Entry, Descent, Landing and Ascent
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AAS 13-250 Hohmann Spiral Transfer with Inclination Change Performed
AAS 13-250 Hohmann Spiral Transfer With Inclination Change Performed By Low-Thrust System Steven Owens1 and Malcolm Macdonald2 This paper investigates the Hohmann Spiral Transfer (HST), an orbit transfer method previously developed by the authors incorporating both high and low- thrust propulsion systems, using the low-thrust system to perform an inclination change as well as orbit transfer. The HST is similar to the bi-elliptic transfer as the high-thrust system is first used to propel the spacecraft beyond the target where it is used again to circularize at an intermediate orbit. The low-thrust system is then activated and, while maintaining this orbit altitude, used to change the orbit inclination to suit the mission specification. The low-thrust system is then used again to reduce the spacecraft altitude by spiraling in-toward the target orbit. An analytical analysis of the HST utilizing the low-thrust system for the inclination change is performed which allows a critical specific impulse ratio to be derived determining the point at which the HST consumes the same amount of fuel as the Hohmann transfer. A critical ratio is found for both a circular and elliptical initial orbit. These equations are validated by a numerical approach before being compared to the HST utilizing the high-thrust system to perform the inclination change. An additional critical ratio comparing the HST utilizing the low-thrust system for the inclination change with its high-thrust counterpart is derived and by using these three critical ratios together, it can be determined when each transfer offers the lowest fuel mass consumption. -
Astrodynamics
Politecnico di Torino SEEDS SpacE Exploration and Development Systems Astrodynamics II Edition 2006 - 07 - Ver. 2.0.1 Author: Guido Colasurdo Dipartimento di Energetica Teacher: Giulio Avanzini Dipartimento di Ingegneria Aeronautica e Spaziale e-mail: [email protected] Contents 1 Two–Body Orbital Mechanics 1 1.1 BirthofAstrodynamics: Kepler’sLaws. ......... 1 1.2 Newton’sLawsofMotion ............................ ... 2 1.3 Newton’s Law of Universal Gravitation . ......... 3 1.4 The n–BodyProblem ................................. 4 1.5 Equation of Motion in the Two-Body Problem . ....... 5 1.6 PotentialEnergy ................................. ... 6 1.7 ConstantsoftheMotion . .. .. .. .. .. .. .. .. .... 7 1.8 TrajectoryEquation .............................. .... 8 1.9 ConicSections ................................... 8 1.10 Relating Energy and Semi-major Axis . ........ 9 2 Two-Dimensional Analysis of Motion 11 2.1 ReferenceFrames................................. 11 2.2 Velocity and acceleration components . ......... 12 2.3 First-Order Scalar Equations of Motion . ......... 12 2.4 PerifocalReferenceFrame . ...... 13 2.5 FlightPathAngle ................................. 14 2.6 EllipticalOrbits................................ ..... 15 2.6.1 Geometry of an Elliptical Orbit . ..... 15 2.6.2 Period of an Elliptical Orbit . ..... 16 2.7 Time–of–Flight on the Elliptical Orbit . .......... 16 2.8 Extensiontohyperbolaandparabola. ........ 18 2.9 Circular and Escape Velocity, Hyperbolic Excess Speed . .............. 18 2.10 CosmicVelocities -
Optimisation of Propellant Consumption for Power Limited Rockets
Delft University of Technology Faculty Electrical Engineering, Mathematics and Computer Science Delft Institute of Applied Mathematics Optimisation of Propellant Consumption for Power Limited Rockets. What Role do Power Limited Rockets have in Future Spaceflight Missions? (Dutch title: Optimaliseren van brandstofverbruik voor vermogen gelimiteerde raketten. De rol van deze raketten in toekomstige ruimtevlucht missies. ) A thesis submitted to the Delft Institute of Applied Mathematics as part to obtain the degree of BACHELOR OF SCIENCE in APPLIED MATHEMATICS by NATHALIE OUDHOF Delft, the Netherlands December 2017 Copyright c 2017 by Nathalie Oudhof. All rights reserved. BSc thesis APPLIED MATHEMATICS \ Optimisation of Propellant Consumption for Power Limited Rockets What Role do Power Limite Rockets have in Future Spaceflight