Calhoun: The NPS Institutional Archive Theses and Dissertations Thesis and Dissertation Collection 2016-09 Predicting the accuracy of unguided artillery projectiles Lim, Wee Yeow Monterey, California: Naval Postgraduate School http://hdl.handle.net/10945/50581 NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS PREDICTING THE ACCURACY OF UNGUIDED ARTILLERY PROJECTILES by Wee Yeow Lim September 2016 Thesis Advisor: Morris R. Driels Second Reader: Christopher A. Adams 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 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED (Leave blank) September 2016 Master’s thesis 4. TITLE AND SUBTITLE 5. FUNDING NUMBERS PREDICTING THE ACCURACY OF UNGUIDED ARTILLERY PROJECTILES 6. AUTHOR(S) Wee Yeow Lim 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 10. SPONSORING / ADDRESS(ES) MONITORING AGENCY N/A 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. IRB Protocol number ____N/A____. 12a. DISTRIBUTION / AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE Approved for public release. Distribution is unlimited. 13. ABSTRACT (maximum 200 words) A method for predicting the accuracy of unguided artillery projectiles is presented in this thesis. The goal was to develop a standalone program that would estimate accuracy without the need for a large database of weapon trajectory data. The presented method uses a simplified version of the modified point mass trajectory model and error computation models to predict error metrics that are particularly useful in predicting damage effects on various types of targets using the Joint Weaponeering System (JWS). The developed program is coded in Visual Basic, and the error metrics can typically be computed in less than 30 seconds for most ranges, in the computation precision specified in this thesis. The program was verified by comparing it against the FT 155-AM-02 firing table for the M107(HE) 155mm artillery projectile. The verification results demonstrate that the developed trajectory model closely matches the basic trajectory data to within 2% and ballistic partials to within 7% for most ranges of interest. Accuracy metrics derived from the ballistic partials generated from the developed program are within 10% of those derived from the firing table’s ballistic partials for typical firing ranges. The model is able to take into account wind effects and varying levels of meteorological data staleness. The developed program is named the Indirect Fire Delivery Accuracy Program (IFDAP), and it can be used to predict accuracies for any unguided projectile given the required aerodynamic coefficients, physical properties, and error budgets. 14. SUBJECT TERMS 15. NUMBER OF accuracy, error, artillery, unguided, modified point mass, indirect fire PAGES 139 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 UU 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. PREDICTING THE ACCURACY OF UNGUIDED ARTILLERY PROJECTILES Wee Yeow Lim Captain, Singapore Armed Forces M.Eng., University College London, 2012 Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN MECHANICAL ENGINEERING from the NAVAL POSTGRADUATE SCHOOL September 2016 Approved by: Morris R. Driels Thesis Advisor Christopher A. Adams Second Reader Garth V. Hobson Chair, Department of Mechanical and Aerospace Engineering iii THIS PAGE INTENTIONALLY LEFT BLANK iv ABSTRACT A method for predicting the accuracy of unguided artillery projectiles is presented in this thesis. The goal was to develop a standalone program that would estimate accuracy without the need for a large database of weapon trajectory data. The presented method uses a simplified version of the modified point mass trajectory model and error computation models to predict error metrics that are particularly useful in predicting damage effects on various types of targets using the Joint Weaponeering System (JWS). The developed program is coded in Visual Basic, and the error metrics can typically be computed in less than 30 seconds for most ranges, in the computation precision specified in this thesis. The program was verified by comparing it against the FT 155-AM-02 firing table for the M107(HE) 155mm artillery projectile. The verification results demonstrate that the developed trajectory model closely matches the basic trajectory data to within 2% and ballistic partials to within 7% for most ranges of interest. Accuracy metrics derived from the ballistic partials generated from the developed program are within 10% of those derived from the firing table’s ballistic partials for typical firing ranges. The model is able to take into account wind effects and varying levels of meteorological data staleness. The developed program is named the Indirect Fire Delivery Accuracy Program (IFDAP), and it can be used to predict accuracies for any unguided projectile given the required aerodynamic coefficients, physical properties, and error budgets. v THIS PAGE INTENTIONALLY LEFT BLANK vi TABLE OF CONTENTS I. INTRODUCTION..................................................................................................1 A. BACKGROUND ........................................................................................1 1. Types of Artillery Fire ...................................................................2 2. Errors Associated with Artillery Firing .......................................3 B. PURPOSE ...................................................................................................5 C. PROBLEM DESCRIPTION AND PROPOSED SOLUTION ..............5 D. METHODOLOGY ....................................................................................6 E. OUTLINE OF THESIS .............................................................................6 II. BALLISTICS .........................................................................................................9 A. INTERNAL BALLISTICS .......................................................................9 B. EXTERNAL BALLISTICS ....................................................................10 1. Drag ...............................................................................................10 2. Stability .........................................................................................13 3. Lift (Out of Plane Motion) ..........................................................13 4. Coriolis Effect ...............................................................................20 5. Magnus Effect...............................................................................21 C. TERMINAL BALLISTICS ....................................................................22 III. TRAJECTORY MODELS ..................................................................................25 A. POINT MASS, ZERO DRAG TRAJECTORY MODEL - 2 DOF, RANGE ONLY ..............................................................................25 1. Model Inputs.................................................................................27 2. Range for a Given Firing Angle ..................................................27 3. Firing Angle for a Given Range ..................................................28 4. Firing Tables.................................................................................29 5. Discussion of Model Predictions .................................................30 B. MODIFIED POINT MASS TRAJECTORY MODEL (MPMTM) ................................................................................................31 C. INDIRECT FIRES DELIVERY ACCURACY PROGRAM (IFDAP) TRAJECTORY MODEL - 4 DOF, RANGE, AND DEFLECTION .........................................................................................32 1. Reference Axes .............................................................................33 2. Acceleration ..................................................................................34 3. Velocity..........................................................................................36 4. Displacement ................................................................................36 5. Angular Calculations ...................................................................37 vii 6. Aerodynamic