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College of Engineering

Aerospace and Ocean Engineering

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

University Exemplary Department

C. D. Hall, Head
R. A. Canfield, Assistant Head
Jack E. Cowling Professor: R. L. Simpson
Fred D. Durham Professor: J. A. Schetz
Norris and Laura Mitchell Professor: R. K. Kapania
Professors: R. A. Canfield; A. J. Brown; W. J. Devenport; C.D. Hall;
W. H. Mason; R. W. Walters
Associate Professors: W. L. Neu; C. J. Roy; C.A Woolsey
Assistant Professors: M. Farhood; L.S. McCue; M. Patil; M. Philen;
G.D. Seidel; C. Sultan
Adjunct Professors: W.L. Hallauer, Jr.
Professors Emeritus: E. Cliff; W. C. Durham; Z. Gurdal; O.F. Hughes;
A.K. Jakubowski, E.R. Johnson; C.L. Yates
Faculty Affiliates1: R. Batra; M. Cramer; H. Dankowicz; M. Hajj;
S. Hendricks; M. Hyer; D. Inman; R.D. Moffitt; S. Ragab; W. Scales;
D. Stilwell; D. Telionis
1 Faculty with regular appointments in other departments

AOE students & projects

Overview

    The aerospace and ocean engineering department offers two bachelor of science degree programs which share a broad range of common interests. 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 degree 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 vehicle 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 with coverage of the areas of fluid dynamics, vehicle dynamics and control, propulsion, and structures, including an emphasis on design and synthesis in a team environment.

    The department's curricula are both 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, multi-national corporations to small consulting firms.

    Classroom studies utilize the students' personal computers and departmental computers. 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 full scale U. S. Navy A-6 flight simulator and several other facilities.

    The department encourages student participation 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 and even international team projects which include travel to universities in other parts of the world.

    The Aerospace Engineering and Ocean Engineering programs are accredited by the Engineering Accreditation Commission of ABET, 111 Market Place, Suite 1050, Baltimore, MD, 21202-4012, Telephone (410) 347-7700.

    The department also offers programs of study leading to the M. Engr., M.S., and Ph.D.

    AOE students must meet all 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 in the department office and on the department's web page.

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Aerospace Engineering Program

    A total of 136 credit hours is required for graduation.
First Year
First Semester
CHEM 1035 GENERAL CHEMISTRY
3
CHEM 1045 GENERAL CHEMISTRY LAB
1
ENGE 1024 ENGR EXPLORATION
2
ENGL 1105 FRESHMAN ENGLISH
3
MATH 1114 ELEMENTARY LINEAR ALGEBRA
2
MATH 1205 CALCULUS
3
ELECTIVE*
3
Credits
17
Second Semester
ENGE 1114 EXPLORATION OF ENGINEERING DESIGN
2
ENGL 1106 FRESHMAN ENGLISH
3
MATH 1206 CALCULUS
3
MATH 1224 VECTOR GEOMETRY
2
PHYS 2305 FOUNDATIONS OF PHYSICS I
4
ELECTIVE*
3
Credits
17
Second Year
First Semester
AOE 2074 COMPUTATIONAL METHODS
3
AOE 2104 INTRO TO AEROSPACE ENGINEERING
3
ESM 2104 STATICS
3
MATH 2224 MULTIVARIABLE CALCULUS
3
PHYS 2306 FOUNDATIONS OF PHYSICS I
4
ELECTIVE*
1
Credits
17
Second Semester
AOE 3094 MATERIALS FOR AEROSPACE AND OCEAN ENGINEERING
3
AOE 3104 AIRCRAFT PERFORMANCE
3
ESM 2204 MECHANICS OF DEFORMABLE BODIES
3
ESM 2304 DYNAMICS
3
MATH 2214 INTRO TO DIFFERENTIAL EQUATIONS
3
ELECTIVE*
3
Credits
18
Third Year
First Semester
AOE 3014 AERO/HYDRODYNAMICS
3
AOE 3024 THIN-WALLED STRUCTURES
3
AOE 3034 VEHICLE VIBRATION AND CONTROL
3
MATH 4564 OPERATIONAL METHODS
3
ME 3134 FUNDAMENTALS OF THERMODYNAMICS
3
ELECTIVE* OR AOE 4134 ASTROMECHANICS
3
Credits
18
Second Semester
AOE 3054 AOE EXPERIMENTAL METHODS
3
AOE 3114 COMPRESSIBLE AERODYNAMICS
3
AOE 3124 AEROSPACE STRUCTURES
3
AOE 3134
OR AOE 4140
STABILITY AND CONTROL
SPACECRAFT DYNAMICS AND CONTROL
3
MATH ELECTIVE+
3
ELECTIVE*
3
Credits
18
Fourth Year
First Semester
AOE 3044 BOUNDARY LAYER THEORY
3
AOE 4065 DESIGN*
3
AOE 4134 OR ELECTIVE (OPPOSITE OF JUNIOR YR. CHOICE) * ASTROMECHANICS
3
AOE 4154 AEROSPACE ENGINEERING LABORATORY
1
AOE 4234 AEROSPACE PROPULSION
3
TECHNICAL ELECTIVE+
3
Credits
16
Second Semester
AOE 4066 DESIGN**
3
ELECTIVES*
6
TECHNICAL ELECTIVES++
6
Credits
15

