Graduate Courses for Engineering, Aerospace (ENAE)

Schedule of Classes: Fall | Winter | Spring | Summer
(Only current and next semester available)

ENAE 403 Aircraft Flight Dynamics (3 credits)
Prerequisites: ENAE432 and ENAE414. ENAE majors only or permission of department.
Study of motion of aircraft, equations of motion, aerodynamic force representation, longitudinal and lateral motions, response to controls and to atmospheric disturbances, handling qualities criteria and other figures of merit.

ENAE 404 Space Flight Dynamics (3 credits)
Prerequisite: ENAE301. ENAE majors only or permission of department.
Three-dimensional motion under central fields. Solutions to orbital motion, orbital elements, time elements. Kepler's laws. Orbital maneuvering, rendezvous and station-keeping. Rigid-body attitude dynamics, spacecraft attitude dynamics.

ENAE 414 Aerodynamics II (3 credits)
Prerequisite: ENAE311. ENAE majors only or permission of department. Junior standing. Formerly ENAE371.
Aerodynamics of inviscid incompressible flows. Aerodynamic forces and moments. Fluid statics/buoyancy force. Vorticity, circulation, the stream function and the velocity potential. Bernoulli's and Laplace's equations. Flows in low speed wind tunnels and airspeed measurement. Potential flows involving sources and sinks, doublets, and vortices. Development of the theory of airfoils and wings.

ENAE 415 Helicopter Theory (3 credits)
Prerequisite: ENAE414. For ENAE majors only.
Elementary exposition on the theory and practice of aerodynamics applied to helicopters and other rotary wing aircraft.

ENAE 420 Computational Structural Mechanics (3 credits)
Prerequisite: ENES220, MATH241, Linear Algebra. For ENAE majors only or with permission of department.
Introductory of finite element methods for aerospace engineering modeling and analysis; equips students with ability to understand manuals of commercial finite element analysis software.

ENAE 423 Vibration and Aeroelasticity (3 credits)
Prerequisite: ENAE324. ENAE majors only or permission of department.
Dynamic response of single and multiple degrees of freedom systems, finite element modeling, wing divergence, aileron reversal, wing and panel flutter.

ENAE 424 Design and Manufacture of Composite Prototypes (3 credits)
Two hours of lecture and three hours of laboratory per week. Prerequisite: ENES220. Corequisite: ENAE324. For ENAE majors only.
Manufacturing practices involving composites. Developing a manufacturing process for a composite component integrating the many aspects including cost, schedule, performance. Student teams provide oral and written reports of the design and manufacture of a composite prototype.

ENAE 425 Mechanics of Composite Structures (3 credits)
Prerequisite: MATH246. Corequisite: ENAE324.
Introduction to structures composed of composite materials and their applications in aerospace. In particular, filamentary composite materials are studied. Material types and fabrication techniques, material properties, micromechanics, anisotropic elasticity, introduction to failure concepts.

ENAE 432 Control of Aerospace Systems (3 credits)
Prerequisite: grade of C or better in ENAE283 and ENAE301. Junior standing. For ENAE majors only. Formerly ENAE332.
An introduction to the feedback control of dynamic systems. Laplace transforms and transfer function techniques; frequency response and Bode diagrams. Stability analysis via root locus and Nyquist techniques. Performance specifications in time and frequency domains, and design of compensation strategies to meet performance goals.

ENAE 441 Space Navigation and Guidance (3 credits)
Prerequisites: ENAE432 and ENAE404. ENAE majors only or permission of department.
Principles of navigation. Celestial, radio, and inertial navigation schemes. Navigational and guidance requirements for orbital, planetary, and atmospheric entry missions. Fundamentals of communications and information theory. Link budgets, antennas and telemetry systems.

ENAE 455 Aircraft Propulsion and Power (3 credits)
Prerequisite: ENAE311, ENAE414 and ENME232. ENAE majors only or permission of department.
Thermodynamic cycle analysis, aerothermochemistry of fuels and propellants, operating principles of piston, turbojet, fanjet, and other variations of airbreathing aircraft power units.