Missions?" (Dutch title: \Optimaliseren van brandstofverbruik voor vermogen gelimiteerde raketten De rol van deze raketten in toekomstige ruimtevlucht missies.)" NATHALIE OUDHOF Delft University of Technology Supervisor Dr. P.M. Visser Other members of the committee Dr.ir. W.G.M. Groenevelt Drs. E.M. van Elderen 21 December, 2017 Delft Abstract In this thesis we look at the most cost-effective trajectory for power limited rockets, i.e. the trajectory which costs the least amount of propellant. First some background information as well as the differences between thrust limited and power limited rockets will be discussed. Then the optimal trajectory for thrust limited rockets, the Hohmann Transfer Orbit, will be explained. Using Optimal Control Theory, the optimal trajectory for power limited rockets can be found. Three trajectories will be discussed: Low Earth Orbit to Geostationary Earth Orbit, Earth to Mars and Earth to Saturn. After this we compare the propellant use of the thrust limited rockets for these trajectories with the power limited rockets. -
A Strategy for the Eigenvector Perturbations of the Reynolds Stress Tensor in the Context of Uncertainty Quantification
Center for Turbulence Research 425 Proceedings of the Summer Program 2016 A strategy for the eigenvector perturbations of the Reynolds stress tensor in the context of uncertainty quantification By R. L. Thompsony, L. E. B. Sampaio, W. Edeling, A. A. Mishra AND G. Iaccarino In spite of increasing progress in high fidelity turbulent simulation avenues like Di- rect Numerical Simulation (DNS) and Large Eddy Simulation (LES), Reynolds-Averaged Navier-Stokes (RANS) models remain the predominant numerical recourse to study com- plex engineering turbulent flows. In this scenario, it is imperative to provide reliable estimates for the uncertainty in RANS predictions. In the recent past, an uncertainty estimation framework relying on perturbations to the modeled Reynolds stress tensor has been widely applied with satisfactory results. Many of these investigations focus on perturbing only the Reynolds stress eigenvalues in the Barycentric map, thus ensuring realizability. However, these restrictions apply to the eigenvalues of that tensor only, leav- ing the eigenvectors free of any limiting condition. In the present work, we propose the use of the Reynolds stress transport equation as a constraint for the eigenvector pertur- bations of the Reynolds stress anisotropy tensor once the eigenvalues of this tensor are perturbed. We apply this methodology to a convex channel and show that the ensuing eigenvector perturbations are a more accurate measure of uncertainty when compared with a pure eigenvalue perturbation. 1. Introduction Turbulent flows are present in a wide number of engineering design problems. Due to the disparate character of such flows, predictive methods must be robust, so as to be easily applicable for most of these cases, yet possessing a high degree of accuracy in each. -
Coplanar Air Launch with Gravity-Turn Launch Trajectories
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by AFTI Scholar (Air Force Institute of Technology) Air Force Institute of Technology AFIT Scholar Theses and Dissertations Student Graduate Works 3-23-2004 Coplanar Air Launch with Gravity-Turn Launch Trajectories David W. Callaway Follow this and additional works at: https://scholar.afit.edu/etd Part of the Aerospace Engineering Commons Recommended Citation Callaway, David W., "Coplanar Air Launch with Gravity-Turn Launch Trajectories" (2004). Theses and Dissertations. 3922. https://scholar.afit.edu/etd/3922 This Thesis is brought to you for free and open access by the Student Graduate Works at AFIT Scholar. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of AFIT Scholar. For more information, please contact [email protected]. COPLANAR AIR LAUNCH WITH GRAVITY-TURN LAUNCH TRAJECTORIES THESIS David W. Callaway, 1st Lieutenant, USAF AFIT/GAE/ENY/04-M04 DEPARTMENT OF THE AIR FORCE AIR UNIVERSITY AIR FORCE INSTITUTE OF TECHNOLOGY Wright-Patterson Air Force Base, Ohio APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. The views expressed in this thesis are those of the author and do not reflect the official policy or position of the United States Air Force, Department of Defense, or the United States Government. AFIT/GAE/ENY/04-M04 COPLANAR AIR LAUNCH WITH GRAVITY-TURN LAUNCH TRAJECTORIES THESIS Presented to the Faculty Department of Aeronautics and Astronautics Graduate School of Engineering and Management Air Force Institute of Technology Air University Air Education and Training Command In Partial Fulfillment of the Requirements for the Degree of Master of Science in Aeronautical Engineeering David W. -
