of velocity increment lost (or gained) due to gravity effects, m/s MIL-HDBK-762(MI) p = atmospheric density, kg/m3 p 0 = 1.2250 kg/m 3, atmospheric density at standard sea-level conditions 3 - 1 I N T R O D U C T I O N Performance in the context of this handbook, and specifically in this chapter, relates to velocity and impulse characteristics of the rocket. The analysis and determination of performance requirements involve the determination of the velocity and impulse requirements to deliver a given payload to the target at a specific range. Accuracy requirements are not considered part of the performance discussions; accuracy is the subject of Chapter 4. In the design of any rocket, the study of performance parameters is a necessary early step in the trade-off studies of the concept because the parametric performance data 1. Relate the performance to rocket physical characteristics 2. Serve as the basis for trade-off considerations among competing requirements and characteristics 3. Show the sensitivity of the rocket physical characteristics to variations in performance requirements, propulsion system efficiency), aerodynamic characteristics (primarily drag), and energy management technique. Flight performance characteristics are developed using the simple, 2-degrees-of-freedom (DOF), trajec- tory computer programs. The forces acting on the rocket are considered to be thrust, drag, and that due to gravity. In addition, the thrust and drag forces are assume-d to be aligned with the instantaneous flight path angle. Flight performance data can be determined fairly easily by applying these approximations with relatively small computers. The only input data required are the initial mass, propellant consumption rate, burn time, thrust history, and drag coefficient versus Mach number. Performance trade-off studies generally start with the requirement to deliver a specified payload mass to a specified range or altitude. Additional payload requirements that can be imposed include velocity and approach angle at the target or other warhead requirements. General operational requirements may include a total mass limitation, initial boost thrust limits, and overall length limits. The effects of geometry and packaging may also be included in the flight performance analysis. Other data in the form of propulsion data, mass-estimating relationships, and sizing methodologies may be required. The parametric flight performance data for this chapter have been developed by use of a simple computer program. The computer program is described in par. 3-3; a sample methodology for sizing rockets is presented in par. 3-9. Other data in this chapter are presented to show the relationships among the various rocket motor parameters, rocket mass parameters, and rocket performance. The rocket performance and sizing methodology presented in this chapter is meant to be used for preliminary design estimations. The methodology allows the relatively rapid assessment of several rocket configurations in order to narrow the choice among such configurations. More detailed and precise analyses can then proceed on a more limited number of configurational options that are more likely to meet system specifications. ‘Ihe preliminary rocket design effort must be supported by information from several rocket discipline. Achievable thrust and specific impulse estimates, reasonable mass densities for typical rocket sections, and rough estimates of aerodynamic drag coefficients are required in selecting such rocket parameters as length and diameter. These estimates can be found in other chapters of this handbook, from the available rocket literature, and from experience. Approximation techniques are presented that allow the determination of the propulsive velocity requirements. The required propulsive velocity requirement Vprep is presented in terms of an ideal propulsive velocity requirement VB. V B is the velocity at motor burnout in the absence of drag and gravitational effects. Approximate methods of determining the drag and gravity losses are presented. These losses are presented in terms of a velocity requirement due to drag for boost and coast and a gravity requirement . The total propulsive requirement is calculated from an equation of the form: 3-3 MIL-HDBK-762(MI) 3-3.1.1 Indirect Fire Rockets Range and velocity relationships as a function of Bbo and quadrant elevation (QE) for selected indirect fire rockets are presented in Figs. 3-1,3-2, and 3-3 for 130-mm, 762-mm, and 321-mm rockets, respectively. Figure 3-1. Effect of Burnout Ballistic Coefficient and Burnout Velocity on Range-133-mm Rocket Figure 3-2. Effect of Burnout Ballistic