Aerospace and Ocean Engineering

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• Overview
• Degree Requirements
• Undergraduate Course Descriptions (AOE)

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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: C.J. Roy
Fred D. Durham Professor: J.A. Schetz
Kevin Crofton Professor: M.L. Psiaki
Norris and Laura Mitchell Professor: R. K. Kapania
Professors: A.J. Brown, R.A. Canfield, W.J. Devenport, R.K. Kapania, L. Ma, E.G. Paterson, M.L. Psiaki, P. Raj, C.J. Roy, J.A. Schetz, and C.A. Woolsey
Associate Professors: J.T. Black, O. Coutier-Delgosha, S. Brizzolara, S. England, M. Farhood, K.T. Lowe, M. Patil, M.K. Philen, G.D. Seidel, and C. Sultan
Assistant Professors: C.S. Adams, W.N. Alexander, C.M. Ikeda, S. Choi, L. Massa, B. Srinivasan, K. Vamvoudakis, K.G. Wang, and H. Xiao
Adjunct Professors: E.D. Crede and K. A. Shinpaugh
Professors Emeritus: E.M. Cliff, W.C. Durham, B. Grossman, E.R. Johnson, J.F. Marchman, W.H. Mason, W.L. Neu, R.L. Simpson, and R. Walters
Faculty Affiliates: S. Bailey, R. Batra, R.A. Burdisso, T. Clark, G. Earle, M. Hajj, K. Kochersberger, R. McGwier, W. Scales, D. Stilwell, P. Tarazaga, and L. Watson

Web: www.aoe.vt.edu
E-mail: aoe@vt.edu

Overview

The Department of Aerospace and Ocean Engineering offers two Bachelor of Science degree programs. Students in the department may major in either aerospace engineering or ocean engineering. Many of the course requirements for these degrees are common, because the two curricula share a broad range of common interests. Both programs offer a wide range of technical electives. Students with an interest in both majors may enroll in a double major program.

The objectives of both of the department's programs include the preparation of students for entry-level positions and graduate study in the fields of aerospace engineering and ocean engineering. The department seeks to provide students with a strong background in fundamentals, including theoretical, experimental, and computational aspects of science and engineering, which will facilitate lifelong learning and the ability to pursue advanced study. It also seeks to provide students with a broad education in the aerospace and ocean vehicle fields encompassing fluid dynamics, vehicle dynamics and control, propulsion, and structures, and including an emphasis on design and synthesis in a team environment.

The department's curricula are vehicle oriented, with an emphasis on aircraft and spacecraft in the aerospace program and on ships of all types in the ocean engineering program. The department's systems engineering approach to these technologies makes them increasingly applicable to other fields, such as the automobile industry, high-speed train design, and other transportation related areas. Departmental graduates find positions in these fields, as well as with the aerospace industry, NASA, the Department of Defense, the ship building industry, and maritime agencies. Employers range from large, multinational corporations to small consulting firms.

Classroom studies employ modern computational techniques. Laboratory classes use the department's outstanding experimental facilities which include a large, research-quality subsonic wind tunnel with a twenty-four-foot-long, six-by-six foot cross section test area and state of the art automated control and data collection systems, a 100-foot-long towing tank, a Mach 4 supersonic wind tunnel, a Mach 7 hypersonic wind tunnel, a water tunnel, a 300-foot long asphalt runway, and several other facilities.

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 General Education (Curriculum for Liberal Education) 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.

Degree Requirements

The graduation requirements in effect at the time of graduation apply. When choosing the degree requirements information, always choose the year of your expected date of graduation. Requirements for graduation are referred to via university publications as "Checksheets". The number of credit hours required for degree completion varies among curricula. Students must satisfactorily complete all requirements and university obligations for degree completion.

The university reserves the right to modify requirements in a degree program. However, the university will not alter degree requirements less than two years from the expected graduation year unless there is a transition plan for students already in the degree program.

Please visit the University Registrar website at http://registrar.vt.edu/graduation-multi-brief/index1.html for degree requirements.

