Aerospace and Ocean Engineering
Head, Rolls-Royce Commonwealth Professor of Marine Propulsion: E.G. Paterson
Assistant Head for Academic Affairs: R.A. Canfield
Assistant Head for Laboratory Facilities: M.K. Philen
Assistant Head for Graduate Studies: M. Patil
Fred D. Durham Professor: J.A. Schetz
Kevin Crofton Professor: M.L. Psiaki
NAVSEA Chair Professor: A.J. Brown
Norris and Laura Mitchell Professor: R. K. Kapania
Northrop Gruman Sr Faculty Chair Professor: J.T. Black
Professor of Practice: P. Artis
Professors: J.T. Black, A.J. Brown, R.A. Canfield, O. Coutier-Delgosha, W.J. Devenport, R.K. Kapania, E.G. Paterson, M.L. Psiaki, S.D. Ross, C.J. Roy, J.A. Schetz, C. Sultan, and C.A. Woolsey
Collegiate Professors: P. Raj and K.A. Shinpaugh
Associate Professors: S. Brizzolara, S. England, M. Farhood, K.T. Lowe, M. Patil, M.K. Philen, J.S. Pitt, G.D. Seidel, B. Srinavasan, K.G. Wang, H. Xiao, and G. Young
Assistant Professors: C.S. Adams, W.N. Alexander, S. Choi, C.M. Gilbert, M. Joerger, and L. Massa
Adjunct Professors: A. Basovich, W. Grossman, L. Ma, and W. Oberkampf
Research Professors: A. Borgoltz and M. Kuester
Professors Emeritus: E.M. Cliff, W.C. Durham, B. Grossman, E.R. Johnson, J.F. Marchman, W.L. Neu, R.L. Simpson, and R. Walters
Faculty Affiliates: S. Bailey, R. Batra, R.A. Burdisso, G. Earle, K. Kochersberger, R. McGwier, W. Scales, M.K. Spakovsky, D. Stilwell, P. Tarazaga, L. Watson, and M. Weaver
The Kevin T. Crofton Department of Aerospace and Ocean Engineering offers a Bachelor of Science degree in aerospace and ocean engineering. Students may major in either aerospace engineering or ocean engineering. These majors share many course requirements, because the two curricula cover a broad range of common interests and offer a wide range of technical electives. Students may double major—aerospace with ocean engineering or ocean with aerospace engineering. The Department also offers a minor in naval engineering, which is open to non-AOE students.
The undergraduate programs' educational objectives are that graduates will combine their undergraduate education and post-graduation experience to:
- Be successful in entry-level professional positions or in graduate study in aerospace and ocean engineering.
- Apply the theoretical, experimental and computational fundamentals of science and engineering to professional practice, advanced study and continuing professional development.
- Apply their broad understanding of fluid dynamics, vehicle dynamics and control, propulsion and structures to design and synthesis of aerospace or ocean systems in a team environment.
- Communicate their work effectively to both experts in their field and non-technical individuals.
The department's curricula are vehicle oriented, with an emphasis on propulsion, aero/hydrodynamics, stability and control, vehicle performance, vehicle structures, and energy and the environment. A year-long capstone design experience in the senior year uses the group design process to both better simulate the way design is done in the real world and promote the benefits of collaborative learning.
AOE graduates have been highly successful in the aerospace and ocean fields. About 15% of our graduates continue their studies in graduate school, while most of the rest find excellent employment opportunities in the aerospace and related industries and in the shipbuilding, naval engineering, and ship design fields. Some also choose to go into related fields such as automotive engineering, structural engineering, environmental engineering, as well as into professions such as law or medicine.
AOE is home to a number of unique facilities, including Stability, Open-Jet, Boundary-Layer, Low Speed, Transonic, Supersonic, and Hypersonic Wind Tunnels; the Advanced Propulsion and Power Laboratory (APPL), Space@VT building, the Kentland Experimental Aerial Systems Laboratory (KEAS), the Hydro-Elasticity Laboratory, Hydrodynamics Laboratory, Marine Robotics Laboratory, and Newport News Shipbuilding (NNS) / Aerospace and Ocean Engineering (AOE) Teaching and Research Laboratory.