Coefficient and Burnout Velocity on Range-762-mm Rocket 3-6 MIL-HDBK-762(MI) Figure 3-3. Effect of Burnout Ballistic Coefficient and Burnout Velocity on Range-321-mm Rocket These data were generated by use of a simple, 2-DOF computer program. The program contained a US Standard atmosphere and gravity as a function of altitude over a flat earth. A more complete discussion of equations of motion for a rocket is found in Chapter 4, “Accuracy”. From these figures, the burnout velocity Vbo requirement is shown to be a strong function of the ballistic coefficient Bbo immediately after burnout. The larger the value of Bbo, the lower the burnout velocity Vbo requirement for a given range. The aerodynamic drag coefficient CD for each of the selected rockets is presented in Figs. 3-4 through 3-6, along with a line drawing of each rocket. The boost velocity VB requirement, neglecting drag and gravity effects, is given by where R = g 0 = QE = range from launcher to target, m 9.80665, m/s2, reference acceleration of gravity quadrant elevation angle, measured positive above horizontal, rad. (3-2) This equation is usable for ranges less than .500 km in which a flat earth approximation is acceptable. Equations for longer ranges, including an oblate rotating earth, can be obtained from Ref. 1. The burnout velocity that would be required in a drag-free environment can be determined from Figs. 3-1 through 3-3 as Bbo approaches infinity. The velocity loss ,due to drag during the coast phase is developed by the following equation: ( 3 - 3 ) Rewriting, ( 3 - 4 ) 3 - 7 MIL-HDBK-762(MI) w h e r e (3-5) = velocity lost to drag during the coast phasse, m/s tbo = time of rocket motor burnout, s timp = time of flight termination due to impact or warhead detonation, s C D C = instantaneous drag coefficient during coast, dimensionless q = instantaneous dynamic pressure, Pa A ref = rocket reference area, m 2 m bo = rocket mass at motor burnout, kg Bbo = rocket ballistic coefficient immediately after rocket motor burnout, kg/m 2 CDbo = aerodynamic drag coefficient, immediately after rocket motor burnout, dimensionless. Eq. 3-4 shows to be the product of the reciprocal of Bbo multiplied by the integral of the drag coefficient variation from burnout to impact multiplied by the dynamic pressure. The velocity loss during coast for the 130-mm rocket is presented in Fig. 3-7. Fig.3-7 shows that a rocket with a burnout ballistic coefficient Bbo of 10 4kg/m 2 will lose approximately half or more of the boost velocity Vbo as a result of drag. This maximum drag loss reduces the range to approximately 70% of the drag-free range. An additional velocity loss resulting from drag occurs during boost. The boost velocity loss is described Figure 3-4. Drag Coefficient vs Mach Number-HO-mm Rocket 3-8 MIL-HDBK-762(MI) Figure 3-7. Coast Drag Velocity Loss-130-mm Indirect Fire Rocket 3-11 MIL-HDBK-762(MI) Figure 3-8. Boost Drag Velocity Loss-Indirect Fire Rocket where V B = no-loss boost velocity from Eq. 3-9, m/s p 0 = 1.2250 km/m 3, atmospheric density at sea level R = range traversed during the coast (unpowered) portion of direct fire flight, m. The effects of gravity are not insignificant, but a small positive flight path angle can compensate for the losses at the ranges usually encountered in direct fire rockets. The boost velocity loss for typical direct fire rockets is presented in Fig. 3-9. The propulsive velocity requirement Vprop for typical direct fire rockets, neglecting gravity, is 3-3.1 .3 Sounding Rockets The drag-free boost velocity requirement VB for a vertically launched rocket is a function of the maximum altitude Hmax and is given by (3-11) (3-12) where H m a x = maximum altitude to be achieved, m. The drag loss during coast is presented in Fig. 3-10. The drag loss during boost is presented in Fig. 3-11. Eq. 3-7 given an additional loss term required in the calculation of boost velocity which is the velocity loss caused by gravity. 