Astronautics and Space Engineering MSc

• Dr Joan Pau Sanchez Cuartielles

To provide a critical understanding of the basic principles of Astrodynamics and Mission Analysis and of their application to typical mission analysis problems.

Astrodynamics - Keplerian orbital motion

• Newton’s Law of Gravitation.
• Equations of Motion for a two body system.
• Motion in a Central Field. Conic Sections.
• The Geometry of the Ellipse. Kepler's Laws.
• The Position-Time Problem.
• The Energy Integral.
• The Satellite Orbit in Space.

Astrodynamics - Orbit Perturbations. 

• Variation of Parameters.
• Perturbations Caused by Earth Oblateness.
• Perturbations Caused by a Third Body.
• Triaxiality Perturbations.

Mission analysis

• Orbit Selection for Mission Design.
• Hohmann Transfer and Inclinations Changes.
• Hyperbolic Passage.
• Patched Conics Interplanetary trajectories.

On completion of this module the student should :

• Be able to apply appropriate techniques to solve a range of practical astrodynamics and mission analysis problems
• Be able to describe widely used orbit types and their applications, and evaluate the perturbations on these orbits
• Be able to plan impulsive orbital manoeuvres to achieve mission design requirements.

To demonstrate how to develop the design of a space system, from the initial mission objective, through requirements definition, concept development and trade-off, and through to a baseline design.

• Brief history & context: Background to the development of space, agencies, funding, future missions.
• Introduction to space system design methodology: requirements, trade-off analysis, design specifications, system budgets.
• Spacecraft sub-systems design: Structure & configuration; Power, the power budget and solar array and battery sizing; Communications and the link budget; Attitude determination and control; Orbit determination and control; Thermal control.
• Mission and payload types Spacecraft configuration: examples of configuration of spacecraft designed for various mission types; case study.
• Introduction to cost engineering.
• Space and Spacecraft Environment: Radiation, vacuum, debris, spacecraft charging, material behaviour and outgassing.
• Assembly, Integration and Test processes; Launch campaign; Space mission operations.

To provide an understanding of the thermofluid dynamic concepts underlying rocket and air-breathing space propulsion and of your implications for launch vehicle and spacecraft system performance and design.

Introduction: The interactions between propulsion system, mission & spacecraft design.

Launch Vehicle Performance: Mission requirements, Vehicle dynamics, Tsiolkovski rocket equation, Launch vehicle sizing & multi-staging, Illustrative launcher performance (Scout, Ariane, Shuttle programmes) - launch site / range safety constraints, Geostationary orbit acquisition.
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Expendable Launch Vehicles - Current Options: Vehicle design summaries, Orbital transfer vehicles, Comparative launch costs, Reusable launchers.

Propulsion Fundamentals: Systems classification, Nozzle flows, Off-design considerations (under/over-expanded flows), Thermochemistry.

Space Propulsion Systems and Performance: Propellants and combustion, Solid and liquid propellant systems, Engine cycles: Spacecraft propulsion - orbit raising, station-keeping and attitude control, Propellant management at low-g - alternative storage and delivery systems: Electric propulsion, Separately-powered rocket performance, Low thrust manoeuvres, Thruster concepts and configurations.

Air-Breathing Propulsion for Launcher Applications:Motivation, Concepts and Mach number Constraints: Ramjet cycle analysis - implications of alternative fuels, intake design, Supersonic combustion, Air liquefaction cycles, Future trends in launcher configuration.

To provide knowledge of the fundamentals of control engineering for the analysis and design of control systems in aerospace applications.

• Feedback control system characteristics.
• Control system performance.
• Stability of Linear Feedback Systems.
• Root locus method.
• Frequency response method.
• Nyquist stability.
• Classical controller design.
• State variable controller design.
• Robust control.

On successful completion of this module a you should be able to:
1. Analyse and explain the stability, characteristics, behaviour and robustness of single input/ single- output feedback control systems.
2. Design controllers for single-input single-output systems.
3. Use modern PC-based CAD software to solve control engineering problems and design control systems using classical methods.
4. Recognise and explain the advantages and limitations of feedback and recognise the importance of robustness.

The course is aimed at giving potential Finite Element USERS basic understanding of the inner workings of the method.

The objective is to introduce users to the terminology, basic numerical and mathematical aspects of the method. This should help students to avoid some of the more common and important user errors, many of which stem from a "black box" approach to this technique. Some basic guidelines are also given on how to approach the modelling of structures using the Finite Element Method.

• Background to Finite Element Methods (FEM) and its application.
• Introduction to FE modelling: Idealisation, Discretisation, Meshing and Post Processing.
• Tracking and controlling errors in a finite element analysis. ‘Do’s and don’ts’ of modelling.
• Illustration of basics of FEM using the Direct Stiffness method to define both terminology and theoretical approach.
• Problems of large systems of equations for FE, and solution methods. 
• Damage modelling and its validation process.
• Digitalisation of materials and analysis for design optimisation.
• NASTRAN application sessions.