Spacecraft Guidance Techniques for Maximizing Mission Success
Utah State University DigitalCommons@USU All Graduate Theses and Dissertations Graduate Studies 5-2014 Spacecraft Guidance Techniques for Maximizing Mission Success Shane B. Robinson Utah State University Follow this and additional works at: https://digitalcommons.usu.edu/etd Part of the Mechanical Engineering Commons Recommended Citation Robinson, Shane B., "Spacecraft Guidance Techniques for Maximizing Mission Success" (2014). All Graduate Theses and Dissertations. 2175. https://digitalcommons.usu.edu/etd/2175 This Dissertation is brought to you for free and open access by the Graduate Studies at DigitalCommons@USU. It has been accepted for inclusion in All Graduate Theses and Dissertations by an authorized administrator of DigitalCommons@USU. For more information, please contact [email protected]. SPACECRAFT GUIDANCE TECHNIQUES FOR MAXIMIZING MISSION SUCCESS by Shane B. Robinson A dissertation submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in Mechanical Engineering Approved: Dr. David K. Geller Dr. Jacob H. Gunther Major Professor Committee Member Dr. Warren F. Phillips Dr. Charles M. Swenson Committee Member Committee Member Dr. Stephen A. Whitmore Dr. Mark R. McLellan Committee Member Vice President for Research and Dean of the School of Graduate Studies UTAH STATE UNIVERSITY Logan, Utah 2013 [This page intentionally left blank] iii Copyright c Shane B. Robinson 2013 All Rights Reserved [This page intentionally left blank] v Abstract Spacecraft Guidance Techniques for Maximizing Mission Success by Shane B. Robinson, Doctor of Philosophy Utah State University, 2013 Major Professor: Dr. David K. Geller Department: Mechanical and Aerospace Engineering Traditional spacecraft guidance techniques have the objective of deterministically min- imizing fuel consumption. -
Richard Dalbello Vice President, Legal and Government Affairs Intelsat General
Commercial Management of the Space Environment Richard DalBello Vice President, Legal and Government Affairs Intelsat General The commercial satellite industry has billions of dollars of assets in space and relies on this unique environment for the development and growth of its business. As a result, safety and the sustainment of the space environment are two of the satellite industry‘s highest priorities. In this paper I would like to provide a quick survey of past and current industry space traffic control practices and to discuss a few key initiatives that the industry is developing in this area. Background The commercial satellite industry has been providing essential space services for almost as long as humans have been exploring space. Over the decades, this industry has played an active role in developing technology, worked collaboratively to set standards, and partnered with government to develop successful international regulatory regimes. Success in both commercial and government space programs has meant that new demands are being placed on the space environment. This has resulted in orbital crowding, an increase in space debris, and greater demand for limited frequency resources. The successful management of these issues will require a strong partnership between government and industry and the careful, experience-based expansion of international law and diplomacy. Throughout the years, the satellite industry has never taken for granted the remarkable environment in which it works. Industry has invested heavily in technology and sought out the best and brightest minds to allow the full, but sustainable exploitation of the space environment. Where problems have arisen, such as space debris or electronic interference, industry has taken 1 the initiative to deploy new technologies and adopt new practices to minimize negative consequences. -