The department encourages students to seek internships and to participate in the Cooperative Education Program, which gives qualified students valuable industrial experience while working toward their engineering degrees. The department's required design courses often include multidisciplinary projects.
The Aerospace Engineering and Ocean Engineering programs are accredited by the Engineering Accreditation Commission of ABET, www.abet.org. The department also offers programs of study leading to M. Engr., M.S., and Ph.D. degrees.
AOE students must meet all Pathways requirements and only certain "free" electives and courses designated as "P/F Only" may be taken on a Pass/Fail basis. Lists of approved electives including technical, math, Liberal Education, and other electives are available on the department's web page: www.aoe.vt.edu/undergrad/undergrad-advising/index-undergrad-advising.html.
The graduation requirements in effect during the academic year of admission to Virginia Tech apply. Requirements for graduation are listed on checksheets. Students must satisfactorily complete all requirements and university obligations for degree completion. The university reserves the right to modify requirements in a degree program.
Please visit the University Registrar's website at https://www.registrar.vt.edu/graduation-multi-brief/checksheets.html for degree requirements.
Undergraduate Course Descriptions (AOE)
2024: THIN-WALLED STRUCTURES Basic structural elements of stringer-stiffened thin-walled structures, forces, moments, stresses, and deformation of segmented bars/beams, flexure stress and deflection of beams principal plane, plane of bending and plane of loading for beams with asymmetric cross sections, stresses, and twist due to torsion, shear flow and shear center in open and closed stiffened thin-walled structures, stiffened multicell beams, materials properties and selection. Pre: (ESM 2104, ESM 2204) or ESM 2114, (MATH 2224 or MATH 2224H or MATH 2204 or MATH 2204H). Co: MATH 2214. (3H,3C)
2054: ELECTRONICS FOR AEROSPACE AND OCEAN ENGINEERS Electrical circuits. Discrete passive and active electrical components. Phasors and impedence. AC power analysis. Digital electronics. Electronics for autonomous and piloted aerospace and ocean systems. Electronics for vehicle navigation, guidance, and control. Instrumentation and data acquisition systems. (2H,3L,3C)
2074 (ESM 2074): COMPUTATIONAL METHODS Solving engineering problems using numerical methods and software, truncation and round-off error, root finding, linear and polynomial regression, interpolation, splines, numerical integration, numerical differentiation, solution of linear simultaneous equations. A grade of C- or better is required in the prerequisite. Pre: ENGE 1114 or ENGE 1216 or ENGE 1434 or ENGE 1414. (2H,1.5L,2C)
2104: INTRODUCTION TO AEROSPACE ENGINEERING AND AIRCRAFT PERFORMANCE Overview of aerospace engineering from a design perspective; introductory aerodynamics, lift, drag, and the standard atmosphere; aircraft performance, stability, and control; propulsion; structures; rocket and spacecraft trajectories and orbits. Co: ESM 2104 or ESM 2114. Pre: PHYS 2305. (3H,3C)
2114: FUNDAMENTALS OF FLIGHT TRAINING AOE Foundational course to prepare students with knowledge of basic aeronautics to take the Federal Aviation Administration Knowledge Exam, a requirement for the award of a private pilot’s license. Explores airplane systems and functions, flight operations, weather, aeronautical navigation, communications, human factors, and federal aviation regulations. (3H,3C)
2204: INTRODUCTION TO OCEAN ENGINEERING Introduction to the design of ocean vehicles and offshore structures. Buoyancy. Hull geometry, body plan drawing, coefficients of form. Hydrostatic calculations. Intact and damaged stability of ocean vehicles and offshore structures. Large angle stability. Stability criteria for design and related rules and regulations. Marine economics. Pre: PHYS 2305. Co: MATH 2204. (3H,3C)
2664 (ECE 2164): EXPLORATION OF THE SPACE ENVIRONMENT This introductory course covers a broad range of scientific, engineering, and societal aspects associated with the exploration and technological exploitation of space. Topics covered include: science of the space environment, space weather hazards and societal impacts, orbital mechanics and rocket propulsion, spacecraft subsystems, applications of space-based technologies. (3H,3C)
2974: INDEPENDENT STUDY Variable credit course.
