Aerospace Engineering
Undergraduate Courses
AE 2110. Introduction to Incompressible Fluid Dynamics
Cat I (offered at least 1x per Year).
This course covers the fundamentals of inviscid and viscous incompressible fluid dynamics. Topics presented will be considered from the following: fluid kinematics and deformation; integral conservation laws of mass, momentum and energy for finite systems and control volumes; differential conservation laws of mass, momentum and energy; the Navier-Stokes equations; the streamfunction and the velocity potential. Applications will be considered from the following topics: hydrostatics; incompressible, inviscid, irrotational (potential) flows; incompressible boundary layer flows; viscous incompressible steady internal and external flows; and dimensional analysis.
AE 2310. Introduction to Aerospace Control Systems
Cat I (offered at least 1x per Year).
This course introduces feedback control systems analysis and design for applications to aircraft and spacecraft. Topics include: linear dynamical systems modeling of aircraft and spacecraft motion, including linearization; identification and transient response analysis of typical modes of motion; time- and frequency domain analysis; Bode plots; criteria for stability; design of stability augmentation and, attitude and orbital control systems using linear state feedback or PID control; numerical simulation of controlled and uncontrolled aircraft and spacecraft motion.
AE 2320. Introduction to Orbital Mechanics
Cat I (offered at least 1x per Year).
An introductory course that covers the fundamentals of space flight. Topics studied include: two-body orbital dynamics, classification of orbits, and time of flight analysis; geocentric orbits and impulsive maneuvers: orbit shaping, escape trajectories, Hohmann and non-Hohmann transfers; orbital elements in 3D; interplanetary Hohmann and generalized transfers, intercepts, flybys.
AE 2410. Introduction to Aerospace Structures
Cat I (offered at least 1x per Year).
This course provides a concise overview of statics and then focuses on basic stress analysis applied to simple aerospace structures. Topics in stress analysis include: concepts of stress and strain; basic constitutive relations; one-dimensional response to axial loading; thermal stresses; statically determinate and indeterminate problems; shear forces, bending moments, bending stresses and deflections in beams with symmetric cross-sections; two-dimensional stress transformation and Mohrs circle; and an introduction to energy methods in structural analysis.
AE 3110. Fundamentals of Compressible Fluid Dynamics
Cat I (offered at least 1x per Year).
In this course, students are introduced to various compressibility phenomena such as compression (shock) and expansion waves. Conservation laws and thermodynamic principles are applied to the description of flows in which compressibility effects are significant. One-dimensional models are applied to analysis of flow in variable area ducts, normal and oblique shock waves, expansion waves, and flows with friction and heat addition. Numerous applications from engineering are investigated including supersonic inlets, rocket nozzles, supersonic wind tunnels, gas delivery systems, and afterburning jet engines.
AE 3120. Fundamentals of Aerodynamics
Cat I (offered at least 1x per Year).
This course introduces students to the aerodynamics of airfoils, wings, and aircraft in the subsonic and supersonic regimes. Topics covered include: prediction of aerodynamic forces (lift, drag) and moments, dynamic similarity, experimental techniques in aerodynamics, Kutta-Joukowski theorem, circulation, thin airfoil theory, panel methods, finite wing theory, subsonic compressible flow over airfoils, linearized supersonic flow, and viscous flow over airfoils.
AE 3310. Fundamentals of Navigation and Communication
Cat I (offered at least 1x per Year).
This course covers methods and current technologies in the analysis, synthesis, and practice of aerospace guidance, navigation, and communications systems. Topics covered include: attitude- and position kinematics, inertial navigation systems, global satellite navigation systems, communication architectures for satellite navigation, satellite link performance parameters and design considerations, tropospheric and ionospheric effects on radio-wave propagation, least squares estimation, and the Kalman filter.
AE 3420. Fundamentals of Aerospace Structures
Cat I (offered at least 1x per Year).