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Ocean Engineering Program

    A total of 136 credit hours is required for graduation.
First Year
First Semester
CHEM 1035 GENERAL CHEMISTRY
3
CHEM 1045 GENERAL CHEMISTRY LAB
1
ENGE 1024 ENGR EXPLORATION
2
ENGL 1105 FRESHMAN ENGLISH
3
MATH 1114 ELEMENTARY LINEAR ALGEBRA
2
MATH 1205 CALCULUS
3
ELECTIVE*
3
Credits
17
Second Semester
ENGE 1114 EXPLORATION OF ENGINEERING DESIGN
2
ENGL 1106 FRESHMAN ENGLISH
3
MATH 1206 CALCULUS
3
MATH 1224 VECTOR GEOMETRY
2
PHYS 2305 FOUNDATIONS OF PHYSICS I
4
ELECTIVE*
3
Credits
17
Second Year
First Semester
AOE 2074 COMPUTATIONAL METHODS
3
AOE 2204 INTRO TO OCEAN ENGINEERING
3
ESM 2104 STATICS
3
MATH 2224 MULTIVARIABLE CALCULUS
3
PHYS 2306 FOUNDATIONS OF PHYSICS I
4
ELECTIVE*
1
Credits
17
Second Semester
AOE 3094 MATERIALS FOR AEROSPACE AND OCEAN ENGINEERING
3
AOE 3204 NAVAL ARCHITECTURE
3
ESM 2204 MECHANICS OF DEFORMABLE BODIES
3
ESM 2304 DYNAMICS
3
MATH 2214 INTRO TO DIFFERENTIAL EQUATIONS
3
ELECTIVE*
3
Credits
18
Third Year
First Semester
AOE 3014 AERO/HYDRODYNAMICS
3
AOE 3024 THIN-WALLED STRUCTURES
3
AOE 3034 VEHICLE VIBRATION AND CONTROL
3
MATH 4564 OPERATIONAL METHODS
3
ME 3134 FUNDAMENTALS OF THERMODYNAMICS
3
ELECTIVE*
3
Credits
18
Second Semester
AOE 3054 AOE EXPERIMENTAL METHODS
3
AOE 3224 OCEAN STRUCTURES
3
AOE 3264 RESISTANCE AND PROPULSION OF SHIPS
3
AOE 4214 OCEAN WAVE MECHANICS
3
AOE 4244 MARINE ENGINEERING
3
STAT 4705 PROBABILITY AND STATISTICS FOR ENGINEERS
3
Credits
18
Fourth Year
First Semester
AOE 3044 BOUNDARY LAYER THEORY
3
AOE 4254 OCEAN ENGINEERING LABORATORY
1
AOE 4065 SHIP DESIGN
3
AOE 4334 SHIP DYNAMICS
3
TECHNICAL ELECTIVES++
6
Credits
16
Second Semester
AOE 4066 SHIP DESIGN
3
ELECTIVES*
9
TECHNICAL ELECTIVES++
3
Credits
15

