** Aircraft Flight Systems, Flight Dynamics, and Flight Simulation
Aerodynamics, Fluid Dynamics, and Propulsion
Structures, Design, and Optimization
Space Systems Engineering
Engineering Physics
Research Seminars and Professional Courses**

Some courses are listed as having prerequisites or recommended preparation. Prerequisites are graduate courses that are offered at UTIAS and will not be waived without permission of the instructor. Recommended preparation is background knowledge from undergraduate studies that is very important to the course. If unsure about this background knowledge, contact the course instructor. It is possible under some circumstances to take undergraduate courses (without credit) to make up for background deficiencies.

## Aircraft Flight Systems, Flight Dynamics, and Flight Simulation

### AER 0503H Aeroelasticity

**Lecture Course**

Static aeroelastic phenomena are studied, including divergence of slender wings and control reversal. Various methods of solution are considered such as closed form, matrix format iteration and the Rayleigh-Ritz approach. A Study of vibration and flutter of wings and control surfaces is presented with particular emphasis on those parameters which affect flutter speed.

### AER 1202H Advanced Flight Dynamics

**Lecture Course**

Introduction to the dynamics of aircraft. Topics considered include derivation of equations of motion; small perturbation methods; stability derivative estimation; longitudinal and lateral static stability and dynamic stability; response to control input(open-loop control); and closed-loop flight control system design.

### AER 1211H Human Control Of Flight Systems

**Lecture Course**

Introductory course. Topics include: mathematical models of man/machine systems, experimental results, examples, linear modelling, stability, nonlinear modelling, optimal control model, control tasks and applications, flight simulation techniques.

### AER 1216H Fundamentals of UAVs

**Lecture course**

Unpiloted aircraft, known as UAVs, drones or aerial robots, are very quickly becoming a major sector of the aerospace industry. They are increasingly used in aerial photography, inspection of infrastructure, delivery of small packages and other applications requiring inexpensive and flexible flight. The basic physical, scientific and engineering principles necessary to design a remote-controlled fixed-wing or quad-rotor UAV are explained in this course. These include aerodynamics, propulsion, structures and control. A key part of this course will be a group project to create a detailed design of a UAV that is capable of performing a specific function.

### AER 1217H Design of Autonomous UAVs

**Lecture course**

AER 1216H “Fundamentals of UAVs” or equivalent with permission of the instructor

## Aerodynamics, Fluid Dynamics, and Propulsion Courses

### AER 0510H Aerospace Propulsion

**Lecture Course**

Scope and history of jet and rocket propulsion; fundamentals of air-breathing and rocket propulsion; fluid mechanics and thermodynamics of propulsion including boundary layer mechanics and combustion; principles of aircraft jet engines, engine components and performance; principles of rocket propulsion, rocket performance, and chemical rockets; environmental impact of aircraft jet engines.

*Recommended Preparation:*

AER 310H “Gasdynamics” or equivalent

### AER 1301H Kinetic Theory of Gases

**Lecture Course**

Introductory discussion of significant length dimensions; different flow regimes, continuum, transition, collision-free; and a brief history of gas kinetic theory. Equilibrium kinetic theory; the article distribution function; Maxell-Boltzmann distribution. Collision dynamics; collision frequency and mean free path. Elementary transport theory, transport coefficients, mean free path method. Boltzmann equation; derivation, Boltzmann H-theorem, collision operators. Generalized transport theory; Maxwell’s equations of change; approximate solution techniques, Chapman -Ensog perturbative and Grad series expansion methods, moment closures; derivation of the Euler and Navier-Stokes equations, higher-order closures. Free molecular aerodynamics. Shock waves.

