College of Engineering : [catalog]. - Aerospace … open to studentsenrolled in the College of...

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College of Engineering : [catalog].University of Michigan.Ann Arbor, Mich. : The University of Michigan,

http://hdl.handle.net/2027/mdp.39015021656460

Open Access, Google-digitizedhttp://www.hathitrust.org/access_use#oa-google

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Courses in Aerospace Engineering 119

Unless a phrase such as "Junior Standing", "Senior Standing" or "Graduate Standing" is part of the list of prerequisites for a course, a student

may' elect an advanced level course relative to his current status if the

other prerequisites are satisfied. If the difference in standing level is

greater than one academic year, it is usually not wise to elect an advanced

level course without first consulting the department or the instructor

offering the course.

Aerospace Engineering

Department Office: 1077 East EngineeringSee Page 118 for statement on Course Equivalence.

200. General Aeronautics and Astronautics. Prerequisite: Physics 140, I and II.(').

Introduction to aerospace engineering. Elementary problems designed to orientthe student in the program of aerospace engineering, together with a discussion of the current state of aerospace developments and the role of the engineer. Recitations and demonstrations.

201. Conquest of Air and Space. II. (2).An introduction to the physical principles of flight within the atmosphere andin space, to the major historical developments in the conquest of air and space,and to the current state of aerospace developments and their role in nationaland world affairs. Not open to students enrolled in the College of Engineering.

314(Eng. Mech. 314). Structural Mechanics L Prerequisite: Eng. Mech. 211 or319. I and II. (4).

Review of plane states of stress and strain. Basic equations of plane elasticityand selected problems; failure criteria and applications; energy principles ofstructural theory; thin-walled beam theory.

320. Aerodynamics I. Prerequisite: preceded or accompanied by Eng. Mech. 340

and Math. 450. I and II. (4).Development of the fundamentals of aerodynamics which form the basis forthe study of modern aircraft. Calculation of the forces and moments actingon wings and bodies in incompressible inviscid flow and comparison with ex

periment.

330. Propulsion I. Prerequisite: Mech. Eng. 335, Aero. Eng. 320 or Mech. Eng.336. I and H. (3).

Introduction to aerothermodynamics and applications to problems in flightpropulsion. Discussion of the momentum theorem, one dimensional flow sys

tems with heat addition, shock waves, diffusers, compressors, and turbines.

390. Undergraduate Seminar. Prerequisite: Junior standing. I and II. (1).A series of seminars by noted outside speakers designed to acquaint under

graduates with both current problems and state of the art of the aerospace

industry. Will involve a short term project or paper pertinent to one of theseminar topics.

414(Eng. Mech. 414). Structural Mechanics II. Prerequisite: Aero. Eng. 314. Iand II. (4).

Introduction to plate theory. Stability of structural elements; columns andbeam columns; plates in compression and shear; secondary instability of columns. Introduction to matrix methods of deformation analysis; structural dynamics. Lectures and laboratory.

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120 Courses in Aerospace Engineering

415. Principles of Structural Mechanics. Prerequisite: Eng. Mech. 211 or 319.

I. (3).An accelerated coverage of the material in Aero. Eng. 314 and 414 designedprimarily for graduate students. Not open to students who have elected Aero.Eng. 314 or 414.

420. Aerodynamics II. Prerequisite: Aero. Eng. 320, and preceded or accom

panied by Aero. Eng. 330. I and II. (4).Continuation of Aerodynamics I. Viscous and compressible fluid theory appliedto the calculation of the forces and moments on wings and bodies and comparison with experiment. Loads on an airplane. Lectures and laboratory.

421. Topics in Fluid Mechanics. Prerequisite: Aero. Eng. 420. (3).Topics include free surface phenomena, flow separation, flow in tubes, lubrication, flow in a gravity-free environment. The objective of the course is toextend the student's background in gas dynamics to the fundamental aspectsof other fluid phenomena of importance in aerospace and other industrial applications. Lectures and demonstrations.

425. Principles of Aerodynamics. Prerequisite: Eng. Mech. 324. (3).An accelerated coverage of the material in Aero. Eng. 320 and 420 designedprimarily for graduate students. Not open to students who have elected Aero.Eng. 320 or 420.

430. Propulsion II. Prerequisite: Aero. Eng. 330. I and II. (4).Performance and analysis of flight-propulsion systems including the reciprocating engine-propeller, turboprop, ramjet, pulsejet, and rocket. Lectures andlaboratory.