2984: SPECIAL STUDY Variable credit course.
2994: UNDERGRADUATE RESEARCH Variable credit course.
2994H: UNDERGRADUATE RESEARCH Variable credit course.
3014: FLUID DYNAMICS FOR AEROSPACE AND OCEAN ENGINEERS Fundamentals of fluids: stress, statics, viscosity, laminar and turbulent flow. Conservation of mass and momentum. Vorticity, circulation, and lift. Navier-Stokes equations. Ideal flow in two dimensions, streamlines, stream function, velocity potential, superposition. Thin airfoil theory. Physics of laminar and turbulent boundary layers and of transition. Boundary layer equations and basic tools for boundary layer calculation. Collaborative problem solving. Pre: (2104 or 2204), MATH 2214 or MATH 2214H, ESM 2304. (3H,3C)
3034: SYSTEM DYNAMICS AND CONTROL Free and forced response of first, second, and higher order linear, time-invariant (LTI) systems in frequency and time domains. Modeling of low-order mechanical systems. Transmission and absorption of vibrations. Transient and steady state performance specifications. Introduction to closed-loop control using proportional-integral-derivative (PID) feedback. Closed-loop stability analysis using root locus method. Pre: ESM 2304, (MATH 2214 or MATH 2214H). (3H,3C)
3044: BOUNDARY LAYER AND HEAT TRANSFER Concepts of viscous flows and physical properties equations of laminar motion with heat and mass transfer; exact and approximate solutions; finite-difference methods; transition to turbulence; analysis in turbulent flows. Conduction and convective heat transfer. Pre: 3014, (3164 or 3264 or ME 2134 or ME 3134), MATH 4564. (3H,3C)
3054: EXPERIMENTAL METHODS Fundamental terminology of experimental work and testing in aerospace and ocean engineering. Flow quantities, displacement, and strain measurements of simple structures in both static and dynamic settings. Analog and digital instrumentation. Data acquisition systems and appropriate software. Through teamwork design, prepare, and conduct an experiment, and document its results and findings. Statistical concepts. Pre: 2024, 2054, 3014, 3034. (2H,3L,3C)
3094 (MSE 3094): MATERIALS & MANUFACTURING FOR AERO & OCEAN ENGINEERS This course introduces the student of Aerospace and/or Ocean Engineering to the fundamental properties of materials typically required for structural design. The performance characteristics of metals, ceramics, polymers, and composites are presented and contrasted. Foundation principles underlying materials manufacturing are also presented with the goal of providing an understanding of how processing affects material properties and performance. Must have a C- or better in pre-requisite CHEM 1035. Non-MSE Majors only. Pre: CHEM 1035. Co: ESM 2204, PHYS 2305. (3H,3C)
3114: AERODYNAMICS & COMPRESSIBILITY Inviscid aerodynamics. Wings and wing theory for low speed flight. How and when compressibility becomes important. Integral form of the conservation equations and thermodynamics. One-dimensional steady compressible flow, nozzle flows. Compressible flow with heat addition. Oblique shock waves and Prandtl-Meyer expansions. Supersonic airfoils. Aerodynamics at subsonic and transonic speeds. Pre: 3014. Co: 3164. (3H,3C)
3124: AEROSPACE STRUCTURES Inertia loads on aerospace structures, introduction to 3D elasticity including strain-displacement relations, stress-strain relations, stress transformation, and equations of equilibrium, plane stress and plane strain elasticity, stress concentration factors, aerospace materials and failure criteria, margins of safety analysis, plate bending, structural stability. Pre: 2024 or 3024. (3H,3C)