### AER 1303H Advanced Fluid Mechanics

**Lecture Course**

This course is intended to be a first graduate-level course in fluid mechanics, and assumes that students have had at least one introductory fluid mechanics course at the undergraduate level. The course starts with a review of vectors, tensors and related theorems; flow kinematics; derivations of the differential forms of the governing equations of fluid motion. Then the following subjects are covered: exact solutions (solutions with parallel boundaries, solutions with circular symmetry, pulsating flows, stagnation-point flows, etc); special forms of governing equations (Kelvin’s theorem, vorticity transport theorem, equations for inviscid flow (Euler); and boundary layer theory (boundary layer equations, boundary layer on a flat plate: Blasius solution, approximate solutions, effect of pressure gradient, separation, perturbation techniques, stability of boundary layers, etc

### AER 1304H Fundamentals of Combustion

*Ö. L. Gülder*

**Lecture Course**

This course starts with a review of chemical thermodynamics, statistical mechanics, equilibrium chemistry, chemical kinetics, and conservation equations. Then, the following subjects are covered: chemical and dynamic structure of laminar premixed, diffusion, and partially premixed flames; turbulent premixed combustion; turbulent diffusive combustion in one and two-phase flows; aerodynamics and stabilization of flames; ignition, extinction and combustion instabilities; non-intrusive combustion diagnostics and flame spectroscopy.

### AER 1306H Special Topics in Reacting Flows

*Ö. L. Gülder*

**Reading Course**

This course provides the students who are intending a career in combustion/reacting flows, fluid mechanics or propulsion an opportunity to do an in-depth study of some of the current academic research areas with implications of practical importance. It will also be suitable for graduate students who have a good background in essentials of their research area, but need a specialized course to cover material not available in other graduate courses. Intention is not to replace or to overlap with the literature review of the students theses work. The course will cover 3 to 4 topics from the following: non-intrusive experimental techniques in isothermal and reacting flows; activation energy asymptotics; high-speed combustion; metal combustion in propulsion; thermo-acoustics in propulsion systems; soot formation and oxidation kinetics; theory of partially-premixed turbulent combustion; synthesis of nano-materials by combustion; high-pressure combustion.

Topic selection will depend on the interests of the students taking the course. Similar topics will be added as needed.

*Prerequisite: *

AER 1304H “Fundamentals of Combustion” or equivalent

### AER 1308H Introduction to Modern Flow Control

**Lecture Course**

This course presents the fundamental aspects of modern flow control. The framework of the course will be cast starting with a brief review of the development of flow control from its birth at the turn of the 20th century to current state of the art techniques and methodologies. The key concepts, fundamental to modern flow control, will thus be extracted and categorises throughout the course: including topics such as flow instabilities; dynamic and closed-loop control; actuators and sensors; modeling and simulations.

### AER 1310H Turbulence Modelling

**Lecture Course**

This course presents an overview of numerical modelling techniques for the prediction of turbulent flows. The emphasis is on the capabilities and limitations of engineering approaches commonly used in computational fluid dynamics (CFD) for the simulation of turbulence. Topics include: Introduction to turbulent flows; definition of turbulence; features of turbulent flows; requirements for and history of turbulence modelling. Conservation equations for turbulent flows; Reynolds and Favre averaging; velocity correlations, Reynolds-averaged Navier-Stokes equations (RANS) ; Reynolds stress equations; effects of compressibility. Algebraic models; eddy viscosity and mixing length hypothesis; Cebeci-Smith and Baldwin-Lomax models. Scalar field evolution models; turbulence energy equation; one- and two-equation models; wall functions; low-Reynolds-number effects. Second-order closure models; full Reynolds-stress and algebraic Reynolds stress models. Large-Eddy Simulation (LES) techniques. Direct Numerical Simulation (DNS) Methods.

### AER 1311H Unsteady Gasdynamics

**Lecture Course**

The following topics are covered: method of characteristics for solving hyperbolic conversation laws; characteristics of rarefaction, compression and shock waves; reflection, collision, refraction and overtaking of shock waves, expansion waves and contact sufaces; Riemann problem and solution; shock waves interacting with an area enlargement and reduction; shock-tube problem.

### AER 1312H High-Temperature Compressible Flows

**Lecture Course**

Introduction to real-gas effects for unsteady compressible gas flows, including the following topics: concept of real gases (real atoms and molecules); partition functions for translation, rotation, vibration (dissociation), and electrical excitation (ionization); thermal and caloric equations of state; thermodynamic equilibrium; Saha equations for dissociation and ionization; specific heats and sound speeds for dissociating and ionizing gases; normal shock structure in real gases; real-gas flows in unsteady one-dimensional rarefaction waves and steady two-dimensional expansion waves.