435. Principles of Propulsion. Prerequisite: Mech. Eng. 335. (3).An accelerated coverage of the material in Aero. Eng. 330 and 430 designedprimarily for graduate students. Not open to students who have elected Aero.Eng. 330 or 430.

439. Aircraft Propulsion Laboratory. Prerequisite: preceded by Aero. Eng. 330.

(2)-Series of experiments designed to illustrate the general principles of propulsion and to introduce the student to certain experimental techniques in thestudy of actual propulsive devices, using full-scale or reduced models of thepulsejet, turbojet, ramjet, and rocket motors.

441. Mechanics of Flight. Prerequisite: Aero. Eng. 320. I and II. (4).Mechanics of a particle applied to the analysis of vehicle flight paths. Orbits,

ballistic trajectories, and trajectories of vehicles in the atmosphere. Rigid bodymechanics applied to translational and rotational vehicle motion. Analysis ofvehicle motion and static and dynamic stability using perturbation theory.Control characteristics.

445. Principles of Mechanics of Flight. Prerequisite: Math. 316. (3).An accelerated coverage of the material in Aero. Eng. 441 designed primarilyfor graduate students. Not open to students who have elected Aero. Eng. 441.

447. Flight Testing. Prerequisite: Aero. Eng. 441. (2).Theory and practice of obtaining flight-test data on performance and stabilityof airplanes from actual flight tests.- No laboratory fee will be charged, but a

deposit covering student insurance and operating expense of the airplane willbe required.

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+49. Principles of Vertical Take-off and Landing Aircraft Prerequisite: Aero.

Eng. 420. (3).Lifting rotor and propellor analysis in vertical and forward flight; ducted fananalysis; helicopter performance analysis; transitional flight problems of VTOLaircraft: stability and control problems of helicopters and VTOL aircraft.

464 (Metcor .-Ocean. 464). Introduction to Aeronomy. Prerequisite: senior or

graduate standing in a physical science or engineering. L (3).An introduction to physical processes in the upper atmosphere; density, tem

perature, composition, and winds; atmospheric radiation transfer processesand heat balance; the ionosphere; rocket and satellite measurement techniques.

465. Aeronomical Measurements. Prerequisite: Aero. Eng. 464 or Elec. Eng. 495.

n. (3).Theory and effectiveness of techniques for making upper atmosphere and spacemeasurements as well as measurements of the lower atmosphere from space.

Photometry, spectrometry, interferometry and radiometry; gas dynamic methods,

mass spectrometry and ionospheric probing.

466. Aeronomical Measurements Laboratory. Prerequisite: preceded or accom

panied by Aero. Eng. 465. II. (2).Measurement projects in gas dynamics and in radiation phenomena in all partsof the electromagnetic spectrum of significance to atmospheric and space re

search. Emphasis is placed on ground based techniques which yield usefulaeronomical data.

471. Automatic Control Systems. Prerequisite: Aero. Eng. 441. (4).Transient and steady-state analysis of linear control systems; transfer functions,

stability analysis, and synthesis methods; airplane transfer functions and syn

thesis of autopilot and powerplant control systems; use of analog computer inthe laboratory for simulation. Lectures and laboratory.

481. Airplane Design. Prerequisite: Aero. Eng. 314 and 441. I and II. (4).Power-required and power-available characteristics of aircraft on a comparativebasis, calculation of preliminary performance, stability, and control characteristics. Design procedure, including layouts and preliminary structural design.

Subsonic and supersonic designs. Emphasis on design techniques and systems

approach. Lectures and laboratory.

482. Sounding Rocket and Payload Design. Prerequisite: Aero. Eng. 314 and441. I and II. (4).

Design of the instrumentation, payload and propulsion units of a soundingrocket for making atmospheric measurements up to satellite altitudes. Measur

ing techniques, instruments, housekeeping, telemetering, environmental tests,

propulsion, staging, stability, heating, trajectories and dispersion. Lectures andlaboratory.

483. Aerospace System Design. Prerequisite: Aero. Eng. 314 and 441 and preceded or accompanied by Aero. Eng. 430. I and II. (4).

Aerospace system design, analysis and integration. Consideration of launch facilities, booster systems, spacecraft systems, communications, data processing and

project management. Lectures and laboratory.

485. Aerospace Communication Systems. Prerequisite: Math. 450, Elec. Eng. 314.

(3)-Introduction to the design of space communications and tracking systems forthe aerospace system designer. Basic principles in the design of space com

munications and tracking systems, including modulation-demodulation tech

niques, frequency and time division multiplexing, methods of data storage,

system gain considerations, power sources, antennas, propagation and trackingmethods. Application to system problems emphasized.