This course focuses on intermediate-level topics in stress analysis relevant to aerospace structures. Topics include: buckling under centric and eccentric loadings with and without lateral loads applied; torsion of solid circular and noncircular cross sections; torsion of thin-walled multi-celled members; flexural shear flow in and shear center of thin walled multi-celled members; bending stresses in beams with unsymmetric cross sections; stresses under combined loadings; and three-dimensional states of stress. The laboratory component of this course provides testing and measurement experience related to buckling of columns under a variety of loadings and support conditions; and to the determination of the shear center and bending response of beams with unsymmetric cross sections.
AE 3430. Fundamentals of Composite Materials
Cat I (offered at least 1x per Year).
This course provides an overview of the processing techniques and mechanical behavior of composite materials relevant to aerospace applications. Topics in this course may include: classification of composites; elasticity of composite materials; the effect of reinforcements on strength and toughness; bonding mechanisms of interfaces in composite; fabrication methods for polymer-matrix composite materials; viscoelasticity and creep of composites; advanced composites materials (bio-composites, nano-composites).
AE 4210. Fundamentals of Air-Breathing Propulsion
Cat I (offered at least 1x per Year).
This course introduces the principles of operation of air-breathing engines, including gas-turbines (turbojets, turbofans, and turboprops), ramjets, and scramjets. Topics covered include: engine thrust and efficiency analysis; working principles and performance analysis of diffusers, compressors, combustors, and nozzles; parametric cycle analysis; effect of irreversibilities on performance. The topics covered are also relevant to the operation of gas-turbines used for power generation.
AE 4220. Fundamentals of Rocket Propulsion
Cat I (offered at least 1x per Year).
This course provides a study of rocket propulsion systems for launch vehicles and spacecraft. Dynamics, performance, and optimization of rocket-propelled vehicles are presented. Performance and component analysis of chemical propulsion systems are covered including flight dynamics, vehicle staging, nozzle design, and thermochemistry of bipropellant and monopropellant thrusters. Different classes of electric thrusters are introduced along with the concept of optimal specific impulse.
AE 4310. Fundamentals of Aircraft Dynamics and Control
Cat I (offered at least 1x per Year).
This course covers models of fixed-wing aircraft dynamics, and the design of aircraft control systems. Topics include: aircraft performance, longitudinal and lateral flight dynamics, simulation methodologies, natural modes of motion, static and dynamic stability, and aircraft control systems (such as autopilot design, flight path control, and automatic landing).
AE 4320. Fundamentals of Spacecraft Dynamics and Control
Cat I (offered at least 1x per Year).
The course covers broad topics in spacecraft attitude dynamics, stability and control. The course includes a review of particle and two-body dynamics and introduction to rigid body dynamics. Orbital and attitude maneuvers are presented. Attitude control devices and momentum exchange techniques such as spinners, dual spinners, gravity gradient, and geomagnetic torques are presented. Attitude sensors/actuators are presented and the attitude control problem is introduced. Open-loop stability analysis for a variety of equilibrium conditions is discussed. Control using momentum exchange and mass expulsion (thrusters) devices is discussed. The analyses and designs will be implemented using scientific computing software such as MATLAB.
AE 4410. Fundamentals of Structural Dynamics
Cat I (offered at least 1x per Year).
This course introduces the analysis of vibrations of flexible bodies encountered as elements of aircraft and space structures. Topics include: modeling of aerospace structures with lumped parameters using Newtons Law and Lagranges equations, free- and forced- vibration response of single degree of freedom systems and multi-degree of freedom systems, design of simplified vibration absorption systems, dynamic testing, modal analysis for determining structural response of lumped and continuous systems.
AE 4510. Aircraft Design
Cat I (offered at least 1x per Year).
This course introduces students to design of aircraft systems. Students complete a conceptual design of an aircraft in a term-long project. Students are exposed to the aircraft design process, and must establish design specifications, develop and analyze alternative designs, and optimize their designs to meet mission requirements. Students work together in teams to apply material learned in the areas of aerodynamics, aerospace materials, structures, propulsion, flight mechanics, and stability and control, to the preliminary design of an aircraft. The project requirements are selected to reflect real-life aircraft mission requirements, and teams are required to design systems which incorporate appropriate engineering standards and multiple realistic constraints. The teams present their design in a final report and oral presentation.