3134: AIR VEHICLE DYNAMICS Nonlinear kinematic and dynamic equations of aircraft motion; estimation of stability derivatives from aircraft geometry; determination of steady motions; linearization; longitudinal and lateral-directional small perturbation equations; static and dynamic stability of equilibrium flight. Pre: 3034. (3H,3C)
3144: SPACE VEHICLE DYNAMICS Attitude representations and equations of rotational motion for rigid and multibody spacecraft; attitude determination; linearization and stability analysis of steady motions; effect of the gravity gradient; torque thrusters and momentum exchange devices. Pre: 3034, 3154. (3H,3C)
3154: ASTROMECHANICS This course teaches the application of Newton’s Laws to the dynamics of spaceflight. Topics include the two-body problem equations of motion, Kepler’s Laws, classical orbital elements, energy and time-of-flight relations, orbit specification and determination, orbital maneuvering and orbit transfers, patched conic approximations, and relative motion. Pre: ESM 2304. (3H,3C)
3164: AEROTHERMODYNAMICS AND PROPULSION SYSTEMS The fundamental principles of aerothermodynamics applied to aerospace propulsion system performance analysis and design. Foundations of thermodynamics, heat transfer, compressible fluid mechanics, and combustion. Applications of principles to air-breathing and rocket engines. Pre: 3014. Co: 3114. (3H,3C)
3214: OCEAN WAVE MECHANICS Introduction to theory of wave in deep and shallow water, including wave generation and propagation. Description of wave statistics and spectral representation for realistic ocean conditions. Introduction to ocean acoustics. Co: 3014, MATH 4564 (3H,3C)
3224: OCEAN STRUCTURES Overview of surface ship, submarine and offshore structural systems, materials and loadings. Application of beam and plate bending and buckling theories. Frame structural analysis. Fatigue analysis. Pre: 2024. (3H,3C)
3234: OCEAN VEHICLE DYNAMICS Nonlinear kinematic and dynamic equations of rigid vessel motion in water; hydrostatic and hydrodynamic forces in calm water; motion response to regular and irregular waves; single, multiple and coupled motions degrees of freedom; spectral analysis of response of random seas; statistical analysis of extreme motion response; impact of seakeeping criteria on ocean vehicles design; principles of hydroelasticity; principles of maneuvering of surface and underwater vehicles. Pre: 3014, 3034, 3214. (3H,3C)
3264: THERMODYNAMICS AND MARINE PROPULSION Fundamental thermodynamics and power cycles; marine propulsion plants and transmission systems; methods of estimating resistance of ocean vehicles; propulsion devices and their efficiencies; introduction to propeller theory; cavitation. Pre: 2204, 3014. (3H,3C)
3354: AVIONICS SYSTEMS A systems approach to avionics architecture for both civil and military aircraft. Emphasis on system architecture, accepted development processes, sensors, navigation, and certification. Evolution of communications, data models, and sensors required to support autonomous flight as well as the exposures to physical cyber security threats faced by flight management, navigation, and data interchange systems. Pre: (2054 or ECE 2054), (AOE 3034 or ME 3534 or ME 4504). (3H,3C)
3804: SPECIAL TOPICS IN AIRCRAFT SYSTEMS Advanced undergraduate topics in aircraft systems. Covers technical, environmental, and economic challenges and opportunities in contemporary and future aircraft. Function and integration of propulsion, airborne auxiliary power, navigation, flight controls, cargo, landing gear, cabin systems, fuel, and other subsystems. May be repeated with different content for a maximum of 9 credits. Pre: 2104. (3H,3C)
3984: SPECIAL STUDY Variable credit course.