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490. Directed Study. (To be arranged).Individual study of specialized aspects of aerospace engineering. Primarily for

undergraduates.

510. Energy Theorems and Matrix Methods in Structural Mechanics L Prerequisite: Aero. Eng. 414 or Eng. Mech. 411 or 412. (3).

The principle of virtual work and the theorems of minimum potential andminimum complementary energy. Variational calculus, the Rayleigh-Ritz method,

Galerkin's method. Solution by finite differences. The matrix force and dis

placement methods. Applications to simple structures and structural elements such as beams, frames, and plates. Static and dynamic problems.

514(Eng. Mech. 511). Foundations of Structural Mechanics I. Prerequisite: Aero.

Eng. 414 (3).Elements of the analysis of structures. Includes plates of various shapes, load

ing, and boundary conditions, effects of in-plane loading; shells of revolution,

cylindrical shells, bending and membrane theories; plastic analysis of structuresbeams, frames, plates; plastic collapse mechanism. Applications of aerospaceinterest.

515(Eng. Mech. 512). Foundations of Structural Mechanics II. Prerequisite: Aero.

Eng. $14. (3).Behavior of structures in a thermal environment, heat conduction, aerodynamicheating of high speed vehicles, thermal stresses and deflections, thermal instabilities, discussion of material properties at elevated temperatures. Elements ofthe theory of linear viscoelasticity.

520. Gasdynamics L Prerequisite: Aero. Eng. 420 or 425. (3).Gasdynamics at an intermediate level: Thermodynamics; the conservation equations; vorticity theorems; unsteady one-dimensional flow; the method of characteristics; stationary and moving shock waves; two-dimensional steady flow

including method of small perturbations.

521. Experimental Gasdynamics.. Prerequisite: Aero. Eng. 330 and 420. (3).Experimental methods in modern gasdynamics; physical principles and interpretation. Shop practice and theory of instrument design; mechanics, electronics,and optics. Measurement of velocity, pressure, density, temperature, composition,energy and mass transfer in fluids and plasmas. Transducers and laboratoryinstrumentation in gasdynamic research.

522. Gasdynamics II. Prerequisite: Aero. Eng. 520. (3).Similarity laws for two- and three-dimensional high speed flows; two-dimensional incompressible flows by conformal mapping; examples of flows with

viscosity, including simple cases of compressible boundary layer flow; introduction to electromagnetic theory, and the equations for magnetohydrodynamicflow.

525. Aerodynamics of High-Speed Flight. Prerequisite: Aero. Eng. 420 or 425. (3).Treatment of problems in the aerodynamics of flight at supersonic and hypersonic velocities; linearized theory of wings with arbitrary planform and bodiesof revolution; wing-body interference; hypersonic aerodynamics, aerodynamicheating, real gas effects.

530. Propulsion III. Prerequisite: Aero. Eng. 430. (3).Continuation of Aero. Eng. 430. Further treatment of aircraft engine performance, including off-design operation, and study of selected problems in thefield of propulsion.

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532. Introduction to Gaskinetics and Real Gas Effects. Prerequisite: Aero. Eng.420. (3).

A study of some modern topics of flow problems not covered in the traditionalgasdynamics of ideal gases: concepts of gaskinetics, aerodynamics of free molecules, shock transition layer, real gas effects, high temperature effects, multi-component flows, etc.

535. Rocket Propulsion. Prerequisite: Aero. Eng. 430 or 435. (3).Analysis and performance of liquid and solid propellant rocket power plants;propellant thermochemistry, heat, transfer, system considerations, advanced

rocket propulsion techniques.

540. Space Dynamics I. Prerequisite: Eng. Mech. 340. (4).Kinematics of motion, particle dynamics, orbital motion and calulation of orbital parameters, Lagrange's equation. Rigid body dynamics including Euler'sequations, the Poinsot construction, spin stabilization, the rotation matrix.Vibrations of coupled systems, orthogonality relationships, generalized co-ordinates and system parameters.

542. Astrodynamics I. Prerequisite: Aero. Eng. 441. I. (3).The study of motion of spacecraft in a vacuum and in the atmosphere withemphasis on preliminary mission planning. Analysis of trajectories in suborbital,orbital, lunar, and interplanetary operations. Aerodynamic forces and heatingcharacteristics and their effect on the selection of flight paths during entry intoplanetary atmospheres.