ENAE 457 Space Propulsion and Power (3 credits)
Prerequisites: ENAE311, ENME232 and (PHYS270 and 271 {Formerly: PHYS263}). ENAE majors only or permission of department. Senior standing.
Thermodynamic cycle analysis, aerothermochemistry of fuels and propellants, operating principles of rocket, ion, and other exoatmospheric power units.

ENAE 464 Aerospace Engineering Laboratory (3 credits)
Two hours of lecture and three hours of laboratory per week. Prerequisites: ENAE311; ENAE324; ENAE432; and ENAE362. ENAE majors only or permission of department.
Application of fundamental measuring techniques to measurements in aerospace engineering. Includes experiments in aerodynamics, structures, propulsion, flight dynamics and astrodynamics. Correlation of theory with experimental results.

ENAE 471 Aircraft Flight Testing (3 credits)
Prerequisite: ENAE414;. Corequisite: ENAE403. For ENAE majors only.
Provides basic instruction to aircraft flight testing and demonstrates need for systematic, well-proven technique to allow for accurate airplane performance. Concepts of aerodynamics, airplane performance, and stability and control. Emphasis on single-engine general aviation type aircraft.

ENAE 480 Fundamentals of Engineering Design (3 credits)
Two hours of lecture and two hours of laboratory per week. Prerequisite: ENES102, ENES220, ENAE202 or equivalent. For Aerospace engineering majors only or with permission of department. Credit will be granted for only one of the following: ENAE480 or ENAE488P. Formerly ENAE488P.
Presents broad overview at advanced level of designing a part as it relates to design philosophies in solving engineering and manufacturing problems. Emphasis is placed on manufacturing requirements and their effects on product processing.

ENAE 481 Principles of Aircraft Design (3 credits)
Prerequisites: ENAE324, ENAE362 and ENAE432. Corequisite: ENAE414. ENAE majors only or permission of department.
Aircraft design principles blending both synthesis and analysis. The iterative nature of the design process. Applied aerodynamics. Elements of aircraft performance calculation and optimization. Design of aircraft including payload, crew and avionics provisions, propulsion selection and sizing, aerodynamic configuration optimization, mass properties, stability and control characteristics, and vehicle subsystems. Individual student projects in aircraft design.

ENAE 482 Aeronautical Systems Design (3 credits)
Two hours of lecture and three hours of laboratory per week. Prerequisites: ENAE403; ENAE423; ENAE455; and ENAE481. Senior standing. For ENAE majors only.
Senior capstone design course in the aeronautics track. Introduction of computerized methods for sizing and performance analysis. More comprehensive methods to predict weight, aerodynamics and propulsion system characteristics. Consideration in design disciplines such as vulnerability, maintainability, produceability, etc. Groups of students will complete, brief and report on a major design study to specific requirements.

ENAE 483 Principles of Space Systems Design (3 credits)
Prerequisites: ENAE324; ENAE432; ENAE362; and ENAE404. ENAE majors only or permission of department.
Principles of space systems analysis and vehicle design. Launch vehicle performance analysis and optimization. Design of vehicle systems including avionics, power, propulsion, life support, human factors, structures, actuator and mechanisms, and thermal control. Design processes and design synthesis. Individual student projects in vehicle design.

ENAE 484 Space Systems Design (3 credits)
Three hours of lecture and six hours of discussion/recitation per week. Prerequisites: ENAE423; ENAE441; ENAE457; and ENAE483. For ENAE majors only.
Senior capstone design course in the space track. Group preliminary design of a space system, including system and subsystem design, configuration control, costing, risk analysis, and programmatic development. Course also emphasizes written and oral engineering communications.

ENAE 488 Topics in Aerospace Engineering (1-4 credits)
Technical elective taken with the permission of the student's advisor and instructor. Lecture and conference courses designed to extend the student's understanding of aerospace engineering. Current topics are emphasized.