4004: STATE-SPACE CONTROL Control design and analysis for linear, state-space system models. Properties of linear, time-invariant control systems: Input/output stability, internal stability, controllability, and observability. Performance and robustness measures. State feedback control design methods: pole placement, linear-quadratic control. State observers and output feedback control. Applications to control of mechanical systems including ocean, atmospheric, and space vehicles. Pre: 3034. (3H,3C)
4024 (ESM 4734): AN INTRODUCTION TO THE FINITE ELEMENT METHOD The finite element method is introduced as a numerical method of solving the ordinary and partial differential equations arising in fluid flow, heat transfer, and solid and structural mechanics. The classes of problems considered include those described by the second-order and fourth-order ordinary differential equations and second-order partial differential equations. Both theory and applications of the method to problems in various fields of engineering and applied sciences will be studied. Pre: (CS 3414 or MATH 3414 or AOE 2074 or ESM 2074) or (MATH 2224 or MATH 2224H or MA TH 2204 or MATH 2204H). (3H,3C)
4054 (ESM 4444): STABILITY OF STRUCTURES Introduction to the methods of static structural stability analysis and their applications. Buckling of columns and frames. Energy method and approximate solutions. Elastic and inelastic behavior. Torsional and lateral buckling. Use of stability as a structural design criterion. Pre: 2024 or 3024 or CEE 3404. (3H,3C)
4064: FLUID FLOWS IN NATURE Course designed to build upon and broaden a basic traditional engineering knowledge of fluid flows into areas concerning a variety of natural occurrences and phenomena that involve fluid motions in important ways. Drag of sessile systems and motile animals, gliding and soaring, flying and swimming, internal flows in organisms, low Reynolds number flows, fluid-fluid interfaces, unsteady flows in nature and wind engineering. Pre: 3014 or CEE 3304 or ESM 3024 or ME 3404. (3H,3C)
4065-4066: AIR VEHICLE DESIGN Fundamental principles of innovative air vehicle design. Qualitative and quantitative decision-making tools. Multidisciplinary design teams with emphasis on ethics and professionalism. Project risks and mitigation plans. Oral presentations for design reviews. Written engineering design report. 4065: Proven conceptual design process. Tradeoff studies. Air vehicle weight estimation. Air vehicle concepts feasibility assessment; 4066: Preliminary design tools and processes. Efficient and light-weight air vehicles. Air vehicle design validation. Pre: 2104, 3054, 3114, 3124, 3134, 3164 for 4065; 4065 for 4066. Co: 4105 for 4065; 4106 for 4066. (2H,3L,3C)
4084 (ESM 4084): ENGINEERING DESIGN OPTIMIZATION Use of mathematical programming methods for engineering design optimization including linear programming, penalty function methods, and gradient projection methods. Applications to minimum weight design, open-loop optimum control, machine design, and appropriate design problems from other engineering disciplines. Pre: (MATH 2224 or MATH 2204 or MATH 2204H). (3H,3C)
4105-4106: EXPERIMENTS FOR AEROSPACE DESIGN Methods for the planning, implementation, assessment and use of experiments in aerospace design problems. 4105: Experiment design, advanced sensor systems, additive manufacturing, uncertainty, data analysis and reporting. 4106: Application of experiments as an integral component of engineering design. Co: 4065 or 4165 for 4105. Co: 4066 or 4166 for 4106. Pre: 3054 for 4105; 4105 for 4106. (3L,1C)
4114: APPLIED COMPUTATIONAL AERODYNAMICS Development of computational methods for application to wing aerodynamic problems. Incompressible airfoil codes. Panel methods and vortex lattice methods. Finite difference techniques. Transonic and supersonic applications. Pre: 3044, 3114. (3H,3C)
4124: CONFIGURATION AERODYNAMICS Aerodynamic design of flight vehicles, with emphasis on nonlinear flowfields and configuration concepts. Aerodynamic analysis and design for transonic, supersonic, hypersonic flows, and low speed high alpha flight. Includes case studies of classic configurations and aerodynamic design papers. Pre: 3014, 3114. (3H,3C)
