MULTISTAGE LAUNCH VEHICLE DESIGN WITH THRUST PROFILE AND TRAJECTORY OPTIMIZATION A THESIS SUBMITTED TO THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES OF MIDDLE EAST TECHNICAL UNIVERSITY BY EZGİ CİVEK COŞKUN IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN MECHANICAL ENGINEERING SEPTEMBER 2014 Approval of the thesis: MULTISTAGE LAUNCH VEHICLE DESIGN WITH THRUST PROFILE AND TRAJECTORY OPTIMIZATION submitted by EZGİ CİVEK COŞKUN in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering Department, Middle East Technical University by, Prof. Dr. Canan Özgen ____________________ Dean, Graduate School of Natural and Applied Sciences Prof. Dr. Süha Oral ____________________ Head of Department, Mechanical Engineering Prof. Dr. M. Kemal Özgören ____________________ Supervisor, Mechanical Engineering Department, METU Examining Committee Members: Prof. Dr. Reşit Soylu ____________________ Mechanical Engineering Department, METU Prof. Dr. M. Kemal Özgören ____________________ Mechanical Engineering Department, METU Prof. Dr. Tuna Balkan ____________________ Mechanical Engineering Department, METU Prof. Dr. Ozan Tekinalp ____________________ Aerospace Engineering Department, METU Prof. Dr. Yücel Ercan ____________________ Mechanical Engineering Department, TOBB-ETU Date: 05.09.2014 I hereby declare that all information in this document has been obtained and presented in accordance with academic rules and ethical conduct. I also declare that, as required by these rules and conduct, I have fully cited and referenced all material and results that are not original to this work. Name, Last Name : Ezgi CİVEK COŞKUN Signature : iv ABSTRACT MULTISTAGE LAUNCH VEHICLE DESIGN WITH THRUST PROFILE AND TRAJECTORY OPTIMIZATION Civek Coşkun, Ezgi Ph.D., Department of Mechanical Engineering Supervisor: Prof. Dr. M. Kemal Özgören September 2014, 198 pages In the frame of this thesis, a Matlab® based design tool utilizing a general purpose optimal control solver GPOPS-II® was developed for the optimization of ascent trajectories of multistage launch vehicles. This tool can be utilized both for preliminary mission design of an existing launch vehicle and conceptual design of a new launch vehicle. In the preliminary mission design of an existing launch vehicle, maximizing payload mass is a very common performance measure. Therefore, a trajectory optimization code was developed to determine the optimal trajectory in terms of position and velocity, and the control functions corresponding to that trajectory while maximizing the payload mass. Whereas in the conceptual design of a new launch vehicle, minimization of gross lift-off mass for a specific mission is the primary objective, and staging is an effective way to reduce the vehicle gross lift-off mass. For this purpose, a staging optimization code was developed to determine the staging parameters (mass distribution between stages, propellant and structural mass of each individual stage) which minimize the gross lift-off mass. In this thesis, staging and trajectory optimization codes were integrated by two different manners, namely the decoupled and the coupled approaches, so as to determine the sizing, burn time and thrust time history of each stage together with the optimal trajectory of the launch vehicle. Thus, a quick and effective method to find optimal vehicle configurations in the early design phases was achieved. Keywords: Launch vehicle, staging optimization, trajectory optimization, thrust profile optimization, GPOPS-II v ÖZ İTKİ PROFİLİ VE YÖRÜNGE ENİYİLEMESİ İLE ÇOK KADEMELİ FIRLATMA ARACI TASARIMI Civek Coşkun, Ezgi Doktora, Makina Mühendisliği Bölümü Tez Yöneticisi: Prof. Dr. M. Kemal Özgören Eylül 2014, 198 sayfa Bu tez kapsamında, çok kademeli fırlatma araçlarının yükseliş yörüngesinin eniyilenmesine yönelik olarak GPOPS-II® genel amaçlı optimal kontrol çözücüsünü kullanan Matlab® tabanlı bir tasarım aracı geliştirilmiştir. Bu araç, hem varolan bir fırlatma aracının yörünge tasarımında hem de yeni bir fırlatma aracının kavramsal tasarımında kullanılabilecektir. Varolan bir fırlatma aracının yörünge tasarımında, faydalı yük kütlesinin ençoklanması çok yaygın bir başarım ölçüsüdür. Bu sebeple, faydalı yük kütlesini ençoklayan konum ve hız cinsinden eniyi yörüngenin ve bu yörüngeye ilişkin kontrol fonksiyonlarının belirlenmesi için bir yörünge eniyileme kodu geliştirilmiştir. Yeni bir fırlatma aracının kavramsal tasarımında ise, belirli bir görev için toplam kalkış ağırlığının enazlanması birincil amaç olup, bunun en etkili yolu kademelendirmedir. Bu amaçla, kademelendirme parametrelerinin (kütlenin kademeler arasındaki dağılımı, her bir kademenin yakıt ve yapısal ağırlığı) belirlenmesi için bir kademelendirme eniyileme kodu