ENAE 499 Elective Research (3 credits)
Prerequisites: senior standing in ENAE major and permission of department, instructor, and student's advisor. Repeatable to 6 credits if content differs.
Undergraduate research project and paper conducted under the direction of an aerospace engineering faculty member to be presented at a conference or competition.

ENAE 601 Astrodynamics (3 credits)
Prerequisites: ENAE 404 and ENAE 441.
Mathematics and applications of orbit theory, building upon the foundations developed in ENAE 404 and ENAE 441. Topics include two body orbits, solutions of Kepler's equation, the two-point boundary value problem, rendezvous techniques, and Encke's method.

ENAE 602 Spacecraft Attitude Dynamics and Control (3 credits)
Prerequisites: ENAE 404 and ENAE 432.
Rigid body rotational dynamics of spacecraft; forced and unforced motion, torques produced by the orbital environment; orbit/attitude coupling; gas jet, momentum wheel, and magnetic torque actuators. Elementary feedback attitude regulators and algorithms for linear and nonlinear attitude tracking.

ENAE 631 Helicopter Aerodynamics I (3 credits)
Prerequisites: ENAE 311 and ENAE 414 or permission of both department and instructor.
A history of rotary-wing aircraft, introduction to hovering theory, hovering and axial flight performance, factors affecting hovering and vertical flight performance, autorotation in vertical descent, concepts of blade motion and control, aerodynamics of forward flight, forward flight performance, operational envelope, and introduction to rotor acoustics.

ENAE 632 Helicopter Aerodynamics II (3 credits)
Prerequisites: {ENAE 631; and ENAE 311 and ENAE 414 or equivalent} or permission of department.
Basic aerodynamic design issues associated with main rotors and tail rotors, discussion of detailed aerodynamic characteristics of rotor airfoils, modeling of rotor airfoil characteristics, review of classical methods of modeling unsteady aerodynamics, the problem of dynamic stall, review of methods of rotor analysis, physical description and modeling of rotor vortical wakes, discussion of aerodynamic interactional phenomena on rotorcraft, advanced rotor tip design, physics and modeling of rotor acoustics.

ENAE 633 Helicopter Dynamics (3 credits)
Prerequisite: ENAE 631 or permission of both department and instructor.
Flap dynamics. Mathematical methods to solve rotor dynamics problems. Flap-lag-torsion dynamics and identify structural and inertial coupling terms. Overview on rotary wing unsteady aerodynamics. Basic theory of blade aeroelastic stability and ground and air resonance stability, vibration analyses and suppression.

ENAE 634 Helicopter Design (3 credits)
Prerequisite: ENAE 631 or permission of both department and instructor.
Principles and practice of the preliminary design of helicopters and similar rotary wing aircrafts. Design trend studies, configuration selection and sizing methods, performance and handling qualities analyses, structural concepts, vibration reduction and noise. Required independent design project conforming to a standard helicopter request for proposal (RFP).

ENAE 635 Helicopter Stability and Control (3 credits)
Prerequisite: {ENAE 631 and ENAE 642,} or permission of department.
Advanced dynamics as required to model rotorcraft for flight dynamic studies. Development of helicopter simulation models and specifications of handling qualities. Methods for calculation of trim, poles, frequency response, and free flight response to pilot inputs.

ENAE 640 Atmospheric Flight Mechanics (3 credits)
Prerequisite: ENAE 403 or permission of department.
Studies in the dynamics and control of flight vehicles. Fundamentals of the dynamics of rigid and non-rigid bodies and their motion under the influence of aerodynamic and gravitational forces.

ENAE 641 Linear System Dynamics (3 credits)
Prerequisite: ENAE 432.
Linear systems; state space, multi-input, multi-output models; eigenstructure; controllability, observability, singular value analysis; multivariable Nyquist condition; observer design; introduction to Kalman filtering. Full state feedback techniques including pole placement and LQR/LQG techniques; introduction to loop shaping and robustness.