3-12 MIL-HDBK-762( MI) Figure 3-9. Boost Drag Velocity Loss-Direct Fire Rocket The total propulsive velocity requirement Vprop for the sounding rocket is given by (3-13) 3-3.1 .4 Surface-To-Air Rockets The drag-free boost velocity VB for vertically launched rockets to a given altitude is given by (3-14) where H = altitude desired, m t al t = estimated or required time to altitude, s. The velocity loss from drag during coast is presented in Fig. 3-12. The boost velocity loss from drag is presented in Fig. 3-13. The boost velocity loss from gravity is approximated by Eq. 3-7. Thus, the total propulsive velocity requirement Vprop for surface-to-air rockets may be expressed as (3-15) 3-3.1 .5 Air-To-Surface Rockets Air-to-surface rockets are similar to direct fire rockets except they are fired from airplanes or helicopters. The altitude of fire for free rockets is generally less than 2 km. The velocity requirement VB for air-to- surface rockets can be estimated from the direct fire Eq. 3-9, except that R is now interpreted as the slant range from aircraft to target. The velocity loss during coast can be estimated from Eq. 3-10, where R is again interpreted as the coast slant range from aircraft to target. Air-to-surface rockets generally have a range of less than 8 km. 3-13 MIL-HDBK-762(MI) Figure 3-12. Coast Drag Velocity Loss-Surface-to-Air Rocket 3 - 1 6 MIL-HDBK-762(MI) Figure 3-13. Boost Drag Velocity Loss-Surface-to-Air Rocket are performed. An iteration procedure may be required unless the velocity requirements are developed parametrically in terms of the burnout ballistic coefficient Bbo. The paragraphs that follow will develop the mass characteristics of the rocket by using the velocity requirement and propulsive system parameters. For the purposes of this chapter, rocket mass will be grouped into two major components, i.e., 1. Payload mass mpld, i.e., all mass forward of the forward motor-closure 2. Motor mass mm, i.e., all mass aft of the forward motor-closure. The relationship between the propulsion system ideal velocity Videal and the rocket gross mass is given by the Ideal Velocity Equation (3-18) or (3-19) where I S P = rocket motor specific impulse, s m 0 = rocket gross mass at ignition, kg m p = usable propellant mass of motor, kg r b = m0/ ( m0 — mp), booster mass ratio, dimensionless. The Ideal Velocity Equation relates the burnout velocity of a rocket to specific rocket motor parameters, i.e., ISP and rb. Note that gravity and aerodynamic velocity effects are not included, hence the name ideal. The propulsive velocity of a multistage rocket can be developed in a manner similar to Eq. 3-19. Ref. 4 presents the equations for calculating the ideal velocity of a propulsion system for a multiple stage rocket system. The booster mass ratio rb and the specific impulse ISP determine the ideal burnout velocity of the 3-17 MIL-HDBK-762(MI) propulsion system. The ideal burnout velocity is presented in Fig. 3-14 for various values or rb and ISP. The variation in mass of the rocket may be estimated from the propellant consumed by using Eq. 3-21. The specific impulse ISP of the motor is related to the thrust FB of the rocket booster motor and propellant Figure 3-14. Effect of Ideal Burnout Velocity on Booster-Mass Ratio 3-18 MIL-HDBK-762(MI) Some large ballistic rockets are launched vertically; however, they require a maneuver to tilt the rocket onto a ballistic path. The discussion that follows will be limited to the nonmaneuvering types of rockets. Among the methods that have been used to impart propulsive energy to indirect-fire rocket systems are 1. Boost 2. Boost/sustain 3. Staged boost. Each method is briefly discussed in the paragraphs that follow. In the boost method, the booster motor fires for a portion of the flight time after which there is a coast phase to the target. This approach is the least complex of the three and has been used extensively in the field of unguided ballistic rockets. The boost! sustain method consists of an initial thrust by the booster motor, followed by a sustaining thrust of lesser magnitude. Although this approach offers performance advantages over the boost approach for some applications, it requires a more complex and costly motor construction. In the staged-boost method, the total thrust is delivered by a series of booster motors, each of which is jettisoned upon burnout. This is the most efficient means of energy management, but its use is limited to those cases for which mass considerations override the cost and reliability penalties of staging, and for which the hazards of falling motor cases can be tolerated. The staged-boost approach is most efficient for very long-range and extreme velocity applications. As the range increases, the growth factor Q increases. An all-boost system would require a larger growth factor than that of the first stage of a staged-boost system. This is so because the mpld of the first stage is the mass of the second stage rocket motor and the second stage mpld. 3 - 4 . 