AE 4520. Spacecraft and Mission Design
Cat I (offered at least 1x per Year).
This course introduces students to design of spacecraft and missions. Students are introduced to the process of designing a spacecraft and major subsystems to meet a specific set of objectives or needs. In addition, students will learn about different spacecraft subsystems and what factors drive their design. Students complete a term-long spacecraft design project conducted by teams. The project addresses orbital mechanics, the space environment, attitude determination and control, telecommunications, space structures, and propulsion, along with other spacecraft subsystems. The project requirements are selected to reflect real-life missions, and teams are required to design systems which incorporate appropriate engineering standards and multiple realistic constraints. The teams present their design in a final report and oral presentation.
PH 2550. Atmospheric and Space Environments
Cat I (offered at least 1x per Year).
This course introduces the ambient atmospheric and space environments encountered by aerospace vehicles. Topics include: the sun and solar activity; the solar wind; planetary magnetospheres; planetary atmospheres; radiation environments; galactic cosmic rays; meteoroids; and space debris.
Graduate Courses
AE 5031. Applied Computational Methods for Partial Differential Equations
The course provides at an entry graduate level the theory and practice of finite difference and finite elements methods for partial differential equations (PDEs) encountered in fluid dynamics and solid mechanics. Topics covered include: classification of partial PDEs and characteristics; direct and iterative solution methods for solution of algebraic systems; finite difference and finite element spatial discretization; temporal discretization; consistency, stability and error analysis; explicit and implicit finite differencing and finite element schemes for linear hyperbolic, parabolic, elliptic PDEs. The course requires completion of several projects using MATLAB. Students cannot receive credit for this course if they have taken AE/ME 5108 Computational Fluid Dynamics.
AE 5032. Aerospace Engineering Seminar
(0 credits) The Seminar is a degree requirement for all graduate students and is offered during A, B, C, and D term. The Seminar consists of presentations by experts on technical and broader professional topics. Presentations are also offered by graduate students on topics related to their directed research, dissertation, or industrial experiences. The Seminar is offered in pass/fail mode based on attendance.
AE 5093. Special Topics
Arranged by individual faculty with special expertise, these courses survey fundamentals in areas that are not covered by the regular aerospace engineering course offerings. Exact course descriptions are disseminated by the Aerospace Engineering Program in advance of the offering.
AE 5095. Independent Study
An independent study may be used as a substitute for an existing AE course or as an opportunity to study an aerospace engineering topic not currently offered as a course at WPI. The course can be offered to a student or a group of students. The requirements and deliverables are specific to the topic and are determined by the instructor.
AE 5098. Directed Research
These courses are offered by aerospace engineering faculty and cover diverse topics that range from 1 to 8 credits and may be completed in one or multiple terms. These courses provide M.S. and B.S./M.S. students the opportunity to gain research experience on topics of their interest. The required deliverables for successful completion of Directed Research are defined by the faculty offering the course and take into account the credits and topic involved.
AE 5131. Incompressible Fluid Dynamics
This course presents topics in incompressible fluid dynamics at the introductory graduate level. Topics are chosen from: continuum fluids; kinematics and deformation for Newtonian fluids; integral and differential form of the mass conservation, momentum and energy equations; potential flows; unidirectional steady incompressible viscous flows; unidirectional transient incompressible viscous flows; boundary layers; vortical flows. Students cannot receive credit for this course if they have taken AE/ME 5101 Fluid Dynamics or AE/ME 5107 Applied Fluid Dynamics.