ENAE 642 Atmospheric Flight Control (3 credits)
Prerequisites: ENAE 432 and ENAE 403, or equivalents.
Exposure to flight guidance and control. Draws heavily from vehicle dynamics as well as feedback theory, and careful treatment of the non-linear aspects of the problem is critical. Conventional sythesis techniques are stressed, although modern methods are not ignored. Multivariable system analysis is included, along with flight-control design objectives and hardware limitations. Emphasis on aircraft and missiles.

ENAE 644 Optimal Control of Aerospace Systems (3 credits)
Prerequisites: ENAE 432, ENAE 403 or ENAE 404, or equivalents.
Formal optimization of linear and non-linear dynamic systems, developed rigorously via the calculus of variations - first and second variations. Treatment of dynamic constraints, terminal conditions, fixed and free final times. Numerical techniques to the non-linear optimization problem are stressed. Investigation of optimal aerodynamic shapes, trajectory optimization, optimal flight guidance. Final project includes numerical analysis.

ENAE 651 Smart Structures (3 credits)
Topics related to the analysis, design, and implementation of smart structures and systems: modeling of beams and plates with induced strain actuation; shape memory alloys; electro-rheological fluids; magnetostrictor and electrostricter actuators and fiber optic sensors.

ENAE 652 Computational Structural Mechanics (3 credits)
Prerequisite: permission of both department and instructor.
Fundamentals of structural mechanics and computational modeling. Finite element modeling of two- and three-dimensional solids, plates and shells. Geometrically nonlinear behavior. Structural stability such as buckling and postbuckling.

ENAE 653 Nonlinear Finite Element Analysis of Continua (3 credits)
Prerequisite: ENAE 652 or equivalent.
Finite element formulation of nonlinear and time dependent processes. Introduction to tensors, nonlinear elasticity, plasticity and creep. Application to nonlinear solids including aerospace structures, such as shells undergoing finite rotations.

ENAE 654 Mechanics of Composite Structures (3 credits)
Prerequisite: ENAE 452 or permission of both department and instructor.. Corequisite: ENAE 423 or equivalent.
An introduction to structures composed of composite materials and their applications in aerospace. In particular, filamentary composite materials are studied. Material types and fabrication techniques, material properties, micromechanics, anisotropic elasticity, introduction to failure concepts.

ENAE 655 Structural Dynamics (3 credits)
Prerequisite: ENAE 452 or permission of department.
Advanced principles of dynamics necessary for structural analysis; solutions of eigenvalue problems for discrete and continuous elastic systems, solutions to forced response boundary value problems by direct, modal, and transform methods.

ENAE 656 Aeroelasticity (3 credits)
Prerequisite: ENAE 655 or permission of department.
Topics in aeroelasticity: wing divergence; aileron reversal; flexibility effects on aircraft stability derivatives; wing, empennage and aircraft flutter; panel flutter; aircraft gust response; and aeroservoelasticity of airplanes.

ENAE 661 Advanced Propulsion I (3 credits)
Prerequisites: ENAE 455; and ENAE 457.
Special problems of thermodynamics and dynamics of aircraft power plants; jet, rocket and ramjet engines. Plasma, ion and nuclear propulsion for space vehicles.

ENAE 662 Advanced Propulsion II (3 credits)
Prerequisite: ENAE 661.
Special problems of thermodynamics and dynamics of aircraft power plants; jet, rocket and ramjet engines. Plasma, ion and nuclear propulsion for space vehicles.

ENAE 670 Fundamentals of Aerodynamics (3 credits)
Prerequisite: permission of department.
Introduction to aerodynamics for aerospace engineering students specializing in fields other than aerodynamics. Broad coverage of flight regimes, inviscid theory, incompressible theory, subsonic compressible flow, linearized supersonic flow, hypersonic flow, viscous flows, Navier-Stokes equations, boundary layer theories.