543. Structural Dynamics. Prerequisite: Aero. Eng. 414 or 540. (3).Natural frequencies and mode shapes of elastic bodies. Nonconservative elastic

systems. Structural and viscous damping. Influence coefficient methods for typicalflight structures. Response of structures to random and shock loads. Lab demonstration.

544. Aeroelasticity. Prerequisite: Aero. Eng. 414 or 540. (3).An introduction to aeroelasticity. Vibration and flutter of elastic bodies exposedto fluid flow. Static divergence and flutter of airplane wings. Flutter of flatplates and thin walled cylinders at supersonic speeds. Oscillations of structuresdue to vortex shedding.

590. Directed Study. (To be arranged).Individual study of specialized aspects of aerospace engineering. Primarily forgraduates.

596. Aurora and Airglow. Prerequisite: permission of instructor. II. (3).Morphology and physics of the aurora and airglow. Emission spectra in the

aurora and their atomic and molecular origin; proton aurora; metastable excitation; calculation of emission profiles. Night- and day-glow; pre-dawn andpost-twilight enhancements; mid-latitude red arc; excitation mechanisms.

610. Energy Theorems and Matrix Methods in Structural Mechanics II. Pre

requisite: Aero. Eng. 510. (3).Application of energy methods and matrix methods to shells, built-up shell-type structures, and problems in three-dimensional elasticity. Nonlinear problems in structural mechanics that arise from large amplitude deformations.Static and dynamic problems.

620. Dynamics of Viscous Fluids. Prerequisite: Aero. Eng. 520. (3).Navier-Stokes equations; low Reynolds number flows; incompressible and com

pressible laminar boundary layers; boundary layer stability and transition to

turbulence; turbulent boundary layers, wakes, and jets.

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621. Dynamics of Compressible Fluids. Prerequisite: Aero. Eng. 520. (3).Theory of characteristics; shock-wave phenomena; interaction problems; hodo-

graph transformation; transonic flow.

622. Hypersonic Aerodynamics. Prerequisite: Aero. Eng. 520. (3).Inviscid flow past thin bodies at high Mach number; blunt-body methods;

blastwave theory; viscous interaction, nonequilibrium flows.

624. Linearized Aerodynamic Theory. Prerequisite: Aero. Eng. 520. (3).Application of conformal mapping in the study of thin airfoils; three dimensional subsonic and supersonic wing theory; forces acting on oscillating wings;slender-body theory; higher approximations.

625. Methods of Theoretical Aerodynamics. Prerequisite: Aero. Eng. 520. (3).Application of methods for solving partial differential equations which arise

in aerodynamics problems. Subsonic and supersonic wing theory, sound waves,

viscous flows, boundary-layer theory, shock waves. Emphasis on the use of fundamental solutions and superposition in linear problems and asymptotic methodsin nonlinear problems. Similarity solutions, characteristics.

627. Continuum Theory of Fliuds. Prerequisite: Aero. Eng. 520. (3).Physical concepts underlying the flow of fluids acted upon by stresses arisingfrom viscosity and from electromagnetic and gravity fields. Invariant analysisof stress-strain relations. Maxwell's equations, analysis of electromagnetic stresses

and energy dissipation in moving media, the equations of motion and energyin a moving fluid, and some solutions of the complete equations.

628. Statistical Theory of Fluids. Prerequisite: Aero. Eng. 532. (3).A study of the flows of neutral and charged particles from the viewpoint ofkinetic theory; Chapman-Enskog theory of transport phenomena, dynamics ofrarefied gases, plasma kinetics without external magnetic field, plasma oscillations and Landau damping, micro-instabilities, plasma interactions.

632. Gas Flows with Chemical Reactions. Prerequisite: Aero. Eng. 532, 620. (3).Thermodynamics of gas mixtures, chemical kinetics, conservation equations formulti-component reacting gas mixtures. Deflagration and detonation waves.

Nozzle flows and boundary layers with reaction and diffusion.

640. Space Dynamics n. Prerequisite: Aero. Eng. 540. II. (2).Hamilton's equations, canonical transformations, and Hamilton-Jacobi theory.Applications to orbital problems. General perturbation theory. Introduction to

special relativity.

642. Astrodynamics n. Prerequisite: Aero Eng. 542. II. (3).Orbit determination. Systems of canonical equations. Perturbation theory withapplications to the motion of an artificial satellite. Lunar and planetary theories.