AE 5132. Compressible Fluid Dynamics
This course presents applications of compressible fluid dynamics at an introductory graduate level. Topics are chosenfrom: conservation laws; propagation of disturbances; compressible flow with friction; method of characteristics,analysis and design of supersonic nozzles, diffusers, and inlets; transonic and supersonic thin-airfoil theory; three-dimensional compressible flows; compressible boundary layers; hypersonic flows; unsteady compressible flows. Students cannot receive credit for this course if they have taken AE 5093 ST: Applied Compressible Fluid Dynamics.
AE 5133. Kinetic Theory of Gases and Applications
The course presents kinetic theory of gases and its application to equilibrium flows and nonequilibrium flows at the introductory graduate level. Fundamental topics are chosen from: equilibrium kinetic theory; binary collisions; the Boltzmann equation; transport theory and equations. Application topics are chosen from: free molecular aerodynamics; shocks; non equilibrium flows. Students cannot receive credit for this course if they have taken AE/ME 5102Advanced Gas Dynamics.
AE 5134. Plasma Dynamics
The course introduces concepts of partially ionized gases (plasmas) and their role in a wide range of science and engineering fields. Fundamental topics include: motion of charged particles in electromagnetic fields; equilibrium kinetic theory; collisions; transport theory; fluid equations; magnetohydrodynamic models; sheaths. Application topics are chosen from: plasma diagnostics; plasma discharges; spacecraft/environment interactions, and plasma-assisted materials processing. Students cannot receive credit for this course if they have taken AE/ME 5110 Introduction to Plasma Dynamics.
AE 5231. Air Breathing Propulsion
This is an introductory graduate level course that covers principles of operation, design, and performance analysis of air-breathing propulsion engines. Topics will be chosen from: jet propulsion theory; cycle analysis of turbojets, turbofans, and ram compression engines; gas dynamics of inlet and nozzle flows; thermochemistry and chemical equilibrium; combustor modeling; hypersonic propulsion; and operation of detonation engines. Students cannot receive credit for this course if they have taken AE 5106 Air Breathing Propulsion.
AE 5232. Spacecraft Propulsion
This course introduces concepts needed to evaluate the performance of the most commonly used electric and chemical spacecraft propulsion systems. Fundamental topics in electric propulsion include plasma generation and ion acceleration, magnetic field design, and beam neutralization. Applications include electrostatic ion and Hall thrusters. Fundamental topics in chemical propulsion include propellant thermochemistry and ideal performance. Applications include bipropellant and monopropellant chemistry, catalyst-bed, and nozzle design considerations. Discussion of each class of thruster will be supplemented with specific examples of flight hardware. Students cannot receive credit for this course if they have taken AE/ME 5111 Spacecraft Propulsion.
AE 5233. Combustion
This course introduces the principles that govern the conversion of chemical energy to thermal energy in reacting flows or combustion. Topics will be chosen from: chemical thermodynamics; chemical kinetics; transport phenomena; conservation equations; deflagrations; detonations; and diffusion flames. The course will also include discussions on energy landscape; combustion in propulsion and power generation devices; and pollutant formation. Students cannot receive credit for this course if they have taken AE5093 ST Principles of Combustion.
AE 5234. Sustainable Energy Systems
The course provides an introduction to sustainable energy systems, outlining the challenges in meeting the energy needs of humanity and exploring possible solutions. Specific topics include: the current energy infrastructure;historical energy usage and future energy needs; electricity generation from the wind; ocean energy (marine hydrokinetic energy; wave energy); tethered energy systems, energy for transportation; fuel cells; solar-photovoltaic systems; geo-thermal and solar-thermal energy; energy storage; and engineering economics. Students cannot receive credit for this course if they have taken AE/ME 5105 Renewable Energy.
