Mississippi State University Scholars Junction Theses and Dissertations Theses and Dissertations 8-9-2019 Multistage 2-DOF rocket trajectory simulation program for freshmen level engineering students Zachery Doucet Follow this and additional works at: https://scholarsjunction.msstate.edu/td Recommended Citation Doucet, Zachery, "Multistage 2-DOF rocket trajectory simulation program for freshmen level engineering students" (2019). Theses and Dissertations. 3252. https://scholarsjunction.msstate.edu/td/3252 This Graduate Thesis - Open Access is brought to you for free and open access by the Theses and Dissertations at Scholars Junction. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of Scholars Junction. For more information, please contact [email protected]. Template C with Schemes v4.0 (beta): Created by L. Threet 2/5/19 Multistage 2-DOF rocket trajectory simulation program for freshmen level engineering students By TITLE PAGE Zachery Doucet A Thesis Submitted to the Faculty of Mississippi State University in Partial Fulfillment of the Requirements for the Degree of Master of Science in Aerospace Engineering in the Department of Aerospace Engineering Mississippi State, Mississippi August 2019 Copyright by COPYRIGHT PAGE Zachery Doucet 2019 Multistage 2-DOF rocket trajectory simulation program for freshmen level engineering students By APPROVAL PAGE Zachery Doucet Approved: ____________________________________ Keith Koenig (Major Professor) ____________________________________ Yang Cheng (Committee Member) ____________________________________ Calvin R. Walker (Committee Member) ____________________________________ David S. Thompson (Graduate Coordinator) ____________________________________ Jason M. Keith Dean Bagley College of Engineering Name: Zachery Doucet ABSTRACT Date of Degree: August 9, 2019 Institution: Mississippi State University Major Field: Aerospace Engineering Major Professors: Keith M. Koenig Title of Study: Multistage 2-DOF rocket trajectory simulation program for freshmen level engineering students Pages in Study: 108 Candidate for Degree of Master of Science With the growing interest in space exploration, the need for professionals to be prepared for the job is ever more present. This project aims to satisfy that goal by presenting a MATLAB program for use by freshmen level engineering students that provides results for rocket trajectories within acceptable margins of accuracy. The initial stages of development were shaped by the decision to keep the program accessible to someone within the target demographic. As a result, a three-degree of freedom system was chosen, with focus put on amateur rocketry including high power rockets. Various methods were used to provide outputs for rocket flight paths that could be compared to field tests. The solution methods available are Euler and fourth-order Runge-Kutta that utilize the equations of motion for a perpendicular- parallel or x-y coordinate frame. Trajectory simulations and field tests were conducted to have reference cases to confirm the accuracy of the program. DEDICATION This thesis is dedicated to the memory of my beloved grandfather, Raymond Vallimont. Although one of the greatest inspirations for my academic pursuit, he did not live to see me complete my education. This one is for you Gramps. ii ACKNOWLEDGEMENTS Throughout the writing of this thesis I have received a great deal of support and assistance. I would first like to thank my major professor, Dr. Keith Koenig, whose expertise and patience were invaluable in the formulating of the research topic and the methodology used. In addition, I would like to thank the fellow members of my committee, Dr. Yang Cheng and Mr. Calvin Walker for their patience and support throughout the project. I would also like to thank my professors and instructors here at Mississippi State University, who have provided me with the tools and knowledge to complete this thesis. The Mississippi State University Space Cowboys rocket team also has my thanks for providing me with data that was beneficial to completing this project. Additionally, there are my friends who offered great support and provided countless happy distractions over the years, such as my colleagues Tyler Howell, Jonathon Lee and Sepehr Zangeneh, and my dear friends William Orrin Cole and William Streaker. Finally, I would like to thank my parents, Jean and Joseph Doucet, and grandmother, Mary Ann Vallimont, who have provided me with invaluable advice, love and support over the years. Whether it be the counsel of my father, the sympathetic ear of grandmother, or the strong push to do and be the best I can be from my mother, I know you are always there for me. iii TABLE OF CONTENTS DEDICATION ................................................................................................................................ ii ACKNOWLEDGEMENTS ........................................................................................................... iii LIST OF TABLES ........................................................................................................................ vii LIST OF FIGURES ..................................................................................................................... viii NOMENCLATURE ...................................................................................................................... xi CHAPTER I. INTRODUCTION .............................................................................................................1 II. DEVELOPMENT PROCESS ...........................................................................................3 2.1 Goal of Development ............................................................................................3 2.1.1 MATLAB as the program of choice ................................................................4 2.1.2 OpenRocket as a reference case ......................................................................4 2.2 The Briggs Multistage Supersonic Rocket Flight Simulator .................................5 2.2.1 Development of Vcr ..........................................................................................8 2.2.2 The Exclusion of Lift .....................................................................................10 2.3 The Coordinate Frames .......................................................................................10 2.3.1 The Parallel-Perpendicular Coordinate Frame ..............................................10 2.3.1.2 1st Order Euler Equations ........................................................................11 2.3.1.3 4th Order Runge-Kutta Equations ............................................................13 2.3.2 The X-Y Coordinate Frame ...........................................................................13 2.3.2.2 1st Order Euler Equations ........................................................................15 2.3.2.3 4th Order Runge-Kutta Equations ............................................................16 2.4 Drag Profiles ........................................................................................................16 2.4.2 No Fins Model ...............................................................................................21 2.4.3 Small Fins Model ..........................................................................................21 2.4.4 Large Fins Model ..........................................................................................22 2.4.5 Delta Fins Model ...........................................................................................24 III. PROGRAM BREAKDOWN ..........................................................................................26 3.1 Startup Scripts .....................................................................................................28 3.1.1 Simulator.m ...................................................................................................29 iv 3.1.2 Menu scripts ..................................................................................................30 3.1.2.2 Parameters Menu .....................................................................................31 3.1.2.3 Program Menu & Program Editor ...........................................................32 3.2 Initialization Scripts .............................................................................................33 3.2.1 Rocket and Motor Parameters .......................................................................34 3.2.2 Initial Launch Conditions ..............................................................................37 3.3 Thrust Selection ...................................................................................................40 3.3.1 Average Thrust Values ..................................................................................41 3.3.2 Interpolated Thrust and Motor Data ..............................................................41 3.4 Drag Selection .....................................................................................................43 3.4.1 Actual Drag ...................................................................................................44 3.4.2 Constant Drag ................................................................................................44 3.4.3 Fin Type Profiles ...........................................................................................45 3.5 Solution