650. Computational Methods for Flight Simulation. Prerequisite: Aero. Eng.540, and C.I.C.E. 482 or Elect. Eng. 365. (2).

Equations of motion for aircraft and aerospace vehicles. Axis systems andaxis transformations including body, stability, flight-path, navigational, andinertial axes. Euler angles, direction cosines, and quaternions. Simulation of

flat earth trajectories, low-eccentricity orbits, lunar and planetary trajectories.Use of conservation laws and constraint methods. Mechanization in six degreesof freedom using analog, hybrid, and digital computers.

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651. Computation of Aerospace Trajectories. Prerequisite: Aero. Eng. 640. (2).Error analysis of numerical integration methods. Comparison of Cavell's method,

Enke's method and variation-of-parameters in terms of accuracy and convenience.MAD programming of integration methods. Student programming and solution

of trajectory problems.

670. Guidance and Navigation of Aerospace Vehicles. Prerequisite: a course in

feedback control. II. (3).Principles of space vehicle, homing and ballistic missile guidance systems intwo and three dimensions. Explicit, linear perturbation, and velocity-to-begained guidance modes. Mechanization by inertial and other means, includingstrapped-down and stable-platform inertial systems. Celestial navigation procedures with deterministic and redundant measurements. Application of Kal-mari Altering to recursive navigation theory.

671. Guidance and Control Laboratory. Prerequisite: preceded or accompaniedby Aero. Eng. 670 and Aero. Eng. 674. (2).

Simulation of aircraft, missile, and space vehicle autopilot sytems on analogand hybrid computer systems. Digital and analog solution of missile and space

vehicle guidance problems.

674. Control of Aircraft, Missiles, and Space Vehicles. Prerequisite: C.I.C.E. 550.

(2)-

Analysis and synthesis of autopilots for aircraft and cruise-type missiles. Designof thrust-vector control systems including effects of elastic structures and fuelsloshing. Attitude control systems for space vehicles; mechanization using jetthrusters and inertia wheels; gravity gradient moments.

675. Optimization of Space Trajectories. Prerequisite: permission of instructor.II. (3).

Necessary and sufficient conditions for ordinary extremum and variational problems, with emphasis on the problem of Bolza. Applications of the calculus ofvariations to optimal space trajectories. Problems with control and state variable

inequality constraints. Iterative computational methods for two-point boundary-value problems, including the gradient method, Newton's method, and quasi-linearization.

676. Optimal Guidance. Prerequisite: Aero. Eng. 675 or C.I.C.E. 540. (3).Optimum guidance modes, including the path-adaptive mode, iterative guidancemode, and neighboring optimum guidance. The effect of normality and conjugate points in guidance analysis. Applications to space missions involving highthrust, low thrust, impulsive thrust and re-entry. Necessary conditions for

singular guidance problems. Future needs in guidance theory.

721. Turbulence. Prerequisite: Aero. Eng. 620. (3).Physical and mathematical description of turbulence in boundary layers, wakes,

jets, and behind grids; turbulent fields; theories for turbulent mass, momentum, heat, and particle diffusion.

726. Introduction to Plasma Dynamics. Prerequisite: permission of instructor.

(3)-

Physical properties of a plasma; particle orbit theory; collective phenomena ina plasma; kinetic equations for a plasma; instabilities; transport phenomenaand derivation of the magnetohydrodynamic equations.

729. Special Topics in Gasdynamics. Prerequisite: permission of instructor. (Tobe arranged).

Advanced topics of current interest.

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126 Courses in Business Administration

730. Energy Transfer in High Temperature Gas Flows. Prerequisite: Aero. Eng.

532 and 620. (3).Energy transfer processes as related to high temperature gas flows; unsteady

heat conduction, convection in non-reactive and reactive flows, transport properties, ablation and gaseous radiation.

800. Seminar. (To be arranged).

810. Seminar in Structures. (To be arranged).

820. Seminar in Aerodynamics. (To be arranged).

830. Seminar in Propulsion. (To be arranged).

840. Seminar in Mechanics of Flight. (To be arranged).

870. Seminar in Instrumentation. (To be arranged).

880. Seminar in Space Technology. Prerequisite: permission of instructor. (Tobe arranged).

882. Seminar in Guided Missiles. Prerequisite: permission of instructor. (To be

arranged).Primarily for military officers.

895(Elec. Eng. 895). Seminar in Space Research. Prerequisite: permission of in

structor. (To be arranged).Detailed analyses of objectives, procedures, and results of research being carriedout at The University of Michigan. Topics will include the following: structureof the upper atmosphere; measurement of temperature, pressure, density, com

position, and winds. The ionosphere; measurement of ion and electron densityand temperature. Investigation of radio waves incident on the earth at fre

quencies absorbed by the ionosphere by means of instrumented satellites.