Perturbation Theory in Celestial Mechanics
Perturbation Theory in Celestial Mechanics Alessandra Celletti Dipartimento di Matematica Universit`adi Roma Tor Vergata Via della Ricerca Scientifica 1, I-00133 Roma (Italy) ([email protected]) December 8, 2007 Contents 1 Glossary 2 2 Definition 2 3 Introduction 2 4 Classical perturbation theory 4 4.1 The classical theory . 4 4.2 The precession of the perihelion of Mercury . 6 4.2.1 Delaunay action–angle variables . 6 4.2.2 The restricted, planar, circular, three–body problem . 7 4.2.3 Expansion of the perturbing function . 7 4.2.4 Computation of the precession of the perihelion . 8 5 Resonant perturbation theory 9 5.1 The resonant theory . 9 5.2 Three–body resonance . 10 5.3 Degenerate perturbation theory . 11 5.4 The precession of the equinoxes . 12 6 Invariant tori 14 6.1 Invariant KAM surfaces . 14 6.2 Rotational tori for the spin–orbit problem . 15 6.3 Librational tori for the spin–orbit problem . 16 6.4 Rotational tori for the restricted three–body problem . 17 6.5 Planetary problem . 18 7 Periodic orbits 18 7.1 Construction of periodic orbits . 18 7.2 The libration in longitude of the Moon . 20 1 8 Future directions 20 9 Bibliography 21 9.1 Books and Reviews . 21 9.2 Primary Literature . 22 1 Glossary KAM theory: it provides the persistence of quasi–periodic motions under a small perturbation of an integrable system. KAM theory can be applied under quite general assumptions, i.e. a non– degeneracy of the integrable system and a diophantine condition of the frequency of motion. -
Session 6:Analytical Approximations for Low Thrust Maneuvers
Session 6: Analytical Approximations for Low Thrust Maneuvers As mentioned in the previous lecture, solving non-Keplerian problems in general requires the use of perturbation methods and many are only solvable through numerical integration. However, there are a few examples of low-thrust space propulsion maneuvers for which we can find approximate analytical expressions. In this lecture, we explore a couple of these maneuvers, both of which are useful because of their precision and practical value: i) climb or descent from a circular orbit with continuous thrust, and ii) in-orbit repositioning, or walking. Spiral Climb/Descent We start by writing the equations of motion in polar coordinates, 2 d2r �dθ � µ − r + = a (1) 2 2 r dt dt r 2 d θ 2 dr dθ aθ + = (2) 2 dt r dt dt r We assume continuous thrust in the angular direction, therefore ar = 0. If the acceleration force along θ is small, then we can safely assume the orbit will remain nearly circular and the semi-major axis will be just slightly different after one orbital period. Of course, small and slightly are vague words. To make the analysis rigorous, we need to be more precise. Let us say that for this approximation to be valid, the angular acceleration has to be much smaller than the corresponding centrifugal or gravitational forces (the last two terms in the LHS of Eq. (1)) and that the radial acceleration (the first term in the LHS in the same equation) is negligible. Given these assumptions, from Eq. (1), dθ r µ d2θ 3 r µ dr ≈ ! ≈ − (3) 3 2 5 dt r dt 2 r dt Substituting into Eq. -
Modeling Rocket Flight in the Low-Friction Approximation
Undergraduate Journal of Mathematical Modeling: One + Two Volume 6 | 2014 Fall Article 5 2014 Modeling Rocket Flight in the Low-Friction Approximation Logan White University of South Florida Advisors: Manoug Manougian, Mathematics and Statistics Razvan Teodorescu, Physics Problem Suggested By: Razvan Teodorescu Follow this and additional works at: https://scholarcommons.usf.edu/ujmm Part of the Mathematics Commons UJMM is an open access journal, free to authors and readers, and relies on your support: Donate Now Recommended Citation White, Logan (2014) "Modeling Rocket Flight in the Low-Friction Approximation," Undergraduate Journal of Mathematical Modeling: One + Two: Vol. 6: Iss. 1, Article 5. DOI: http://dx.doi.org/10.5038/2326-3652.6.1.4861 Available at: https://scholarcommons.usf.edu/ujmm/vol6/iss1/5 Modeling Rocket Flight in the Low-Friction Approximation Abstract In a realistic model for rocket dynamics, in the presence of atmospheric drag and altitude-dependent gravity, the exact kinematic equation cannot be integrated in closed form; even when neglecting friction, the exact solution is a combination of elliptic functions of Jacobi type, which are not easy to use in a computational sense. This project provides a precise analysis of the various terms in the full equation (such as gravity, drag, and exhaust momentum), and the numerical ranges for which various approximations are accurate to within 1%. The analysis leads to optimal approximations expressed through elementary functions, which can be implemented for efficient flight -