2 P A R A M E T R I C P E R F O R M A N C E D A T A The relationship between growth factor and range for an indirect fire rocket system is a function of the following parameters: QE = launch elevation angle, deg ISP = rocket motor specific impulse, s PMF = propellant mass fraction, dimensionless Bbo = burnout ballistic coefficient immediately after burnout, kg/m 2 G = initial boost acceleration ratio, dimensionless F S/ FB = ratio of sustainer motor to rocket booster motor thrust, dimensionless IS/ IB = ratio of sustainer motor total impulse to booster motor total impulse, dimensionless. The angle at which the rocket must be launched to achieve maximum range is of initial interest to the designer. Fig. 3-16 presents the effect of initial acceleration ratio G and growth factor Q on the optimum launch angle for an all-boost system with fixed values of ISP, PMF, and Bbo. Although the data would be different if these parameters were varied, the trends of the curve are worth noting. Low G-rockets require higher launch angles to achieve maximum range. Higher growth factors Q also require higher launch angles (QE) because the Qs are equivalent to longer boost burning times at any given G. For a boost/ sustain system, as shown in Fig. 3-17, the optimum launch angle will be slightly greater than for an all-boost system. As the ratio FS/ FB is decreased and/or the ratio IS/ IB is increased, an increase in the optimum launch angle is indicated. One noteworthy point about Fig. 3-17—and other figures where FS/FB or IS/ FB are depicted—is that when either ratio is zero, the all-boost case is indicated. Fig. 3-18 presents the relationship between Q and range R for an all-boost system with the QE optimized and PMF, ISP, and Bbo held constant. Note that the lower accelerations permit more efficient energy management because they require a lower growth factor for any specified range. In this sense, the selection of G is also an energy-management technique. Although Fig. 3-18 is constructed for only one value each of ISP, PMF, and Bbo, it is indicative of trends. Therefore, we may say that the growth factor Q for a given range will be inversely proportional to ISP, PMF, and Bbo. The designer would, of course, examine trade-offs among these parameters as discussed later in this chapter. Another trend of significance to the designer or to the originator of requirements may be noted on Fig. 3-18. Examination of the curve shows that significant increases in range can be obtained for relatively minor rocket mass increases. For example, a 3-21 MIL-HDBK-762(MI) Figure 3-16. Indirect Fire—Roost; Effect of Initial Acceleration Level on Optimum Launch Quadrant Elevation Figure 3-17. Indirect Fire—Boost/Sustain; Effect of Impulse Ratio on Optimum Launch Quadrant Elevation growth factor of about Q = 2 is required for a range of 30 km; however, a 25% increase in rocket mass (an increase of Q from 2.0 to 2.5) doubles the range to 60 km. The relationship between Q and range R for a boost sustain system will be dependent upon the choice of sustainer parameters in addition to the parameters discussed for the all-boost system. There is no unique method for determining optimum sustainer parameters since the choice will depend upon which charac- teristics, e.g., mass or accuracy, of the rocket the designer is attempting to optimize. The designer has a choice of methods to provide the sustainer impulse. This can be accomplished with separate booster and sustainer motors or by one motor with two thrust levels. In the case of separate motors, it is possible to achieve high specific impulse with each motor, but the propellant mass fraction of the combination is usually lower than for a single motor. In the case of a single motor with two thrust levels, the specific impulse of the sustainer motor will be less than that for the booster motor if a constant- geometry nozzle is used (due to decreased chamber pressure during the sustainer phase). For this discussion it will be assumed that a single motor with two thrust levels and fixed nozzle geometry is used. The relationship between the ratio of FS/FB and the resulting ratio IS IB of specific impulses is presented in Fig. 3-19; both ratios are expressed as percent. 3-22 MIL-HDBK-762(MI) Figure 3-18. Indirect Fire—Boost; Effect of Range on Growth Factor Figure 3-19. Boost/Sustain Engine; Variation of Specific Impulse with Thrust 3 - 2 3 MIL-HDBK-762(MI) 3 - 5 P A R A M E T R I C P E R F O R M A N C E D A T A F O R D I R E C T - F I R E S Y S T E M S 3 - 5 . 