Interpretation of infrared data from meteorological satellites. Research in attitude control of multistage sounding rockets.

900. Research. (To be arranged).Specialized individual or group problems of research or design nature supervised by a member of the staff.

Business Administration— School of Business Administration

Office: 164 Business Administration

Professors Danielson, Dixon, Dykstra, Gies, D. Jones, Leabo. Pilcher, Rewoldt,

Ryder, Southwick, and Spivey; Associate Professors Wilhelm, Jean and Miller;Assistant Professors Brophy, Karson and Taylor.

The courses listed below are of special interest to engineering students. Inthe election of such courses attention is called to the administrative rules ofthe School of Business Administration which affect elections as follows:

1) No student shall elect courses in the School of Business Administrationwho does not have at least third-year standing (sixty credit hours). This does

not apply to Accounting 271 and 272 which arc listed as sophomore-level courses

in the Economics Department of the College of Literature, Science, and theArts.

2) Juniors may elect courses numbered 300 to 399 inclusive, and seniorsmay elect any course numbered 300 to 499 inclusive, provided they have satis

fied particular course prerequisites.

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AEROSPACE ENGINEERING / 113

an advanced level course relative to his current status if the other prerequisitesare satisfied. If the difference in standing level is greater than one academic

year, it is usually not wise to elect an advanced level course without first con

sulting the department or the instructor offering the course.


Department Office: 1077 East EngineeringSee 2 for statement on Course Equivalence.

200. General Aeronautics and Astronautics. Prerequisite: Physics 140, I and II. (2).Introduction to aerospace engineering. Elementary problems designed to orient the

student in the program of aerospace engineering, together with a discussion of the

current state of aerospace developments and the role of the engineer. Recitations anddemonstrations.

201. Conquest of Air and Space. II. (2).An introduction to the physical principles of flight within the atmosphere and inspace, to the major historical developments in the conquest of air and space, and to

the current state of aerospace developments and their role in national and worldaffairs. Not open to students enrolled in the College of Engineering.

314(Eng. Mech. S14). Structural Mechanics I. Prerequisite: Eng. Mech. 211. II. (4).Review of plane states of stress and strain. Basic equations of plane elasticity andselected problems; failure criteria and applications; energy principles of structuraltheory; thin-walled beam theory.

$20. Aerodynamics I. Prerequisite: preceded or accompanied by Eng. Mech. 340 andMath. 450. I and II. (4).

Development of the fundamentals of aerodynamics which form the basis for the studyof modern aircraft. Calculation of the forces and moments acting on wings and bodiesin incompressible inviscid flow and comparison with experiment.

330. Propulsion I. Prerequisite: Mech. Eng. 335, Aero. Eng. 320 or Mech. Eng. 336. I.and II. (3)

Introduction to aerothermodynamics and applications to problems in flight propulsion.Discussion of the momentum theorem, one dimensional flow systems with heat addition, shock waves, diflusers, compressors, and turbines.

390. Undergraduate Seminar. Prerequisite: Junior standing. I and II. (1).A series of seminars by noted outside speakers designed to acquaint undergraduateswith both current problems and state of the art of the aerospace industry. Will involvea short term project or paper pertinent to one of the seminar topics.

4H(Eng. Mech. 414). Structural Mechanics n. Prerequisite: Aero. Eng. 314. I and II.

Introduction to plate theory. Stability of structural elements; columns and beam columns; plates in compression and shear; secondary instability of columns. Introductionto matrix methods of deformation analysis; structural dynamics. Lectures and laboratory.

415. Principles of Structural Mechanics. Prerequisite: Eng. Mech. 211 or 319. I. (3).An accelerated coverage of the material in Aero. Eng. 314 and 414 designed primarilyfor graduate students. Not open to students who have elected Aero. Eng. 314 or 414.

420. Aerodynamics II. Prerequisite: Aero. Eng. 320, and preceded or accompanied by

Aero. Eng. 330. I and II. (4).Continuation of Aerodynamics I. Viscous and compressible fluid theory applied to thecalculation of the forces and moments on wings and bodies and comparison withexperiment. Loads on an airplane. Lectures and laboratory.

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114 / AEROSPACE ENGINEERING

421. Topics in Fluid Mechanics. Prerequisite: Aero. Eng. 420. (3).Topics include free surface phenomena, flow separation, flow in tubes, lubrication,

flow in a gravity-free environment. The objective of the course is to extend the stu

dent's background in gas dynamics to the fundamental aspects of other fluid phenomena of importance in aerospace and other industrial applications. Lectures and demonstrations.

