Session 6:Analytical Approximations for Low Thrust Maneuvers
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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 -
Aerospace Engine Data
AEROSPACE ENGINE DATA Data for some concrete aerospace engines and their craft ................................................................................. 1 Data on rocket-engine types and comparison with large turbofans ................................................................... 1 Data on some large airliner engines ................................................................................................................... 2 Data on other aircraft engines and manufacturers .......................................................................................... 3 In this Appendix common to Aircraft propulsion and Space propulsion, data for thrust, weight, and specific fuel consumption, are presented for some different types of engines (Table 1), with some values of specific impulse and exit speed (Table 2), a plot of Mach number and specific impulse characteristic of different engine types (Fig. 1), and detailed characteristics of some modern turbofan engines, used in large airplanes (Table 3). DATA FOR SOME CONCRETE AEROSPACE ENGINES AND THEIR CRAFT Table 1. Thrust to weight ratio (F/W), for engines and their crafts, at take-off*, specific fuel consumption (TSFC), and initial and final mass of craft (intermediate values appear in [kN] when forces, and in tonnes [t] when masses). Engine Engine TSFC Whole craft Whole craft Whole craft mass, type thrust/weight (g/s)/kN type thrust/weight mini/mfin Trent 900 350/63=5.5 15.5 A380 4×350/5600=0.25 560/330=1.8 cruise 90/63=1.4 cruise 4×90/5000=0.1 CFM56-5A 110/23=4.8 16 -
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. -
Flight and Orbital Mechanics
Flight and Orbital Mechanics Lecture slides Challenge the future 1 Flight and Orbital Mechanics AE2-104, lecture hours 21-24: Interplanetary flight Ron Noomen October 25, 2012 AE2104 Flight and Orbital Mechanics 1 | Example: Galileo VEEGA trajectory Questions: • what is the purpose of this mission? • what propulsion technique(s) are used? • why this Venus- Earth-Earth sequence? • …. [NASA, 2010] AE2104 Flight and Orbital Mechanics 2 | Overview • Solar System • Hohmann transfer orbits • Synodic period • Launch, arrival dates • Fast transfer orbits • Round trip travel times • Gravity Assists AE2104 Flight and Orbital Mechanics 3 | Learning goals The student should be able to: • describe and explain the concept of an interplanetary transfer, including that of patched conics; • compute the main parameters of a Hohmann transfer between arbitrary planets (including the required ΔV); • compute the main parameters of a fast transfer between arbitrary planets (including the required ΔV); • derive the equation for the synodic period of an arbitrary pair of planets, and compute its numerical value; • derive the equations for launch and arrival epochs, for a Hohmann transfer between arbitrary planets; • derive the equations for the length of the main mission phases of a round trip mission, using Hohmann transfers; and • describe the mechanics of a Gravity Assist, and compute the changes in velocity and energy. Lecture material: • these slides (incl. footnotes) AE2104 Flight and Orbital Mechanics 4 | Introduction The Solar System (not to scale): [Aerospace -
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. -
6. Chemical-Nuclear Propulsion MAE 342 2016
2/12/20 Chemical/Nuclear Propulsion Space System Design, MAE 342, Princeton University Robert Stengel • Thermal rockets • Performance parameters • Propellants and propellant storage Copyright 2016 by Robert Stengel. All rights reserved. For educational use only. http://www.princeton.edu/~stengel/MAE342.html 1 1 Chemical (Thermal) Rockets • Liquid/Gas Propellant –Monopropellant • Cold gas • Catalytic decomposition –Bipropellant • Separate oxidizer and fuel • Hypergolic (spontaneous) • Solid Propellant ignition –Mixed oxidizer and fuel • External ignition –External ignition • Storage –Burn to completion – Ambient temperature and pressure • Hybrid Propellant – Cryogenic –Liquid oxidizer, solid fuel – Pressurized tank –Throttlable –Throttlable –Start/stop cycling –Start/stop cycling 2 2 1 2/12/20 Cold Gas Thruster (used with inert gas) Moog Divert/Attitude Thruster and Valve 3 3 Monopropellant Hydrazine Thruster Aerojet Rocketdyne • Catalytic decomposition produces thrust • Reliable • Low performance • Toxic 4 4 2 2/12/20 Bi-Propellant Rocket Motor Thrust / Motor Weight ~ 70:1 5 5 Hypergolic, Storable Liquid- Propellant Thruster Titan 2 • Spontaneous combustion • Reliable • Corrosive, toxic 6 6 3 2/12/20 Pressure-Fed and Turbopump Engine Cycles Pressure-Fed Gas-Generator Rocket Rocket Cycle Cycle, with Nozzle Cooling 7 7 Staged Combustion Engine Cycles Staged Combustion Full-Flow Staged Rocket Cycle Combustion Rocket Cycle 8 8 4 2/12/20 German V-2 Rocket Motor, Fuel Injectors, and Turbopump 9 9 Combustion Chamber Injectors 10 10 5 2/12/20 -
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. -
Habitability of Planets on Eccentric Orbits: Limits of the Mean Flux Approximation