### AER 1315H Sustainable Aviation

**Lecture Course**

This course will cover topics relating to the impact of aircraft on the environment, including noise, local and global emissions, and lifecycle analysis. Students will be exposed to means of quantitative assessment of the impact of aviation noise and emissions as well as metrics for assessing global climate effects. Current and future technologies for mitigating environmental problems will be covered.

### AER 1316H Fundamentals of Computational Fluid Dynamics

**Lecture Course**

This course presents the fundamentals of numerical methods for inviscid and viscous flows. The following topics are covered: finite-difference and finite-volume approximations, structured and unstructured grids, the semidiscrete approach to the solution of partial differential equations, time-marching methods for ordinary differential equations, stability of linear systems, approximate factorization, flux-vector splitting, boundary conditions, relaxation methods, and multigrid.

### AER 1318H Topics in Computational Fluid Dynamics

**Lecture Course**

The course first concentrates on the algorithmic details of two specific codes for solving the compressible Navier-Stokes equations, **ARC2D **and **FLOMG **. Topics include generalized curvilinear coordinates, approximate factorization, artificial dissipation, boundary conditions, and various convergence acceleration techniques, including multigrid. This is followed by the following topics: flux-difference splitting and high-resolution upwind schemes, including total variation diminishing schemes.

*Prerequisite:*

AER 1316H “Fundamentals of Computational Fluid Dynamics”

### AER 1319H : Finite Volume Methods for CFD

**Lecture Course**

Introduction to upwind finite-volume methods widely used in computational fluids dynamics (CFD) for thehe solution of high-speed inviscid and viscous compressible flows. Topics include: Brief review of conservation equations for compressible flows; Euler equations; Navier-Stokes equations; one- and two-dimensional forms; model equations. Mathematical properties of the Euler equations; primitive and conserved solution variables; eigensystem analysis; compatibility conditions; characteristic variables, Rankine-Hugoniot conditions and Riemann invariants; Riemann problem and exact solution. Godunov’s method; hyperbolic flux evaluation and numerical flux functions; solution monotonicity; Godunov’s theorem. Approximate Riemann solvers; Roe’s method. Higher-order Godunov-type schemes; semi-discrete form; solution reconstruction including least-squares and Green-Gauss methods; slope limiting. Extension to multi-dimensional flows. Elliptic flux evaluation for viscous flows; diamond-path and average-gradient stencils; discrete-maximum principle. High-order methods; essentially non-oscillatory (ENO) schemes.

### AER 1322H Modern Aircraft Propulsion

**Lecture Course**

This course covers theoretical and practical aspects of aerospace propulsion systems that address modern challenges such as reduced emissions, improved efficiency, greater fuel-flexibility, and rapid travel. Topics covered include:

- Environmental impact of engines: Types of emissions and their effects on climate-change and air-quality, engine noise, design goals for environmentally-friendly propulsion.
- Performance of high-efficiency Brayton-cycle engines: Multi-spool engines, high-bypass-ratio turbofans, open-rotor engines. Design considerations for large fans.
- Cycles for improved efficiency: Intercooled, wave-rotor, and pulse-detonation engines.
- Gas turbine combustion schemes for reduced emissions: Pollutant formation mechanisms, rich-quench-lean combustion, lean premixed combustion, thermo-acoustic instabilities, effects of alternative fuels.
- Elements of high-speed air-breathing propulsion: Ramjets and scramjets.