425. Principles of Aerodynamics. Prerequisite: Eng. Mech. 324. (3).An accelerated coverage of the material in Aero. Eng. 320 and 420 designed primarilyfor graduate students. Not open to students who have elected Aero. Eng. 320 or 420.

430. Propulsion II. Prerequisite: Aero. Eng. 330. I and II. (4).Performance and analysis of flight-propulsion systems including the reciprocatingengine-propeller, turboprop, ramjet, pulsejet, and rocket. Lectures and laboratory.

435. Principles of Propulsion. Prerequisite: Mech. Eng. 335. (3).An accelerated coverage of the material in Aero. Eng. 330 and 430 designed primarilyfor graduate students. Not open to students who have elected Aero. Eng. 330 or 430.

439. Aircraft Propulsion Laboratory. Prerequisite: preceded by Aero. Eng. 330. (2).Series of experiments designed to illustrate the general principles of propulsion andto introduce the student to certain experimental techniques in the study of actualpropulsive devices, using full-scale or reduced models of the pulsejet, turbojet, ramjet,and rocket motors.

441. Mechanics of Flight. Prerequisite: Aero. Eng. 320. I and II. (4).Mechanics of a particle applied to the analysis of vehicle flight paths. Orbits, ballistictrajectories, and trajectories of vehicles in the atmosphere. Rigid body mechanics applied to translational and rotational vehicle motion. Analysis of vehicle motion andstatic and dynamic stability using perturbation theory. Control characteristics.

445. Principles of Mechanics of Flight. Prerequisite: Math. 316. (3).An accelerated coverage of the material in Aero. Eng. 441 designed primarily forgraduate students. Not open to students who have elected Aero. Eng. 441.

447. Flight Testing. Prerequisite: Aero. Eng. 441. (2).Theory and practice of obtaining flight-test data on performance and stability of airplanes from actual flight tests. No laboratory fee will be charged, but a deposit coveringstudent insurance and operating expense of the airplane will be required.

449. Principles of Vertical Take-off and Landing Aircraft. Prerequisite: Aero. Eng.420. (3).

Lifting rotor and propellor analysis in vertical and forward flight; ducted fan analysis:helicopter performance analysis; transitional flight problems of VTOL aircraft; stabilityand control problems of helicopters and VTOL aircraft.

464 (Meteor. -Ocean. 464). Introduction to Aeronomy. Prerequisite: senior or graduatestanding in a physical science or engineering. I. (3).

An introduction to physical processes in the upper atmosphere; density, temperature,composition, and winds; atmospheric radiation transfer processes and heat balance;the ionosphere; rocket and satellite measurement techniques.

465. Aeronomical Measurements. Prerequisite: Aero. Eng. 464 or Elec. Eng. 495. II. (3).Theory and effectiveness of techniques for making upper atmosphere and space mea

surements as well as measurements of the lower atmosphere from space. Photometry,spectrometry, interferometry and radiometry; gas dynamic methods, mass spectrometryand ionospheric probing.

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466. Aeronomical Measurements Laboratory. Prerequisite: preceded or accompaniedby Aero. Eng. 465. II. (2).

Measurement projects in gas dynamics and in radiation phenomena in all parts of the

electromagnetic spectrum of significance to atmospheric and space research. Emphasisis placed on ground based techniques which yield useful aeronomical data.

471. Automatic Control Systems. Prerequisite: Aero. Eng. 441. (4).Transient and steady-state analysis of linear control systems; transfer functions, sta

bility analysis, and synthesis methods; airplane transfer functions and synthesis of

autopilot and powerplant control systems; use of analog computer in the laboratoryfor simulation. Lectures and laboratory.

481. Airplane Design. Prerequisite: Aero. Eng. 314 and 441. I and II. (4).Power-required and power-available characteristics of aircraft on a comparative basis,

calculation of preliminary performance, stability, and control characteristics. Designprocedure, including layouts and preliminary structural design. Subsonic and supersonic designs. Emphasis on design techniques and systems approach. Lectures andlaboratory.

482. Sounding Rocket and Payload Design. Prerequisite: Aero. Eng. 314 and 441. I andII. (4).

Design of the instrumentation, payload and propulsion units of a sounding rocket for

making atmospheric measurements up to satellite altitudes. Measuring techniques,instruments, housekeeping, telemetering, environmental tests, propulsion, staging, sta

bility, heating, trajectories and dispersion. Lectures and laboratory.