ENAE 672 Aerodynamics of Incompressible Fluids (3 credits)
Prerequisite: MATH 463 or permission of instructor.
Fundamental equations in fluid mechanics. Irrotational motion. Circulation theory of lift. Thin airfoil theory. Lifting line theory. Wind tunnel corrections. Perturbation methods.

ENAE 674 Aerodynamics of Compressible Fluids (3 credits)
Prerequisite: ENAE 471 or permission of department.
One-dimensional flow of a perfect compressible fluid. Shock waves. Two-dimensional linearized theory of compressible flow. Two-dimensional transonic and hypersonic flows. Exact solutions of two-dimensional isotropic flow. Linearized theory of three-dimensional potential flow. Exact solution of axially symmetrical potential flow. One-dimensional flow with friction and heat addition.

ENAE 676 Aerodynamics of Viscous Fluids (3 credits)
Prerequisite: ENAE 416 or permission of department.
Derivation of navier stokes equations, some exact solutions: boundary layer equations. Laminar flow-similar solutions, compressibility, transformations, analytic approximations, numerical methods, stability and transition to turbulent flow. Turbulent flow-istropic turbulence, boundary layer flows, free mixing flows.

ENAE 681 Engineering Optimization (3 credits)
Prerequisite: permission of department.
Methods for unconstrained and constrained minimization of functions of several variables. Sensitivity analysis for systems of algebraic equations, eigenvalue problems, and systems of ordinary differential equations. Methods for transformation of an optimization problem into a sequence of approximate problems. Optimum design sensitivity analysis.

ENAE 682 Hypersonic Aerodynamics (3 credits)
Prerequisite: permission of department.
Hypersonic shock and expansion waves, Newtonian theory, Mach methods, numerical solutions to hypersonic inviscid flows, hypersonic boundary layer theory, viscous interactions, numerical solutions to hypersonic viscous flows. Applications to hypersonic vehicles.

ENAE 683 High Temperature Gas Dynamics (3 credits)
Prerequisite: permission of department.
Aspects of physical chemistry and statistical thermodynamics necessary for the analysis of high temperature flows, equilibrium and nonequilibrium chemically reacting flows, shock waves, nozzle flows, viscous chemically reacting flow, blunt body flows, chemically reacting boundary layers, elements of radiative gas dynamics and applications to hypersonic vehicles.

ENAE 684 Computational Fluid Dynamics I (3 credits)
Prerequisite: permission of department.
Partial differential equations applied to flow modelling, fundamental numerical techniques for the solution of these equations, elliptic, parabolic, and hyperbolic equations, elements of finite difference solutions, explicit and implicit techniques. Applications to fundamental flow problems.

ENAE 685 Computational Fluid Dynamics II (3 credits)
Prerequisite: ENAE 684 or permission of department.
Continuation of ENAE 684. Basic algorithms for the numerical solution of two and three dimensional inviscid and viscous flows. Applications to internal and external flow problems.

ENAE 688 Seminar (1-3 credits)

ENAE 691 Satellite Design (3 credits)
Prerequisite: ENAE 483.
Systems design of Earth-orbiting satellites, including geostationary communications satellites and low Earth orbit constellations. Basics of orbital motion, communications, and instrument design. Spacecraft systems, structural design, thermal design, power generation, and attitude determination and control. Launch vehicle interfacing and mission operations.

ENAE 692 Introduction to Space Robotics (3 credits)
Analysis techniques for manipulator kinematics and dynamics. DH parameters, serial and parallel manipulators, approaches to redundancy. Applications of robots to space operations, including manipulators on free-flying bases, satellite servicing, and planetary surface mobility. Sensors, actuators, and mechanism design. Command and control with humans in the loop.

ENAE 693 Space Simulation (3 credits)
Physical characteristics of the space environment, and approaches to simulating them on Earth. Systems modeling; kinematics and dynamics. Required degrees of freedom and levels of fidelity. Physical simulations, including neutral buoyancy, air-bearing, and motion carriages. Instrumentation and data collection, error analysis, correlation, and performance metrics.