*Prerequisite:*

AER 510H “Aerospace Propulsion” or equivalent

### AER 1324H Introduction to Turbulence

**Lecture Course**

This course presents an introduction to the physics, statistical description, and engineering approximations of turbulent flows. Topics covered include:

- The foundations of high Reynolds number flows and their implications; mathematical description of turbulent flow phenomena, including flow equations, vorticity dynamics, Reynolds-averaged equations; motivations behind a statistical description of turbulent flows.
- Review of statistical concepts relevant to turbulent flows, including PDFs, characteristic functions, and correlations.
- A description of the structure and dynamics of homogeneous, isotropic turbulence, focusing on multi-point statistics, energy-transfer concepts, and their application to turbulence decay/dissipation and return to isotropy.
- An introduction to the physical concepts behind engineering turbulence models.

## Structures, Design, and Optimization

### AER 0501H Advanced Mechanics Of Structures

*P. B. Nair*

**Lecture course**

Introduction to the theory of linear elasticity: stress, strain and material constitutive laws. Variational principles and their application: stationary potential energy, stationary complementary potential energy, Reissner’s Principles. The finite element technique: problem formulation; element properties; applications to displacement, vibrations and buckling problems. Introduction to structural optimal design.

### AER 1403H Advanced Aerospace Structures

*C. A. Steeves*

**Lecture course**

This course will provide instruction in three areas crucial to aerospace structural design: thin walled structures, fiber composite materials, and finite element methods. All three will be taught in a manner such that their interrelation is made clear. The course will being with general theories of shells and thin walled structures, which are essential to aircraft design. Composite mechanics and fabrication will be addressed in the context of thin walled structures. Finally, finite element methods of use in modelling thin walled structures and composites will be described. No specific background in any of these three topics is required, but a good knowledge of solid and structural mechanics will be assumed.

### AER 1410H Topology Optimization

*C. A. Steeves*

**Lecture course**

Topology optimization is a relatively new method for the computational design of structures that enables optimal structural design beyond traditional size and shape optimization. Specifically, topology optimization identifies where to put material and where to put holes within the design domain. This course will examine the background to topology optimization, the theory and algorithms necessary to build a topology optimization code, and the two main approaches to topology optimization. At the conclusion of the course, students will be able to program a basic topology optimization code and use a common commercial software package.

### AER 1415H Computational Optimization

*P. B. Nair*

**Lecture course**

This is an introductory graduate-level course on computational optimization and it is assumed that students have had undergraduate level training in multivariable calculus, linear algebra and MATLAB programming. The topics to be covered in this course include: formulation of optimization problems, non-gradient and stochastic search techniques, gradient-based optimization algorithms for unconstrained and constrained problems, numerical methods for sensitivity analysis, surrogate modeling, surrogate-assisted optimization frameworks, applications of optimization algorithms to design, parameter estimation and control.

### AER 1416H Numerical Methods for Uncertainty Quantification

*P. B. Nair*

**Lecture course**

This is an introductory graduate-level course on uncertainty quantification and it is assumed that students have had undergraduate level training in statistics, linear algebra and numerical methods for partial differential equations. The topics to be covered include: verification and validation of computational models, construction of probabilistic uncertainty models, Monte Carlo and Quasi-Monte Carlo simulation methods, importance sampling and variance reduction techniques, sparse quadrature schemes, perturbation methods, polynomial chaos expansions, stochastic Galerkin projection schemes, and an introduction to robust design optimization.

## Space Systems Engineering

### AER 0506H Spacecraft Dynamics And Control I

*C. J. Damaren*

**Lecture course**

Rigid body kinematics and dynamics. Orbital dynamics and control: the two-body problem, orbital perturbations, orbital maneuvers, interplanetary trajectories, the restricted three-body problem. Attitude dynamics and control: torque-free motion, spin stabilization, dual-spin stabilization, disturbance torques, gravity-gradient stabilization, active spacecraft attitude control, bias-momentum stabilization.

### AER 0521H Mobile Robotics and Perception

*T.D. Barfoot*

**Lecture course**

The course addresses fundamentals of mobile robotics and sensor-based perception for applications such as space exploration, search and rescue, mining, self-driving cars, unmanned aerial vehicles, autonomous underwater vehicles, etc. Topics include sensors and their principles, state estimation, computer vision, control architectures, localization, mapping, planning, path tracking, and software frameworks. Laboratories will be conducted using both simulations and hardware kits.