4140: SPACECRAFT DYNAMICS AND CONTROL Space missions and the way pointing requirements affect attitude control systems. Rotational kinematics and attitude determination algorithms. Modeling and analysis of the attitude dynamics of space vehicles. Rigid body dynamics, effects of energy dissipation. Gravity gradient, spin, and dual spin stabilization. Rotational maneuvers. Environmental torques. Impacts of attitude stabilization techniques on mission performance. Pre: 3034, (4134 or 3154). (3H,3C)
4165-4166: SPACE VEHICLE DESIGN Fundamental principles of innovative space vehicle design. Qualitative and quantitative decision-making tools. Multidisciplinary design teams with emphasis on collaboration, ethics, and professionalism. Project risks and mitigation plans. Oral presentations for design reviews. Written engineering design report. 4165: Proven conceptual design process. Parametric analyses. Space vehicle mass estimation. Space vehicle concepts feasibility assessment; 4166: Preliminary design tools and processes. Efficient and light-weight space vehicles. Space vehicle design validation. Pre: 2104, 3054, 3114, 3124, 3144, 3154, 3164 for 4165; 4165 for 4166. Co: 4105 for 4165; 4106 for 4166. (2H,3L,3C)
4174 (ME 4174): SPACECRAFT PROPULSION Spacecraft propulsion systems and their applications in orbital, interplanetary, and interstellar flight. Rocket propulsion fundamentals; advanced mission analysis; physics and engineering of chemical rockets, electrical thrusters, and propellantless systems (tethers and sails); spacecraft integration issues. Pre: 3164 or 4234 or ME 4234. (3H,3C)
4205-4206: EXPERIMENTS FOR OCEAN VEHICLE DESIGN 4205: Facilities, instrumentation, and experiments pertinent to ocean engineering in the field of flow measurements and resistance and propulsion tests of surface and underwater vehicles. Analysis and communication of experimental data through technical report writing. 4206: Assessment of ocean system design through experiments, data analysis, and technical report writing. Pre: 3054 for 4205; 4205 for 4206. Co: 4265 for 4205; 4266 for 4206. (3L,1C)
4234 (ME 4234): AEROSPACE PROPULSION SYSTEMS Design principles and performance analysis of atmospheric and space propulsion engines and systems. Application of thermodynamics, compressible fluid flow and combustion fundamentals to the design of gas turbine and rocket engines and components, including inlets, turbomachines, combustors, and nozzles. Matching of propulsion system to vehicle requirements. Pre: (3114, (3164 or 3264 or ME 3134) or (ME 3404 or ME 3414), ME 2134 or ME 3124). (3H,3C)
4244: NAVAL AND MARINE ENGINEERING SYSTEMS DESIGN Concepts, theory and methods for the design, integration, and assessment of naval and marine engineering systems considering energy conservation, ship arrangements, system deactivation diagrams, reliability, maintenance, system power, shock and weapons effects, machinery sizing, and system vulnerability. Physics-based mechanical, electrical, thermal, sensor, control, weapon systems, hullform and engine (diesel and gas turbine) models are used to predict total system performance. Linear programming methods and flow-based models are used to optimize systems architecture and size components. Pre: 2054, 2204, 3264, 4264. (3H,3C)
4264: PRINCIPLES OF NAVAL ENGINEERING This course studies naval engineering systems and systems engineering processes with particular emphasis on: naval missions; combat system performance including radar; underwater acoustics and sonar; ballistics; weapon propulsion and architecture; weapons effects; ship survivability including underwater explosion and shock waves; surface ship and submarine balance and feasibility analysis; and total ship integration. Senior Standing required. Pre: 2204, (MATH 2224 or MATH 2204 or MATH 2204H), PHYS 2306. (3H,3C)
4265-4266: OCEAN VEHICLE DESIGN Study and application of systems engineering process and ocean engineering principles to the concept exploration, design and development of ocean vehicles including ships, submarines, surface and subsurface autonomous vehicles, boats and yachts. 4265: Emphasis on hullform, power and propulsion, synthesis, balance, metrics and design optimization. 4266: Emphasis on topside/external arrangements, internal arrangements, machinery arrangements, human systems, structural design, and final assessments of intact and damage stability, weights, space, seakeeping, cost, risk, overall balance and feasibility. Most of the work is done in teams. Pre: 2204, 3214, 3224, 3234, 3264 for 4265; 4265 for 4266. Co: 4205 for 4265; 4206 for 4266. (2H,3L,3C)