AE 5331. Linear Control Systems
This course covers analysis and synthesis of control laws for linear dynamical systems. Fundamental concepts including canonical representations, the state transition matrix, and the properties of controllability and observability will be discussed. The existence and synthesis of stabilizing feedback control laws using pole placement and linear quadratic optimal control will be discussed. The design of Luenberger observers and Kalman filters will be introduced. Examples pertaining to aerospace engineering, such as stability analysis and augmentation of longitudinal and lateral aircraft dynamics, will be considered. Assignments and term project (if any) will focus on the design, analysis, and implementation of linear control for current engineering problems. The use of Matlab/Simulink for analysis and design will be emphasized. Recommended background: Familiarity with Matlab. Students cannot receive credit for this course if they have taken AE/ME 5220 Control of Linear Dynamical Systems.
AE 5332. Nonlinear Control Systems
Overview of stability concepts and examination of various methods for assessing stability such as linearization and Lyapunov methods. Introduction to various design methods based on linearization, sliding modes, adaptive control, and feedback linearization. Demonstration and performance analysis on engineering systems such as flexible robotic manipulators, mobile robots, spacecraft attitude control and aircraft control systems. Theoretical foundations of machine learning via adaptive functional estimation of dynamical systems. Control synthesis and analysis is performed using Matlab/Simulink. Prerequisites: Fluency with the theory of linear dynamical systems and control (AE 5331 or similar). Fluency with Matlab. Students cannot receive credit for this course if they have taken AE/ME 5221 Control of Nonlinear Dynamical Systems.
AE 5333. Optimal Control for Aerospace Applications
This course covers the synthesis of optimal control laws for linear and nonlinear dynamical systems, with a strong focus on aerospace engineering applications. Topics covered include: necessary conditions for optimal control based on the Pontryagin Minimum Principle will be introduced, and including cases of fixed and free terminal time and boundary conditions; will be discussed. Feedback optimal control will be discussed, and the Hamilton-Jacobi-Bellman equation will be introduced. The special case of linear quadratic optimal control; basic numerical techniques such as pseudospectral optimization; and modern machine learning techniques such as reinforcement learning will be discussed. Examples throughout the course will be based on air- and space vehicle applications, such as flight trajectory optimization. Assignments and term project (if any) will introduce basic numerical techniques and introduce software packages for optimal control. Prerequisites: Fluency with the theory of linear dynamical systems and control(AE 5331 or similar) and with MATLAB programming. Students cannot receive credit for this course if they have taken AE 5222 Optimal Control.
AE 5334. Spacecraft Dynamics and Control
Overview of spacecraft orbital and rotational motion. Overview and sizing of actuating devices such as gas jet, electric thrusters, momentum wheels and magnetic torquers. Overview and selection of sensing devices such as sun sensors, magnetometers, GPS, IMUs. Formulation of spacecraft maneuvers as control design problems. Estimation techniques for orbit determination and attitude estimation. Static attitude determination methods. Kalman filtering for attitude estimation. Fundamentals of orbit determination. Attitude control based on Lyapunov methods. Case studies on feedback attitude regulators and algorithms for linear and nonlinear attitude tracking. Design and realization of attitude and orbital control schemes using Matlab/Simulink. Prerequisites: Fundamentals of spacecraft orbital motion and attitude dynamics at the undergraduate level. Fluency with the theory of linear dynamical systems and control (AE 5331 or similar) and with Matlab programming. Students cannot receive credit for this course if they have taken AE 5223 Space Vehicle Dynamics and Control.
AE 5335. Autonomous Aerial Vehicles
This course discusses the foundations of autonomy of aerial vehicles including fixed-wing aircraft and quadrotor aircraft. Topics covered include: localization using inertial sensors, GPS, and computer vision; extended Kalman filtering for localization; trajectory planning; feedback guidance for trajectory tracking; and low-level autopilot control design. Whereas this course will review aircraft dynamics, familiarity with this topic at an undergraduate level isbeneficial. Students cannot receive credit for this course if they have taken AE 5224 Air Vehicle Dynamics and Control.