On successful completion of this module you should be able to:

• Appraise the underlying principles and key aspects of practical application of FEA to structural problems. 
• Calculate the main mathematical and numerical aspects of the element formulations for 1D, 2D and 3D elements. 
• Construct and analyse finite element models based on structural and continuum elements with proper understanding of limitations of the FEM. 
• Evaluate results of the analyses and assess error levels. 
• Critically evaluate the constraints and implications imposed by the finite element method. 

To introduce you to the composite materials, manufacturing techniques and analysis methods for the design of aerospace composite structures.

• Introduction; Types of composite materials, especially FRP composites.
• Overview of composites manufacturing techniques.
• Micromechanics and macro mechanics for stiffness and strength analysis of a FRP ply; Macro mechanics, constitutive equation, stiffness and strength analysis of a FRP laminate; Thermal and moisture residual stresses in a FRP laminate.
• Stress analysis of an open section FRP composite structure subjected to various loadings.
• Stress analysis of a closed section FRP composite structure subjected to various loadings.
• Design guidelines and examples for composite structure design and analysis.
• Computer programmes for laminate stress, buckling of laminate and stiffened skin.

The classroom assignment on composite manufacturing techniques will take place towards the end of this module. The date and time will be confirmed by the tutor. The assignment is a one hour written paper that will take place in the classroom under exam conditions. This assignment is formally assessed and is worth 25% of the marks available for this module.

• Professor James Whidborne

To provide a knowledge of modern control techniques for the analysis and design of multivariable aerospace control systems.

Multivariable System Analysis
• Multivariable linear systems theory
• System realizations
• Controllability, observability and canonical forms
• Size of signals and systems

Multivariable Control System Design
• System interconnection and feedback
• Optimal linear quadratic control and estimation
• Uncertainty and conditions for robustness
• H-infinity optimal control

• Dr Joan Pau Sanchez Cuartielles

To provide an introduction to spacecraft kinematics and dynamics, focussing on rigid body dynamics and control of Earth orbiting satellites.

Overview:
• How does spacecraft dynamics relate to satellite control problem?
• AOCS (Attitude & Orbit Control Sub-system) design process
• Interactions with other sub-systems
• Control loop representation

Kinematics:
• Attitude representation: Euler angles, Euler parameters (quaternions)
• Common reference frames (inertial, orbit referenced)
• Transformation between reference frames
• Small angle linearisation (reduction of 3dof control problem to 1dof)

Rigid body dynamics:
• Euler's equations for rigid bodies
• Axisymetric spacecraft & free-body dynamics
• Disturbance torques

Application to spacecraft control:
• Simulating spacecraft free-body kinematics & dynamics in MATLAB
• Sensor basics (sun sensors, star trackers, rate sensors)
• Actuator basics (thrusters, reaction wheels)
• Rate control of rigid body spacecraft
• Attitude control of 3-axis stabilised spacecraft

The aim of this module is to provide an introduction to the principles of aerospace navigation systems based on inertial sensors and satellite navigation as well as to provide an introduction to the principles of sensor fusion, system integration and error analysis and prediction.

GNSS and INS

• Introduction (1 hour)
Overview of navigation principles, typical applications; axis systems and projections (1 hour)
• Inertial Navigation Systems (3 hours)
Principles of inertial navigation; accelerometers, gyroscopes, specific technologies such as Ring Laser Gyros; Axis transformations and mechanisation of IN equations; Errors in inertial navigation, Schuler loop tuning, INS modelling & aiding
• GNSS (6 hours)
Development history: GNSS, GPS, GLONASS, EGNOS, Galileo; GPS system architecture (ground, space, user segments); Code (CDMA) and carrier techniques; signal processing (correlation), integer ambiguities; Error sources (natural, other); Augmentation: differential GPS (local, wide area), other sensors (e.g. INS); Applications / issues: user groups (aviation, space), integrity (RAIM), accuracy, reliability

Sensors and Data Fusion

• Error Characteristics of Aircraft Sensors, INS, GPS, VOR, DME (2 lectures)
• Random Signals And Random Processes (1 lecture)
• Measurement In Noise (1 lecture)
• Error Analysis (2 lectures)
• Discrete Kalman Filter (2 lectures)
• Case Study: Barometric Aiding For INS (1 lecture)
• Case Study: GPS models (1 lecture)

To provide an introduction to the state-of-the-art in applied mathematics and techniques in astrodynamics and trajectory design.

1. Refresher of Matlab Programming:
• The Matlab Environment
• Matrices and Operators
• Scripts and Functions
• Loops
• Programmer’s toolbox
2. Lambert Arc:
• Two-body orbital boundary-value problem
• Minimum energy transfer
• F & G Solutions for elliptic orbits
• Differential Correctors and Continuation methods
3. Pork-chop plots:
• Hohmann transfer and Patched Conics
• Lambert arc grid search and visualization
• Earth Escape and C3
• Synodic Period
4. Low thrust trajectory design:
• Gravity losses
• Method of variation of parameters and sub-optimal control laws
• Edelbaum Solution
• Shape-base methods
5. Circular Restricted Three Body Problem:
• Synodic reference frame
• Equations of motion
• Jacobi Integral
• Equilibrium Points
• Zero Velocity Curves
6. Libration Point Orbits:
• Stability of the equilibrium points
• Classification of Fixed Points
• Periodic Orbits near L1 and L2