4274: INTERMEDIATE SHIP STRUCTURAL ANALYSIS Analysis of plate bending, buckling, and ultimate strength using computational tools and methods. Calculation of elastic buckling of stiffened panels. Eigenvalue methods for buckling and vibration. Incremental plastic collapse; other progressive collapse. Ultimate strength of large structural modules due to combined loads. Introductory level finite element analysis. Pre: 3224. (3H,3C)
4324: ENERGY METHODS FOR STRUCTURES Work and energy relationships in structures, flexibility and stiffness influence coefficients, Maxwell and Betti-Rayleigh reciprocal theorems, strain energy and complementary strain energy for thin-walled structures, Castigliano\031s first and second theorems for trusses and frames, unit action and unit displacement states, direct stiffness method, principles of minimum total potential energy and total complementary energy for bars, beams, and plates, Ritz method, finite element method for bars and beams. Pre: 2024, (3124 or 3224). (3H,3C)
4334: SHIP DYNAMICS Analysis of motions of rigid body vehicles in water, including influence of added mass and buoyancy. Seakeeping motion responses in waves, wave-induced structural loads, random response analysis via spectral analysis, and extreme response analysis. Introduction to hydroelasticity and maneuvering. Pre: 3014, 3034, (3214 or 4214), MATH 4564. (3H,3C)
4344: DYNAMICS OF HIGH-SPEED MARINE CRAFT Introduction to the dynamics of high-speed craft, including surface effect ships, hydrofoil vessels, semi-displacement monohulls and catamarans, and planing vessels. Co: 4334 or 3234. Pre: 3264. (3H,3C)
4404 (MATH 4404): APPLIED NUMERICAL METHODS Interpolation and approximation, numerical integration, solution of equations, matrices and eigenvalues, systems of equations, approximate solution of ordinary and partial differential equations. Applications to physical problems. A student can earn credit for at most one of 3414 and MATH 4404. Pre: MATH 4564, (ESM 2074 or AOE 2074). (3H,3C)
4414: COMPUTER-AIDED SPACE MISSION PLANNING Design and analysis of space missions. Basic orbital mechanics and access between spacecraft and ground station. Advanced orbit visualization. Prediction of spacecraft position observation under constraints. Communications and link budgets. Terrain modeling and impact on performance. Constellation design and coverage. Orbital perturbations. Dynamics of airplanes and space launch vehicles. Interplanetary mission design. Pre: 2074, (4134 or ECE 2164). (1H,1C)
4434: INTRODUCTION TO COMPUTATIONAL FLUID DYNAMICS Euler and Navier-Stokes equations governing the flow of gases and liquids. Mathematical character of partial differential equations. Discretization approaches with a focus on the finite difference method. Explicit and implicit solution techniques and their numerical stability. Introduction to verification, validation, and uncertainty quantification for computational fluid dynamics predictions. Co: AOE 3044 or ME 3404 or ESM 3016. Pre: MATH 2214. (3H,3C)
4454: SPACECRAFT POSITION/NAVIGATION/TIMING AND ORBIT DETERMINATION Position/Navigation/Timing (PNT) measurements and optimal batch filter estimation methods for spacecraft with emphasis on orbit determination; GPS position/velocity/time point solutions; linearized state transition matrices; batch least-squares filter Orbit Determination (OD) solutions from a time series of observations; precision and accuracy assessment using covariance and overlap statistics; one-way and two-way radio range and range-rate observations; optical bearings observations; non-Keplerian orbital effects. Pre: 3154. (3H,3C)