AE 5431. Solid Mechanics for Aerospace Structures
This course is an introductory graduate level course. Fundamental topics will be chosen from the following: three-dimensional states of stress; measures of strain; plane stress and plane strain; thermoelasticity; Airy stress function; and energy methods. Applied topics will be chosen from the following: bending and shear stresses on unsymmetric cross-sections; bending of composite beams; bending of curved beams; torsion of thin-walled noncircular cross sections; and failure criteria. Students cannot receive credit for this course if they have taken AE/ME 5380 Foundations of Elasticity or AE/ME 5381 Applied Elasticity.
AE 5432. Composite Materials
This course covers the anisotropic constitutive behavior and micromechanics of composite materials, and the mechanics of composite structures at an introductory graduate level. Topics covered will be chosen from: classification of composites (reinforcements and matrices), anisotropic elasticity, composite micromechanics, effect of reinforcement on toughness and strength of composites, laminate theory, statics and buckling of laminated beams and plates, statics of laminated shells, residual stresses and thermal effects in laminates. Students cannot receive credit for this course if they have taken AE 5383 Composite materials.
AE 5433. Aeroelasticity
This course provides a graduate-level introduction to static and dynamic aeroelasticity, for conventional aircraft.Students will be presented with analytical and computational techniques used to model and simulate aeroelasticity. Topics covered will be chosen from: divergence; aileron reversal; airload redistribution; sweep effects; unsteady aerodynamics; and flutter of wings. Students cannot receive credit for this course if they have taken AE/ME 5382 Aeroelasticity.
AE 5434. Computational Solid Mechanics
This course presents finite element methods with applications to structures and structural dynamics at introductory graduate level. It focuses on linear elasticity and topics covered will be chosen from: introduction on numerical methods in solids mechanics; variational methods of approximation; formulation of finite elements and interpolation functions; assembly and solution processes; isoparametric formulation; stress recovery procedures; locking phenomenon; and dynamic problems. The course requires completion of several FEM projects and knowledge of a computer programming language.
AE 5435. Fracture Mechanics
This course focuses on the analytical techniques and applications of fracture mechanics at introductory graduate level. In particular, there is an emphasis on cracks in linear elastic and elasto-plastic materials encountered in high integrity aerospace structural applications. Topics covered will be chosen from: stress concentration and stress singularity near cracks, computation of stress intensity factors and asymptotic K fields, linear elastic fracture mechanics, energy methods, stability of crack propagation, cohesive fracture, basics of plasticity theory, plastic zone, small-scale yielding (SSY), HRR asymptotic fields, mixed mode fracture and elasto-plastic crack growth.
AE 6093. Advanced Special Topics
Arranged by individual faculty with special expertise, these courses cover advanced topics that are not covered by the regular aerospace engineering course offerings. Exact course descriptions are disseminated by the Aerospace Engineering Department in advance of the offering.
AE 6999. Ph.D. Qualifying Examination
Admission to Candidacy will be granted when the student has satisfactorily passed the Ph.D. Qualifying Examination (AE 6999). The Qualifying Examination is intended to measure each students fundamental knowledge in two Curricular Areas to be chosen by the student from the following: Fluid Dynamics; Propulsion and Energy; Flight Dynamics and Controls; and Materials and Structures. The AE 6999 Ph.D. Qualifying Examination is graded using a Pass/Fail system as determined by a) the results from the written Candidacy Test in the two Curricular Areas chosen by the student and b) the students performance in graduate courses taken at WPI in the same two Curricular Areas.The written Candidacy Test is typically offered during the first week of B and/or D term. A student will be tested on material from two (2) graduate courses of their choice in one AE Curricular Area and on material from one (1) graduate course of their choice in a second AE Curricular Area. In the term preceding the written Candidacy Test, a student must inform the Graduate Coordinator about their selection of the two Curricular Areas and the three courses. The written Candidacy Test is graded using the Satisfactory/Not Satisfactory Performance (SP/NP) grading system and has no retake.If a student fails to register or fails to earn a Pass in the AE 6999 Ph.D. Qualifying Examination prior to completion of 18 credits after admission to the Ph.D. program, the student must withdraw from the Ph.D. program by end of the B term or D term of the year registered for the Qualifying Examination.