1 D E L I V E R Y T E C H N I Q U E S When the free rocket is used as a direct fire weapon, the ballistic trajectory flown is essentially flat. For example, a ballistic trajectory with a maximum altitude of 30 m at its apex has about the same range versus time relationship as a line-of-sight trajectory for ranges to 5 km. The relationships presented in this paragraph may be used for guided, direct fire rockets because the degree of maneuvering is usually small. Among the commonly employed energy-management techniques for direct fire rockets are 1. Boost 2. Boost/sustain 3. Boost/coast/sustain. The choice here will depend to some extent on the level of performance required and on the intended method of use. Considering the method of use, one must determine whether burning outside the launch tube can be permitted. In the case of direct fire infantry weapons, this usually cannot be permitted, whereas for weapons to be employed on armored vehicles, burning outside the launch tube is no problem aside from accuracy considerations. If burning outside the launch tube is permitted, either the boost or the boost/sustain approaches will be applicable. However, where burning outside the tube is not permitted, the choice is between the boost and the boost/coast/sustain approaches, with the boost approach generally limited to low performance systems by the maximum velocity that can be attained within the limitations of the tube length and the rocket acceleration. Of the three energy-management techniques mentioned, the all-boost technique is the simplest to implement. The boost/sustain requires a more complex motor involving the ignition of the sustainer propellant after the boost propellant is consumed. The boost coast sustain possesses a similar sustainer ignition problem plus an added source of dispersion due to the timing uncertainties associated with the coast phase. In most applications, the coast period is short and the technique approaches the boost sustain technique as a limit. The major application of the boost coast sustain technique would be in a role in which a high impulse is imparted to the rocket within the launch tube, followed by a brief coast period during which the rocket is allowed to move away from the launcher. The high performance is achieved by the sustainer burn. This technique protects the launcher (infantryman or aircraft) from the effects of the rocket plume. 3 - 5 . 2 P A R A M E T R I C P E R F O R M A N C E D A T A The relationship among growth factor, range, and time of flight is a function of the following parameters: ISP = rocket motor specific impulse, s PMF = propellant mass fraction, dimensionless Bbo = ballistic coefficient immediately after motor burnout, kg/m 2 G = initial boost acceleration ratio, dimensionless F S/ FB = ratio of sustainer motor thrust to booster motor thrust, dimensionless IS/ IB = ratio of sustainer motor total impulse to booster motor total impulse, dimensionless. Fig. 3-24 presents the relationship among target range, time of flight, and energy-management tech- nique for a given set of rocket characteristics. The energy-management technique of choice is noted to be all boost, i.e., IS/ IB = 0, in cases where a minimum time of flight is desired. This is usually the case for aerodynamically stabilized free rockets. It is desirable to concentrate, for the remainder of this discussion, on the boost system that has the minimum time of flight. Fig. 3-25 presents trade-offs with respect to growth factor Q, time-to-target t t, range R, and boost acceleration ratio G. Note that the dashed lines of Fig. 3-25 represent the locus of rocket motor burnout points. A performance limit appears to be reached at a growth factor of about 3. Increases beyond this point reduce the time of flight by an insignificant amount. Increasing the boost acceleration ratio G reduces the time of flight, but decreases the percentage of powered flight. For example, from Fig. 3-25(A) at a growth factor of 1.7 and G = 20, the burning distance is about 1.2 km, and 3 km is attained in 7.5s. If G is increased 3-26 MIL-HDBK-762(MI) Figure 3-24. Direct Fire—Boost/Sustain; Effect; of Impulse Ratio on Time to Target to 80, Fig. 3-25(C) shows the burning distance is reduced to about 0.5 km, and 3 km is attained in 6.5s. This illustration points out another of the choices facing the designer, i.e., the trade-off between time to target and percentage of powered flight. Once the designer has examined the trade-offs between range and time to target, he may wish to determine the effects of various design parameters on the rocket mass (growth factor) for a specified performance level. For example, Fig. 3-26 shows the trade-oft among Bbo, G, and Q for a specified performance level of achieving 2 km range in 3s. Fig. 3-27 illustrates the trade-off among PMF, ISP, and Q for the same performance level. In the preceding subparagraphs an attempt has been made to illustrate the types of trade-offs of concern to the designer of direct fire rockets. From the preceding discussion, the following conclusions can be drawn: 1. For minimum time to target, the all-boost system is superior to the boost/sustain system. 