Satisfactory Progress: In addition to the requirements of University Policy 91, after attempting 72 credit hours, students must have passed AOE 2074 and AOE 3104, and after attempting 108 credit hours, students must have passed 24 credit hours of in-major courses and have 2.0 overall and in-major GPAs.

* Electives include 6 credits each from Curriculum for Liberal Education (CLE) Areas 2 and 3, 1 credit from CLE Area 6, and 3 credits from CLE Area 7 (the area 7 course may double count with area 2 or 3). The AOE Department requires that ECON 2005 (Principles of Economics) be one of the courses taken in Area 3. The elective credits must include a 1-3 credit computer programming course in C++ or FORTRAN selected from the following: CS 1044 (Introduction to Programming in C), ENGE 2314 (Engineering Problem Solving With C++), ENGE 2324 (Engineering Problem Solving Using Fortran). Other C++ or FORTRAN courses may be approved by your advisor. Three to eight credits will be free electives.

** AE majors may take either aircraft or spacecraft design. OE majors must take ship design.

+ Choice of MATH 4574 (Vector and Complex Analysis for Engineers) or MATH/AOE 4404 (Applied Numerical Methods) or STAT 4705 (Probability and Statistics for Engineers)

++ The AOE Department requires 9 credits of technical electives of which 6 credits must be an AOE course and the remaining 3 may be selected from a list of 3000 level and higher AOE and other approved technical courses

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Undergraduate Course Descriptions (AOE)

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, numerical solutions of ordinary differential equations. A grade of C- or better required in ENGE prerequisite 1114. Pre: ENGE 1114. Co: MATH 2224.(3H,3C)

2104: INTRODUCTION TO AEROSPACE ENGINEERING
An 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. Must have a C- or better in pre-requisites ENGE 1114 and PHYS 2305. Pre: ENGE 1114, PHYS 2305. (3H,3C)

2204: INTRODUCTION TO OCEAN ENGINEERING
An overview of ocean engineering from a design perspective. Ship types and geometry; stages of ship design; introductory hydrostatics and stability; hydrodynamics; resistance and propulsion; oceanography and waves; loads on ships; ship structural analysis. Must have a C- or better in pre-requisites ENGE 1114 and PHYS 2305. Pre: ENGE 1114, PHYS 2305. (3H,3C)

2974: INDEPENDENT STUDY
Variable credit course.

2984: SPECIAL STUDY
Variable credit course.

2994: 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. A grade of C- or better required in each prerequisite. 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. Must have a C- or better in pre-requisites ESM 2104 and ESM 2204. Pre: ESM 2104, ESM 2204. (3H,3C)

3034: VEHICLE VIBRATION AND CONTROL
Free and forced motions of first order system. Free and forced motions of second order systems both undamped and damped. Frequency and time response. Introduction to control, transfer functions, block diagrams, and closed loop system characteristics. Higher order systems. Must have a C- or better in pre-requisites ESM 2304 and Math 2214. 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. Must have a C- or better in pre-requisites AOE 3014, ME 3134, and Math 4564. 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. Must have a C- or better in pre-requisites AOE 3014, 3024 and 3034. 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. 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. Must have a C- or better in pre-requisites ESM 2104 and co requisite ESM 2304. Pre: ESM 2104. Co: 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. Must have a C- or better in pre-requisite AOE 3024. Pre: 3024. (3H,3C)