Undergraduate Course Descriptions (AOE)

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 inegration, 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. (2H,1.5L,2C)

2104: INTRODUCTION TO AEROSPACE ENGINEERING
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 2214. Pre: ENGE 1216, PHYS 2305. Co: 2074. (3H,3C)

2114: FUNDAMENTALS OF FLIGHT TRAINING
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. (2H,2C)

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. A grade of C- or better is required in each prerequisite. Pre: ENGE 1216, PHYS 2305. Co: MATH 2204. (3H,3C)

2214: INTRO TO PHYS OCEAN FOR OE
Ocean seafloor properties and dynamics. Properties of seawater. Ocean currents and circulation. Physics of ocean waves and tides. Pre: (ENGE 1114 or ENGE 1216), PHYS 2305. (1H,1C)

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: AERO/HYDRODYNAMICS
Two-dimensional potential flow, stream function, velocity potential, flow superposition, circulation and lift, airfoil characteristics. Two-dimensional airfoil theory and panel methods. Three-dimensional lifting line theory and vortex lattice solutions for finite wings. Pre: (3104 or 3204), ESM 2304. (3H,3C)

3024: THIN-WALLED STRUCTURES
Review of mechanics of materials. Stresses in stiffened shell beams. Deformation analysis by energy methods. Multicell beams. Introduction to the matrix stiffness method including truss and beam elements. Pre: ESM 2104, ESM 2204. (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, ME 3134, MATH 4564. (3H,3C)

3054: AOE EXPERIMENTAL METHODS
Principles of measurement and measurement systems; standards, accuracy, uncertainty and statistical concepts. Practical electronics, detectors, transducers and instruments for aerospace and ocean engineering. Signal conditioning systems and readout devices; digital data acquisition, structures, structural dynamics, fluid dynamics, materials and wind-tunnel testing. Pre: 3014, 3024, 3034. (1H,6L,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)

3104: AIRCRAFT PERFORMANCE
Performance of aircraft. Analysis of fluid statics and dynamics affecting aircraft performance. Hydrostatics of the standard atmosphere and development of basic equations of fluid dynamics. Lift and drag. Aircraft static performance. Rates of climb, endurance, range, take off and landing, and turn performance. Pre: (2104 or 2204), ESM 2104. Co: 2074, ESM 2304. (3H,3C)

3114: COMPRESSIBLE AERODYNAMICS
Inviscid, compressible gas dynamics. Continuity, momentum and energy equations, shock waves, Prandtl-Meyer expansions. One-dimensional steady and unsteady flow, Rayleigh line, Fanno line, Shock Tubes. Method of Characteristics, supersonic thin airfoil theory and conical flow. Pre: 3014, ME 3134. (3H,3C)

3124: AEROSPACE STRUCTURES
Aspects of structural analysis pertinent to the design of flight vehicles: aeroelastic divergence, environmental loads, aerospace materials, buckling of thinwalled compression members, and introduction to matrix structural dynamics. Pre: 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. (3H,3C)

3204: NAVAL ARCHITECTURE
Buoyancy of ocean vehicles. Hull geometry, line drawings, coefficients of form. Hydrostatic calculations, development of a computer program for hydrostatic analysis. Review and calculations. Intact and damaged stability of ocean vehicles. Large angle stability. Stability criteria. Viscosity. Stress in a fluid. Basic laws of fluid dynamics. Pre: ESM 2104, (MATH 2224 or MATH 2204 or MATH 2204H), (AOE 2104 or AOE 2204). Co: 2074, ESM 2304. (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 and finite element structural analysis. Pre: 3024. (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: RESISTANCE AND PROPULSION OF SHIPS
Methods of estimating ship resistance; propulsion devices and their efficiencies; Resistance components; Froude scaling of model test data; Methodical series; Planing hulls; Propellers; Waterjets; Propeller design; Computer methods; Advanced marine vehicles. Pre: 3014, 3204. (3H,3C)

4004: COMPUTER-AIDED CONTROL SYSTEM DESIGN
Control design and analysis for linear, state-space system models. Properties of linear, time-invariant control systems: Input/output stability, internal stability, controlability, 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 (CEE 4444) (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: 3024 or CEE 3404. (3H,3C) II.