2. The choice of boost acceleration must result from a consideration of the trade-off between time to target and the percentage of powered flight desired. 3. Increasing PMF, ISp, Bbo, or G results in decreased rocket mass for a given payload weight and specified time to target. 4. Increasing the growth factor beyond about 3.0 results in a negligible performance increase for the range of parameters presented. 3-27 MIL-HDBK-762(MI) Figure 3-25. Direct Fire—Boost; Effect of Growth Factor on Time to Target for Various G Values (cont’d on next page) 3-28 MIL-HDBK-762(MI) Figure 3-26. Direct Fire—Boost; Effect of Ballistic Coefficient on Growth Factor Figure 3-27. Direct Fire—Boost; Effect of Propellant Mass Fraction on Growth Factor 3-31 MIL-HDBK-762(MI) 3 - 6 P A R A M E T R I C P E R F O R M A N C E D A T A F O R S O U N D I N G R O C K E T S 3 - 6 . 1 D E L I V E R Y T E C H N I Q U E S Sounding rockets are generally launched at quadrant elevation angles (QE 85 deg) near the vertical. To simplify data presentation of the significant parameters, a vertical launch is considered. The energy-management techniques that are most commonly used for sounding rockets are 1. Boost 2. Staged boost. Boost/sustain is seldom used. The all-boost system generally is used for low altitude (under 40 km) sounding rockets, and staged boost generally is used for high altitudes (greater than about 90 km). For intermediate altitudes, trade-off studies should be made considering cost and reliability. Fig. 3-28 presents velocity versus summit altitude relationships for the all-boost sounding rocket. The advantages of the all-boost system are simplicity of design and higher reliability. The staged boost will out perform the all-boost system at higher altitudes, but suffers from the disadvantage of being more complex and potentially less reliable. The dropped stages must also be considered a disadvantage because they will also impact the ground. 3 - 6 . 2 P A R A M E T R I C P E R F O R M A N C E D A T A The relationship between Q and peak altitude for a sounding rocket is a function of the following parameters: I S P = rocket motor specific impulse, s PMF = propellant mass fraction, dimensionless Bbo = ballistic coefficient immediately after motor burnout, kg/m 2 G = initial boost acceleration ratio, dimensionless F S/ FB = ratio of sustainer motor thrust to booster motor thrust, dimensionless I S/ IB = ratio of sustainer motor total impulse to booster motor total impulse, dimensionless. In Fig. 3-29 the relationship among Q, energy-management technique G, and peak altitude is presented. The boost/sustain approach for a given altitude, would provide a slight reduction in Q. Although Fig. Figure 3-28. Effect of Burnout Ballistic Coefficient and Burnout Velocity on Summit Altitude—133-mm Rocket 3-32 MIL-HDBK-762(MI) Figure 3-29. Sounding Rocket— Boost; Effect of Growth Factor on Summit Altitude 3-29 presents only one value each of ISP, PMF, and Bbo, a reduction in any of these parameters will result in an increase in the growth factor Q. For a given maximum altitude, Q will be inversely proportional to PMF, ISP, and Bbo. This is shown in Figs. 3-30 and 3-31 for peak altitudes of approximately 45 and 75 km. Although these curves depict the boost/coast case, the boost/sustain curves would be similar at slightly lower Q. The figures indicate that the minimum rocket gross mass m0 results from a high performance motor (high PMF and ISP) and a large burnout ballistic coefficient Bbo for the same payload mass mpld—i.e., results in a low Q. Parametric performance data for staged-boost sounding rockets can be obtained from Ref. 5. Typical performance data for staged-boost sounding rockets are available from Refs. 6 through 8. 3 - 7 P A R A M E T R I C P E R F O R M A N C E D A T A F O R S U R F A C E - T O - A I R R O C K E T S 3 - 7 . 1 D E L I V E R Y T E C H N I Q U E S The unguided surface-to-air rocket flies a ballistic trajectory and may be launched at any QE angle necessary for intercept of the target. Usually, the rocket will be required to attain a given altitude in a given time, and, therefore, the ascent is of interest for parametric data presentation. Energy-management techniques applicable to surface-to-air rockets are 1. Boost 2. Boost/sustain 3. Staged boost. If we consider that minimum time to altitude will be desired for the surface-to-air rocket and that achievable accuracy will limit this type of rocket to low altitude application, typically under 9 km, the boost approach usually will be the most attractive. For this reason the discussion will be limited to the 3-33