A&A 591, A106 (2016) Astronomy DOI: 10.1051/0004-6361/201628073 & c ESO 2016 Astrophysics Habitability of planets on eccentric orbits: Limits of the mean flux approximation Emeline Bolmont1, Anne-Sophie Libert1, Jeremy Leconte2; 3; 4, and Franck Selsis5; 6 1 NaXys, Department of Mathematics, University of Namur, 8 Rempart de la Vierge, 5000 Namur, Belgium e-mail: [email protected] 2 Canadian Institute for Theoretical Astrophysics, 60st St George Street, University of Toronto, Toronto, ON, M5S3H8, Canada 3 Banting Fellow 4 Center for Planetary Sciences, Department of Physical & Environmental Sciences, University of Toronto Scarborough, Toronto, ON, M1C 1A4, Canada 5 Univ. Bordeaux, LAB, UMR 5804, 33270 Floirac, France 6 CNRS, LAB, UMR 5804, 33270 Floirac, France Received 4 January 2016 / Accepted 28 April 2016 ABSTRACT Unlike the Earth, which has a small orbital eccentricity, some exoplanets discovered in the insolation habitable zone (HZ) have high orbital eccentricities (e.g., up to an eccentricity of ∼0.97 for HD 20782 b). This raises the question of whether these planets have surface conditions favorable to liquid water. In order to assess the habitability of an eccentric planet, the mean flux approximation is often used. It states that a planet on an eccentric orbit is called habitable if it receives on average a flux compatible with the presence of surface liquid water. However, because the planets experience important insolation variations over one orbit and even spend some time outside the HZ for high eccentricities, the question of their habitability might not be as straightforward. We performed a set of simulations using the global climate model LMDZ to explore the limits of the mean flux approximation when varying the luminosity of the host star and the eccentricity of the planet. -
Helicopter Turboshafts
Helicopter Turboshafts Luke Stuyvenberg University of Colorado at Boulder Department of Aerospace Engineering The application of gas turbine engines in helicopters is discussed. The work- ings of turboshafts and the history of their use in helicopters is briefly described. Ideal cycle analyses of the Boeing 502-14 and of the General Electric T64 turboshaft engine are performed. I. Introduction to Turboshafts Turboshafts are an adaptation of gas turbine technology in which the principle output is shaft power from the expansion of hot gas through the turbine, rather than thrust from the exhaust of these gases. They have found a wide variety of applications ranging from air compression to auxiliary power generation to racing boat propulsion and more. This paper, however, will focus primarily on the application of turboshaft technology to providing main power for helicopters, to achieve extended vertical flight. II. Relationship to Turbojets As a variation of the gas turbine, turboshafts are very similar to turbojets. The operating principle is identical: atmospheric gases are ingested at the inlet, compressed, mixed with fuel and combusted, then expanded through a turbine which powers the compressor. There are two key diferences which separate turboshafts from turbojets, however. Figure 1. Basic Turboshaft Operation Note the absence of a mechanical connection between the HPT and LPT. An ideal turboshaft extracts with the HPT only the power necessary to turn the compressor, and with the LPT all remaining power from the expansion process. 1 of 10 American Institute of Aeronautics and Astronautics A. Emphasis on Shaft Power Unlike turbojets, the primary purpose of which is to produce thrust from the expanded gases, turboshafts are intended to extract shaft horsepower (shp). -
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. -
Effects of Planetesimals' Random Velocity on Tempo
42nd Lunar and Planetary Science Conference (2011) 1154.pdf EFFECTS OF PLANETESIMALS’ RANDOM VELOCITY ON TEMPO- RARY CAPTURE BY A PLANET Ryo Suetsugu1, Keiji Ohtsuki1;2;3, Takayuki Tanigawa2;4. 1Department of Earth and Planetary Sciences, Kobe University, Kobe 657-8501, Japan; 2Center for Planetary Science, Kobe University, Kobe 657-8501, Japan; 3Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80309-0392; 4Institute of Low Temperature Science, Hokkaido University, Sapporo 060-0819, Japan Introduction: When planetesimals encounter with a of large orbital eccentricities were not examined in detail. planet, the typical duration of close encounter during Moreover, the above calculations assumed that planetesi- which they pass within or near the planet’s Hill sphere is mals and a planet were initially in the same orbital plane, smaller than or comparable to the planet’s orbital period. and effects of orbital inclination were not studied. However, in some cases, planetesimals are captured by In the present work, we examine temporary capture the planet’s gravity and orbit about the planet for an ex- of planetesimals initially on eccentric and inclined orbits tended period of time, before they escape from the vicin- about the Sun. ity of the planet. This phenomenon is called temporary capture. Temporary capture may play an important role Numerical Method: We examine temporary capture us- in the origin and dynamical evolution of various kinds of ing three-body orbital integration (i.e. the Sun, a planet, a small bodies in the Solar System, such as short-period planetesimal). When the masses of planetesimals and the comets and irregular satellites.