ENAE 694 Spacecraft Communications (3 credits)
Brief overview of satellite orbits. Radio frequency communications, noise, and bandwidth limitations. Link budget analysis. Modulation and multiplexing approaches, multiple access systems. Satellite transponder and Earth station technology.

ENAE 696 Spacecraft Thermal Design (3 credits)
Thermal sources in space. Black-body radiation; absorptivity and emissivity; radiative thermal equilibrium. Mutually radiating plates, view angles, and interior conduction. Techniques of spacecraft thermal analysis; approaches to passive and active thermal control.

ENAE 697 Space Human Factors and Life Support (3 credits)
Engineering requirements supporting humans in space. Life support design: radiation effects and mitigation strategies; requirements for atmosphere; water, food, and temperature control. Accommodations for human productivity in space: physical and psychological requirements; work station design; and safety implication of system architectures. Design and operations for extra-vehicular activity.

ENAE 741 Interplanetary Navigation and Guidance (3 credits)
Prerequisites: ENAE 432 and ENAE 601.
Interplanetary trajectory construction; patched and multiconic techniques. Methods of orbit and attitude determination; applied Kalman filtering. Guidance algorithms and B-plane targeting. Interplanetary navigation utilizing in situ and radio techniques.

ENAE 742 Robust Multivariable Control (3 credits)
Prerequisites: ENAE 432 or equivalent, plus graduate-level exposure to linear systems and linear algebra.
Limitations on achievable performance in multivariable feedback systems due to uncertainty. Singular values, matrix norms, multivariable Nyquist stability theory, uncertainty modeling in aerospace systems. Loop-shaping, generalization of Bode design principles. Characterizing the uncertainty, robustness and performance analysis, and synthesis, primarily in the frequency domain. Current research directions. Aerospace examples are used to complement the theory.

ENAE 743 Applied Nonlinear Control of Aerospace Vehicles (3 credits)
Prerequisite: ENAE 641.
Modern methods of analysis and synthesis of multivariable nonlinear control techniques for aircraft, spacecraft, and space manipulator systems. Topics include passivity and Lyapunov theory, feedback linearization, nonlinear observers, Hamiltonian methods, robust controller design, and an introduction to adaptive nonlinear control methods.

ENAE 754 Integrity of Composite Structures (3 credits)
Prerequisite: ENAE 654 or equivalent.
Failure mechanisms of composite structures such as fracture, delamination. Specific areas include crashworthiness, flaws, tapered structures, and joints. Key research areas reflect special applications to aerospace engineering.

ENAE 757 Advanced Structural Dynamics (3 credits)
Prerequisite: ENAE655 or equivalent.
Model correlation and updating of multi degree-of-freedom structural systems. Wave propagation analysis of structural dynamics. Structural health monitoring and damage detection methods. Stationary and non-stationary methods for vibration analysis. Applications include rotorcraft, aircraft, and spacecraft structures.

ENAE 788 Selected Topics in Aerospace Engineering (1-3 credits)

ENAE 791 Launch and Entry Vehicle Design (3 credits)
Prerequisite: ENAE 601.
Design of aerospace vehicles for atmospheric transit to and from space. Generic formulation of atmospheric flight dynamics. Ballistic and lifting entry trajectories. Estimation of vehicle aerodynamic properties and aerothermodynamic heating. Entry thermal protection design. Trajectory analysis of sounding rockets and orbital launch vehicles. Serial, parallel, and hybrid multistaging schemes, optimal multistaging. Constrained trajectory optimization. Launch vehicle economic and reliability analysis, flight termination systems, sensors and actuators.

ENAE 799 Master's Thesis Research (1-6 credits)

ENAE 898 Pre-Candidacy Research (1-8 credits)

ENAE 899 Doctoral Dissertation Research (1-8 credits)