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 sessil 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. I Pre: 3014 or CEE 3304 or ESM 3024 or ME 3404. (3H,3C)

4065-4066: AIRCRAFT DESIGN
Analysis and design of various aeronautical vehicles and systems. Pre: 3054, 3114, 3124, 3134 for 4065; 3054, 3114, 3124, 3134, 4065 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)

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)

4134: ASTROMECHANICS
Application of Newton's Laws to the dynamics of spaceflight. Two-body problem, Kepler's Laws, energy and time relations, orbit specification and determination. Orbital maneuver and transfer, patched conic approximations, relative motion, and elements of optimal maneuvering. Pre: ESM 2304. (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. (3H,3C)

4154: AEROSPACE ENGINEERING LABORATORY
Wind tunnel laboratory experiments related to subsonic and supersonic aerodynamics. Continuation of AOE 3054 for Aerospace Engineering students. Writing of technical laboratory reports; design of experiments. Pre: 3054, 3114, 3124, (3134 or 4140). (3L,1C)

4165-4166: SPACECRAFT DESIGN
Analysis and design of various space vehicles and systems. Pre: 3054, 3114, 3124, 4140 for 4165; 3054, 3114, 3124, 4140, 4165 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: 4234 or ME 4234. (3H,3C)

4214: OCEAN WAVE MECHANICS
Introduction to theory of wave motion in different water depth regions, including wave generation and propagation. Description of wave statistics and spectral representation for realistic ocean conditions. Wave forces on stationary structures. Nonlinear waves, wave properties, and methods of analysis. Pre: 3014, MATH 4564. (3H,3C)

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, ME 3134) or (ME 3404, ME 3124). (3H,3C)

4244 (ME 4244): MARINE ENGINEERING
Analysis of major ship propulsion devices (propellers, water jets). Integration with propulsion plant and machinery. Characteristics of marine steam turbines, nuclear power plants, marine diesels, and marine gas turbines. Shafting system, bearings, and vibration problems. Pre: 3204, (ME 3134 or ME 3124). (3H,3C)

4254: OCEAN ENGINEERING LABORATORY
Continuation of AOE 3054 for Ocean Engineering students using facilities and instrumentation pertinent to ocean engineering. Writing of technical laboratory reports; design of experiments. Pre: 3054, 3264. (1H,2L,1C)

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 or 3204), (MATH 2224 or MATH 2204 or MATH 2204H), PHYS 2306. (3H,3C)

4265-4266: SHIP DESIGN
Study and application of systems engineering process to simultaneous development of ship requirements, concept exploration, selection of ship technologies, and selection of a baseline ship design. Emphasis is on hullform, machinery, ship synthesis and balance, metrics and design optimization in the context of a ship design project. Baseline design selected in the first semester is developed in the second semester. This includes hullform; topside arrangements; internal subdivision and tankage; power and propulsion; auxiliary machinery, general arrangements, machinery weights, space, seakeeping, cost, risk, and overall balance and feasibility. Pre: 3054, 3224, 3264, 4214, 4244 for 4265; 3054, 3224, 3264, 4214, 4244, 4265, 4334 for 4266. Co: 4334 for 4265. (2H,3L,3C)

4274: COMPUTER BASED DESIGN OF OCEAN STRUCTURES
Computer-based structural models for combined finite element analysis, limit state analysis and optimization. Torsion of thin-walled structures. Buckling of stiffened panels and cylinders. Eigenvalue methods for buckling and vibration. Incremental plastic collapse; other progressive collapse. Ultimate strength of large structural modules. Pre: 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, 4214, MATH 4564. (3H,3C)

4344: DYN 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. Pre: 3264, 4334. (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. Partially duplicates 3414. Mathematics majors or minors cannot take both 4404 and 3414. 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)

4974: INDEPENDENT STUDY
Variable credit course.

4984: SPECIAL STUDY
Variable credit course.

4994: UNDERGRADUATE RESEARCH
Variable credit course.

4994H: UNDERGRADUATE RESEARCH
Variable credit course.