*Recommended Preparation:*

AER 372H “Control Systems”

### AER 0525H Robotics

*M. R. Emami*

**Lecture course**

This course extends the fundamentals of analytical robotics to design and control of industrial and aerospace robots and their instrumentation. Topics include forward, inverse, and differential kinematics, screw representation, statics, inverse and forward dynamics, motion and force control of robot manipulators, actuation schemes, task-based and workspace design, position and force sensors, tactile sensing, and vision and image processing in robotic systems. Course instruction benefits from the courseware technology that involves a Java-based on-line simulation and other multimedia means for presenting realistic demonstrations and case studies in the context of teaching advanced notions. A series of experiments in the Robotics Laboratory will also enhance the practical notions of the course content.

### AER 1503H Spacecraft Dynamics And Control II

*C. J. Damaren*

**Lecture course**

Advanced topics in spacecraft dynamics and control. Course includes a project. Topics include input-output stability analysis and Lyapunov stability analysis with applications to spacecraft attitude control; feedforward, feedback, and adaptive controller design. Quaternion feedback. Linear state-space analysis and observer-based compensator design. Flexible spacecraft dynamics: equations of motion, spatial discretization, modal equations, constrained and unconstrained modes. Flexible spacecraft control: spillover, controller discretization, LQG, H-infinity, and positive real design.

**Prerequisite:**

AER 0506H “Spacecraft Dynamics and Control I”

### AER 1512H Multibody Dynamics

*G. M. T. D’Eleuterio*

**Lecture course**

This is a seminar course designed to introduce students to the fundamentals of multibody dynamics with particular emphasis on the dynamics of robotic systems. Each student, in consultation with the course coordinator, will be required to select two topics in the area, investigate them thoroughly and present a seminar on each to the other members of the class. Students may choose topics well-treated in the mechanical literature or ones which are more research-oriented, perhaps requiring some original input on the part of the student.

### AER 1513H State Estimation for Aerospace Vehicles

*T. D. Barfoot*

**Lecture course**

This course introduces the fundamentals of state estimation for aerospace vehicles. Knowing the state (e.g., position, orientation, velocity) of a vehicle is a basic problem faced by both manned and autonomous systems. State estimation is relevant to aircraft, satellites, rockets, landers, and rovers. This course teaches some of the classic techniques used in estimation including least squares and Kalman filtering. It also examines some cutting edge techniques for nonlinear systems including unscented Kalman filtering and particle filtering. Emphasis is placed on the ability to carry out state estimation for vehicles in three- dimensional space, which is complicated by vehicle attitude and often handled incorrectly. Students will have a chance to work with datasets from real sensors in assignments and will apply the principles of the course to a project of their choosing.

### AER 1514H Mobile Robotics

*T. D. Barfoot*

**Lecture course**

This course introduces the basic of controlling mobile robots, with emphasis on techniques for use outdoors. Mobile robots have found application in space exploration (e.g., Mars Exploration Rovers), mining, bomb disposal, search and rescue, and vacuuming our homes. The future will see mobile robotics technology paving the way to such things as home assistants and automated roadways. This course will present the current state of the art in mobile robotics in terms of sensing and algorithms. Concepts will be learned through experimentation with a mobile robotics kit.

Topics include: introduction to mobile robotics, review of probability theory, sensors, computer vision, simultaneous localization and mapping (SLAM), place recognition, terrain assessment, path planning, path tracking, experimental testing.

### AER 1515H Intelligent Robotics

*M. R. Emami*

**Lecture course**

The course addresses theoretical and practical notions of “Intelligent Robotics”. Topics include cognitive models and learning schemes for robotic systems, design issues for biologically-inspired robots, fuzzy-logic and neural-network control of intelligent robots at both planning and execution levels, instrumentation of intelligent robots and sensor fusion, multi-agent robotic systems, and human-robot interaction. The theme of the applications discussed in the course is service and aerospace robotics.