geliştirilmiştir. Bu tezde, kademelendirme ve yörünge eniyilemesi kodları ayrıştırılmış ve bağlaşık olmak üzere iki farklı yaklaşımla fırlatma aracının eniyi yörüngesi ile birlikte her bir kademenin ağırlığı, yanma süresi ve itki zaman eğrisi belirlenecek şekilde birleştirilmiştir. Böylece, kavramsal tasarım aşamasında eniyi fırlatma aracı konfigürasyonunun bulunması için hızlı ve etkili bir yöntem elde edilmiştir. Anahtar Kelimeler: Fırlatma aracı, kademelendirme eniyilemesi, yörünge eniyilemesi, itki profili eniyilemesi, GPOPS-II vi To My Parents and My Grandmother vii ACKNOWLEDGMENTS The first and the foremost, I would like to thank my thesis supervisor Prof. Dr. M. Kemal Özgören, who always makes time to listen to my studies in his busy schedule, for providing useful advices and supporting my efforts. I am extremely grateful to Assoc. Prof. Dr. Anil Rao, who is the principal developer of the optimal control software GPOPS-II, for providing us with this great optimization tool and for his quick and helpful suggestions. I am also thankful to my first promoter Başar Seçkin for introducing me to the field of space rockets. His strong will and determination was the source of my inspiration. I would also like to express my sincere appreciation to Dr. Mehmet Ali Ak for his understanding and encouragement throughout the completion of this thesis work. And, I would like to give special thanks to Dr. Atılgan Toker, the single audience in my thesis defense. I will always remember his concern and sincerity. Love and thanks to my dear mom, dad and grandma for raising me as who I am today. The work presented in this thesis could not have been accomplished without their never-ending support and encouragement. I also would like to thank my brother Barış for his unique sense of humor. The last but not the least, to love of my life, my husband, my best friend, my sweetheart Korhan Coşkun: I am indebted to you for your help in both debugging the computer code and editing the draft, and for your numerous ideas and suggestions that contribute to enhancing this thesis work. Most of all, thank you for being there for me all these years, encouraging me to face the challenges. Ankara, 5 September 2014 viii TABLE OF CONTENTS ABSTRACT .......................................................................................................................... v ÖZ ........................................................................................................................................ vi ACKNOWLEDGMENTS ................................................................................................. viii TABLE OF CONTENTS ..................................................................................................... ix LIST OF TABLES ............................................................................................................. xiii LIST OF FIGURES ............................................................................................................ xv LIST OF SYMBOLS .......................................................................................................... xx LIST OF ABBREVIATIONS ........................................................................................... xxv CHAPTERS ..................................................................................................................... xxvi CHAPTER 1 INTRODUCTION .............................................................................................................. 1 1.1 Motivation ................................................................................................................ 2 1.2 Scope and Objectives ............................................................................................... 4 1.3 Thesis Outline .......................................................................................................... 6 CHAPTER 2 BACKGROUND ................................................................................................................ 7 2.1 Trajectory Optimization Methods ............................................................................ 7 2.1.1 Numerical Methods for Optimal Control ..................................................................... 9 2.1.2 Nonlinear Programming Methods .............................................................................. 11 2.2 Trajectory Optimization Software.......................................................................... 12 2.2.1 Program to Optimize Simulated Trajectories (POST) ................................................ 12 2.2.2 Optimal Trajectories by Implicit Simulation (OTIS) ................................................. 12 2.2.3 Sparse Optimal Control Software