A Tool for Preliminary Design of Rockets Aerospace Engineering
A Tool for Preliminary Design of Rockets Diogo Marques Gaspar Thesis to obtain the Master of Science Degree in Aerospace Engineering Supervisor : Professor Paulo Jorge Soares Gil Examination Committee Chairperson: Professor Fernando José Parracho Lau Supervisor: Professor Paulo Jorge Soares Gil Members of the Committee: Professor João Manuel Gonçalves de Sousa Oliveira July 2014 ii Dedicated to my Mother iii iv Acknowledgments To my supervisor Professor Paulo Gil for the opportunity to work on this interesting subject and for all his support and patience. To my family, in particular to my parents and brothers for all the support and affection since ever. To my friends: from IST for all the companionship in all this years and from Coimbra for the fellowship since I remember. To my teammates for all the victories and good moments. v vi Resumo A unica´ forma que a humanidade ate´ agora conseguiu encontrar para explorar o espac¸o e´ atraves´ do uso de rockets, vulgarmente conhecidos como foguetoes,˜ responsaveis´ por transportar cargas da Terra para o Espac¸o. O principal objectivo no design de rockets e´ diminuir o peso na descolagem e maximizar o payload ratio i.e. aumentar a capacidade de carga util´ ao seu alcance. A latitude e o local de lanc¸amento, a orbita´ desejada, as caracter´ısticas de propulsao˜ e estruturais sao˜ constrangimentos ao projecto do foguetao.˜ As trajectorias´ dos foguetoes˜ estao˜ permanentemente a ser optimizadas, devido a necessidade de aumento da carga util´ transportada e reduc¸ao˜ do combust´ıvel consumido. E´ um processo utilizado nas fases iniciais do design de uma missao,˜ que afecta partes cruciais do planeamento, desde a concepc¸ao˜ do ve´ıculo ate´ aos seus objectivos globais. -
Hybrid Rocket Engine Design Optimization at Politecnico Di Torino: a Review
aerospace Review Hybrid Rocket Engine Design Optimization at Politecnico di Torino: A Review Lorenzo Casalino † , Filippo Masseni † and Dario Pastrone *,† Politecnico di Torino, Dipartimento di Ingegneria Meccanica e Aerospaziale, Corso Duca degli Abruzzi 24, 10129 Torino, Italy; [email protected] (L.C.); fi[email protected] (F.M.) * Correspondence: [email protected] † These authors contributed equally to this work. Abstract: Optimization of Hybrid Rocket Engines at Politecnico di Torino began in the 1990s. A comprehensive review of the related research activities carried out in the last three decades is here presented. After a brief introduction that retraces driving motivations and the most significant steps of the research path, the more relevant aspects of analysis, modeling and achieved results are illustrated. First, criteria for the propulsion system preliminary design choices (namely the propellant combination, the feed system and the grain design) are summarized and the engine modeling is presented. Then, the authors describe the in-house tools that have been developed and used for coupled trajectory and propulsion system design optimization. Both deterministic and robust-based approaches are presented. The applications that the authors analyzed over the years, starting from simpler hybrid powered sounding rocket to more complex multi-stage launchers, are then presented. Finally, authors’ conclusive remarks on the work done and their future perspective in the context of the optimization of hybrid rocket propulsion systems are reported. Citation: Casalino, L.; Masseni, F.; Pastrone, D. Hybrid Rocket Engine Keywords: Hybrid Rocket Engines; multidisciplinary optimization; robust optimization Design Optimization at Politecnico di Torino: A Review. Aerospace 2021, 8, 226.