Prerequisite:

AER 0525H “Robotics”

### AER 1520H Microsatellite Design I

*R. E. Zee*

**Design course**

This is the first of a series of two courses, which are intended to provide graduate students with practical space systems engineering experience. Through two consecutive courses, students can participate in a real Canadian Space Agency ‘MicroSat’ mission, gaining a year’s worth of training under some of the leading spacecraft designers in North America. This two-term apprenticeship allows students to learn and play an active role in spacecraft design, prototyping, assembly, integration, and test. Depending on the stage of the project when students join, they will be exposed to anything from preliminary subsystem design to actual on-orbit operations of a real satellite. Depending on when the student takes the course, he or she will join a coordinated team involved in spacecraft design, prototyping, assembly, integration or test. Students will be exposed to one or more of the following areas: Systems Engineering; Mission Analysis; Power; Communications; Telemetry/Telecommand; Thermal Control; Structure; Attitude Control; On-Board Computers.

Prerequisite:

AER 407 [undergraduate course on ‘Space Systems Design’] or some suitable equivalent

Students will be admitted if they can demonstrate sufficient background in one of the relevant subsystem areas.

For assessment of prerequisite courses, students should contact the course instructor.

### AER 1521H Microsatellite Design II

*R. E. Zee*

**Design course**

The second course permits the student to obtain new and in-depth experience in a particular spacecraft area. In addition, the student is exposed to more elements of the project, considerably increasing the value of the student’s training with time. This course builds on experience gained in AER 1520, and broadens the student’s understanding of practical spacecraft development. Depending on what the student contributed in AER 1520, the student will take his or her work to the next level of maturity.

Course assignments may include the following tasks: Building of Prototypes; Prototype Testing and/or Test Planning; Detailed Design; Assembly, Integration and Test; Launch preparations; On-orbit commissioning of satellites; Satellite operations.

Prerequisite:

AER 1520H “Microsatellite Design I”

## Engineering Physics

### AER 0507H Introduction to Fusion Energy

*J. W. Davis*

**Design course**

Nuclear reactions between light elements provide the energy source for the sun and stars. On earth, such reactions could form the basis of an essentially inexhaustible energy resource. In order for the fusion reactions to proceed at a rate suitable for the generation of electricity, the fuels (usually hydrogen) must be heated to temperatures near 100 million Kelvin. At these temperatures, the fuel will exist in the plasma state. This course will cover: (i) the basic physics of fusion, including reaction cross-sections, particle energy distribution, Lawson criterion and radiation balance, (ii) plasma properties including plasma waves, plasma transport, heating and stability, and (iii) magnetic confinement methods. Topics will be related to current experimental research in the field.

### AER 1717Y & 1720Y Applied Plasma Physics I & II

*P. C. Stangeby*

**Reading courses**

A second and third course in plasma physics and fusion energy for the student intending a career in these fields. Numerous problems are assigned from the text “Plasma Physics and Controlled Fusion “, Vol. 1 by F. F. Chen, Plenum Press, 1984 (AER 1717H ) and “The Plasma Boundry of Magnetic Fusion Devices ” , by P.C. Stangeby, Institute of Physics Publishing, Bristol,U.K., 2000. (AER 1720H )

## Research Seminars and Professional Courses

### AER 1800H Research Seminar In Aerospace Science And Engineering

This is a required course for all new M.A.Sc. students. The course material is based on the student’s thesis, and therefore it will vary from student to student. The objective of the course is to ensure that students devote a significant level of effort to their theses during their first year of graduate studies. Students will present a series of seminars based on their research progress and accomplishments.

### AER 1810H M.Eng. Project

This course is offered to M.Eng. students only. The projects associated with this course generally involve a professionally oriented design activity. Project topics, related to the aerospace field, are selected in consultation with staff. Work includes project identification and definition, literature survey, assesment of available information, and the design phase. Course mark is based on progress during the term, a final project report and a seminar presentation.

### RST 9999Y Thesis/Research

Students registering in the M.A.Sc. and/or Ph.D. programs are required to include this along with their enrolment forms.

### JDE 1000H Ethics in Research

Students registered in the M.A.Sc. and Ph.D. programs are required to participate in this non-credit seminar course during their first or second term of registration.