4474: PROPELLERS AND TURBINES Theory, numerical methods, and experimental techniques for analysis and design of propellers and turbines. Geometry description and creation of computer models. Analysis of inflow from wakes and atmospheric boundary layers. Performance characteristics including open-water and multi-quadrant operation, scale effects, and standard series data. Theoretical analysis and selection of airfoil and hydrofoil sections. Theory and numerical methods for propellers and turbines, including computational fluid dynamics (CFD) simulation. Design of wake-adapted propellers. Design of wind-turbine rotors in steady wind. Structural analysis of propeller and turbine blades. Wind- and water-tunnel testing for thrust and torque. Pre: 3014. (3H,3C)
4514 (ESM 4114): NONLINEAR DYNAMICS AND CHAOS Motion of systems governed by differential equations: stability, geometry, phase planes, bifurcations, Poincare’ sections, point attractors, limit cycles, chaos and strange attractors, Lyapunov exponents. Forced, nonlinear oscillations: jump phenomena, harmonic resonances, Hopf bifurcations, averaging and multiple-scales analysis. Systems governed by discrete maps: return maps, cobweb plots, period-multiplying bifurcations, intermittency, delay coordinates, fractal dimensions. Pre: (ESM 2304 or PHYS 2504), (MATH 2214 or MATH 2214H). (3H,3C)
4604: BOOSTER DESIGN, FABRICATION, AND OPERATION Theory, design, operations, and fabrication methodologies employed to manufacture boosters. The rocket equation, solid, liquid, and hybrid propellant systems, combustion chamber design, vehicle structures, telemetry, guidance and navigation, launch operations, and failure modalities. Pre: 2074, 3124, 3154, 3164. (3H,3C)
4624: FOUNDATIONS OF AERO AND HYDROACOUSTICS Fundamental background to the field of aero/hydroacoustics. Quantifying sound levels, acoustic intensity, the acoustic wave equation, and linear acoustics. Fluid dynamics, turbulence, and thermodynamics in aeroacoustics. Lighthill \031s equation, and Curle\031s equation. Characterization and identification of aeroacoustic sources. Leading and trailing edge noise. Basics of aeroacoustic wind tunnel testing. Pre: 3014, 3054. (3H,3C)
4634: WIND TURBINE TECHNOLOGY AND AERODYNAMICS Aerodynamics and elastic behavior of a modern wind turbine. Internal and aerodynamic loads of wind turbines. Locating wind turbines with respect to fatigue, annual power and noise productions. Aeroelastic behavior of wind turbine blades. Generators, transformers and power converters used in wind energy. Historical, economic, political, and innovation issues related to wind energy and power grid integration. Pre: 3014, 3124. (3H,3C)
4654 (ECE 4154): SPACE WEATHER: THE SOLAR WIND AND MAGNETOSPHERE Solar-terrestrial interactions and space weather: the sun, solar wind, and interplanetary magnetic field; space plasma physics and magnetohydrodynamics; Earth’s magnetosphere and ionosphere; geomagnetic storms and auroral substorms; societal impacts of space weather; planetary magnetospheres; space science instrumentation. Pre: ECE 3105 or AOE 3014. (3H,3C)
4804: SPECIAL TOPICS IN DYNAMICS, CONTROL, AND ESTIMATION Advanced undergraduate topics in dynamics, control, and estimation related to a particular class of aerospace and ocean engineering systems. Sample course topics include navigation and guidance, aircraft flight control, and ocean vessel motion control. May be repeated 2 times with different content for a maximum of 9 credits. Pre: 4004. (3H,3C)
4814: SPECIAL TOPICS IN PROPULSION Advanced undergraduate topics in propulsion for aerospace and ocean vehicles. Covers technical, environmental, and economic challenges and opportunities in contemporary and future propulsion concepts. Comparative analyses of conventional and advanced propulsion systems and propulsion/vehicle integration concepts based upon first principles. Topics include distributed propulsion, green propulsion and propulsion/airframe integration. May be repeated with different content for a maximum of 6 credits. Pre: 3164 or 3264. (3H,3C)
4824: SPECIAL TOPICS IN ENERGY AND THE ENVIRONMENT Advanced undergraduate topics in energy and the environment related to aerospace and ocean engineering systems. Sample course topics include renewable energy and energy management. Pre: 3014. (3H,3C)
4974: INDEPENDENT STUDY Variable credit course.
4984: SPECIAL STUDY Variable credit course.
4994: UNDERGRADUATE RESEARCH Variable credit course.
4994H: UNDERGRADUATE RESEARCH Variable credit course.