Calhoun: The NPS Institutional Archive Theses and Dissertations Thesis Collection 2005-06 Time-optimization of high performance combat maneuvers Carter, Benjamin R. Monterey, California. Naval Postgraduate School http://hdl.handle.net/10945/2176 NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS TIME-OPTIMIZATION OF HIGH PERFORMANCE COMBAT MANEUVERS by Benjamin R. Carter June 2005 Thesis Advisor: R.M. Howard Co-Advisor: I.M. Ross Approved for public release; distribution is unlimited. THIS PAGE INTENTIONALLY LEFT BLANK REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0188 Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instruction, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188) Washington DC 20503. 1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED June 2005 Master’s Thesis 4. TITLE AND SUBTITLE: 5. FUNDING NUMBERS Time-Optimization of High Performance Combat Maneuvers 6. AUTHOR(S) LTjg Benjamin R. Carter, USN 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING Naval Postgraduate School ORGANIZATION REPORT Monterey, CA 93943-5000 NUMBER 9. SPONSORING /MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORING N/A AGENCY REPORT NUMBER 11. SUPPLEMENTARY NOTES The views expressed in this thesis are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government. 12a. DISTRIBUTION / AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE Approved for public release; distribution is unlimited. 13. ABSTRACT (maximum 200 words) Recent developments in post-stall maneuverability and thrust vectoring have opened up new possibilities in the field of air combat maneuvering. High angle of attack maneuvers like the Cobra, Herbst Reversal, and Chakra demonstrate that today’s cutting edge fighters are capable of exploiting the post-stall flight regime for very dynamic and unconventional maneuvers. With the development and testing of Unmanned Combat Aerial Vehicles, even greater maneuvering ability is expected. However, little work has been done to make use of this increased ability by optimizing a wide range of combat maneuvers. The goal of this thesis was to begin that process by finding several time-optimal air combat maneuvers that could be employed by current and future high performance fighter aircraft. 14. SUBJECT TERMS 15. NUMBER OF ACM, air combat maneuvering, maneuver optimization, minimum time maneuvers, Cobra, Herbst, PAGES post-stall, thrust vectoring, F-18, HARV, X-31, DIDO 243 16. PRICE CODE 17. SECURITY 18. SECURITY 19. SECURITY 20. LIMITATION CLASSIFICATION OF CLASSIFICATION OF THIS CLASSIFICATION OF OF ABSTRACT REPORT PAGE ABSTRACT Unclassified Unclassified Unclassified UL NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89) Prescribed by ANSI Std. 239-18 i THIS PAGE INTENTIONALLY LEFT BLANK ii Approved for public release; distribution is unlimited. TIME-OPTIMIZATION OF HIGH PERFORMANCE COMBAT MANEUVERS Benjamin R. Carter Lieutenant Junior Grade, United States Navy B.S., United States Naval Academy, 2002 Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN AERONAUTICAL ENGINEERING from the NAVAL POSTGRADUATE SCHOOL June 2005 Author: Benjamin R. Carter Approved by: Professor R.M. Howard Thesis Advisor Professor I.M. Ross Co-Advisor Distinguished Professor Anthony J. Healey Chairman, Department of Mechanical and Astronautical Engineering iii THIS PAGE INTENTIONALLY LEFT BLANK iv ABSTRACT Recent developments in post-stall maneuverability and thrust vectoring have opened up new possibilities in the field of air combat maneuvering. High angle of attack maneuvers like the Cobra, Herbst Reversal, and Chakra demonstrate that today’s cutting edge fighters are capable of exploiting the post-stall flight regime for very dynamic and unconventional maneuvers. With the development and testing of Unmanned Combat Aerial Vehicles, even greater maneuvering ability is expected. However, little work has been done to make use of this increased ability by optimizing a wide range of combat maneuvers. The goal of this thesis was to begin that process by finding several time- optimal air combat maneuvers that could be employed by current and future high performance fighter aircraft. The aircraft used for this study were the Navion, F-18 HARV and UCAV-X (a fictitious aircraft based on the X-31 EFM). Extremely detailed physical and aerodynamic models were developed for all three aircraft, including thrust vectoring data on the latter two. Different methods of coding the aerodynamic data (including look-up tables and curve-fitting) were experimented with to determine what provided the best balance of accuracy and efficiency. The optimization program used was DIDO, which is a MATLAB-based application package for solving dynamic optimization problems developed at the Naval Postgraduate School. The “aircraft code” that interfaces with DIDO (originally written by a previous thesis student) was modified to function with the HARV and UCAV-X. Further modifications were added to improve numerical stability and decrease run times. Finally, time-optimal maneuvers developed by DIDO were compared to 1) similar maneuvers performed by other test aircraft, 2) optimal maneuvers derived in other studies, and 3) current air combat maneuvers. v THIS PAGE INTENTIONALLY LEFT BLANK vi TABLE OF CONTENTS I. BACKGROUND ..........................................................................................................1 A. AIR-TO-AIR COMBAT .................................................................................1 B. POST-STALL FLIGHT ..................................................................................4 1. Supermaneuverability .........................................................................6 C. THRUST VECTORING .................................................................................8 D. UNMANNED COMBAT AERIAL VEHICLES.........................................10 II. AIR COMBAT MANEUVERING ...........................................................................13 A. DISCUSSION .................................................................................................13 B. PERFORMANCE CRITERIA.....................................................................14 C. SAMPLE MANEUVERS ..............................................................................16 1. Split-S..................................................................................................16 2. Low Yo-Yo..........................................................................................17 3. Rolling Scissors...................................................................................18 4. Cobra...................................................................................................19 5. Herbst Reversal..................................................................................20 D. FAMILIES OF MANEUVERS ....................................................................22 III. EQUATIONS OF MOTION.....................................................................................25 A. INTRODUCTION..........................................................................................25 B. STATES ..........................................................................................................26 1. Position................................................................................................26 2. Velocity................................................................................................26 3. Body Rates ..........................................................................................27 4. Euler Angles .......................................................................................28 C. SIX-DEGREE-OF-FREEDOM EQUATIONS OF MOTION ..................28 1. Position Equations .............................................................................29 2. Velocity Equations .............................................................................29 a. Forces ......................................................................................30 3. Body Rate Equations .........................................................................32 a. Moments ..................................................................................33 4. Euler Angle Equations.......................................................................35 5. Complete Equations...........................................................................36 D. STABILITY AND CONTROL DERIVATIVES ........................................37 E. CONTROLS ...................................................................................................39 IV. AERODYNAMIC MODELS....................................................................................41 A. SELECTED TEST AIRCRAFT...................................................................41 B. NAVION .........................................................................................................41