3134: STABILITY AND CONTROL
Equations of vehicle motion. Linearized analysis. Estimation of stability derivatives, longitudinal and lateral-directional static stability, and control requirements. Dynamic characteristics including stability and mode shapes. Must have a C- or better in pre-requisite AOE 3034. 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. Viscocity. Stress in a fluid. Basic laws of fluid dynamics. Must have a C- or better in pre-requisites ESM 2104 and MATH 2224. Pre: ESM 2104, MATH 2224. Co: 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. Must have a C- or better in pre-requisite ESM 3024. Pre: 3024. (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. Must have a C- or better in pre-requisites AOE 3204 and AOE 3014. Pre: 3204, 3014. (3H,3C)

4004: COMPUTER-AIDED CONTROL SYSTEM DESIGN
Computer-aided design and analysis of control systems for high-order linear systems. Stability and performance design criteria. Root locus, PID, lead/lag, and pole-placement design methods. Introduction to modern state-space modeling methods. Design problems involving aircraft, ship, space, and ground-vehicle systems. 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: 2074, MATH 2224. (3H,3C)

4034: COMPUTATIONAL STRUCTURAL ANALYSIS
Static and vibratory response of framed structures. The matrix eigenvalue problem for buckling and free vibrations. Static response of laminated composite plates by the finite element method. Pre: 3124 or 3224. (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 (CEE 4364): 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: DESIGN
Analysis and design of various space, aeronautical and marine vehicles and systems. Senior standing required. (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. (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. Must have a C- or better in prerequisite ESM 2304. 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. Must have a C- or better in pre-requisites AOE 3034 and 4134. Pre: 3034, 4134. (3H,3C)

4144: AIRCRAFT AUTOMATIC FLIGHT CONTROL
Introduction and history of aircraft automatic flight control. Mathematical models of linear systems elements. Bode amplitude and phase plots of longitudinal and lateral control system analysis. Inputs and system performance assessment. Multiloop flight control systems. Applications to representative aircraft. Pre: 3134, MATH 4564. (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. Must have a C- or better in pre-requisites AOE 3054, AOE 3114, AOE 3124 and AOE 3134. Pre: 3054, 3114, 3124, (3134 or 4140). (3L,1C)

4164: SPECIAL TOPICS IN VEHICLE PERFORMANCE
Three dimensional point-mass equations of motion over flat and spherical Earth. Aerodynamic and propulsive modeling. Numerical integration of equations of motion. Analytic approximations and solutions. Energy state models. Advanced topics. Pre: 3104, 3134. (3H,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)

4204: OCEAN ACOUSTICS
Basic problems and techniques of underwater acoustics; sonar equations, sound propagation in the ocean, generation and detection of underwater sound, background and self noise, reverberation, target strength, applications. Pre: MATH 4564. (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. Must have a C- or better in pre-requisites AOE 3014 and MATH 4564. Pre: 3014, MATH 4564. (3H,3C)

4224: PROBABILISTIC ANALYSIS OF OCEAN SYSTEMS
Representation of random phenomena for ocean systems (waves, vehicle motions, wave-induced loads). Concepts of correlation (for vector processes), power spectra, probability density, envelope processes. Responses of linear dynamic systems, statistics of responses, exceedance probability, extremes. Extension to nonlinear systems. Pre: 3234, 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. Must have a C- or better in pre-requisites AOE 3113 and ME 3134 or ME 3404 and ME 3124. 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. Must have a C- or better in pre-requisites AOE 3204 and ME 3124 or ME 3134. 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. Must have a C- or better in pre-requisites AOE 3054 and AOE 3264. Pre: 3054, 3264. (1H,2L,1C)

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. Must have a C- or better in pre-requisites AOE 3014, AOE 3034, AOE 4214 and MATH 4564. 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 4554 and 3414. Mathematics majors or minors cannot take both 4404 and 3414. X-grade allowed. Pre: MATH 4564, (ESM 2074 or AOE 2074). (3H,3C)

4974: INDEPENDENT STUDY
Variable credit course.

4984: SPECIAL STUDY
Variable credit course.

4994: UNDERGRADUATE RESEARCH
Variable credit course.

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Virginia Tech 2009-2010 Undergraduate Course Catalog and Academic Policies