483. Aerospace System Design. Prerequisite: Aero. Eng. 314 and 441 and preceded or

accompanied by Aero. Eng. 430. I and II. (4).Aerospace system design, analysis and integration. Consideration of launch facilities,booster systems, spacecraft systems, communications, data processing and project management. Lectures and laboratory.

485. Aerospace Communication Systems. Prerequisite: Math. 450, Elec. Eng. 314. (3).Introduction to the design of space communications and tracking systems for the aero

space system designer. Basic principles in the design of space communications and

tracking systems, including modulation-demodulation techniques, frequency and timedivision multiplexing, methods of data storage, system gain considerations, powersources, antennas, propagation and tracking methods. Application to system problemsemphasized.

490. Directed Study. (To be arranged).Individual study of specialized aspects of aerospace engineering. Primarily for undergraduates.

510. Energy Theorems and Matrix Methods in Structural Mechanics I. Prerequisite:Aero. Eng. 414 or Eng. Mech. 411 or 412. (3).

The principle of virtual work and the theorems of minimum potential and minimum

complementary energy. Variational calculus, the Rayleigh-Ritz method, Galerkin'smethod. Solution by finite differences. The matrix force and displacement methods.Applications to simple structures and structural elements such as beams, frames, andplates. Static and dynamic problems.

514(Eng. Mech 511). Foundations of Structural Mechanics I. Prerequisite: Aero. Eng.

414.(3).Elements of the analysis of structures. Includes plates of various shapes, loading, andboundary conditions, effects of in-plane loading; shells of revolution, cylindrical shells,

bending and membrane theories; plastic analysis of structures beams, frames, plates;plastic collapse mechanism. Applications of aerospace interest.

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515(Eng. Mech. 512). Foundations of Structural Mechanics n. Prerequisite: Aero. £ng514. (3).

Behavior of structures in a thermal environment, heat conduction, aerodynamic heat

ing of high speed vehicles, thermal stresses and deflections, thermal instabilities, discussion of material properties at elevated temperatures. Elements of the theory of linearviscoelasticity.

520. Gasdynamics I. Prerequisite: Aero. Eng. 420 or 425. (3).Gasdynamics at an intermediate level: Thermodynamics: the conservation equations:vorticity theorems; unsteady one-dimensional flow; the method of characteristics; sta

tionary and moving shock waves; two-dimensional steady flow including method ofsmall perturbations.

521. Experimental Gasdynamics. Prerequisite: Aero. Eng. 330 and 420. (3).Experimental methods in modern gasdynamics; physical principles and interpretation.Shop practice and theory of instrument design; mechanics, electronics, and optics.Measurement of velocity, pressure, density, temperature, composition, energy and mass

transfer in fluids and plasmas. Transducers and laboratory instrumentation in gas-

dynamic research.

522. Gasdynamics n. Prerequisite: Aero. Eng. 520. (3).Similarity laws for two- and three-dimensional high speed flows; two-dimensional in

compressible flows by confornial mapping; examples of flows with viscosity, includingsimple cases of compressible boundary layer flow; introduction to electromagnetictheory, and the equations for magnetohydrodynamic flow.

525. Aerodynamics of High-Speed Flight. Prerequisite: Aero. Eng. 420 or 425. (3).Treatment of problems in the aerodynamics of flight at supersonic and hypersonicvelocities; linearized theory of wings with arbitrary planforn: and bodies of revolution;wing-body interference; hypersonic aerodynamics, aerodynamic heating, real gas effects.

530. Propulsion III. Prerequisite: Aero. Eng. 430. (3).Continuation of Aero. Eng. 430. Further treatment of aircraft engine performance,including off-design operation, and study of selected problems in the field of propulsion.

532. Introduction to Gaskinetics and Real Gas Effects. Prerequisite: Aero. Eng. 420. (3).A study of some modern topics of flow problems not covered in the traditional gasdynamics of idea gases: concepts of gaskinetics. aerodynamics of free molecules, shocktransition layer, real gas effects, high temperature effects, multicomponent flows, etc.

535. Rocket Propulsion. Prerequisite: Aero. Eng. 430 or 435. (3).Analysis and performance of liquid and solid propellant rocket powerplants; propel-lant thermochemistry, heat, transfer, system considerations, advanced rocket propulsiontechniques.

540. Space Dynamics I. Prerequisite: Eng. Mech. 340. (4).Kinematics of motion, particle dynamics, orbital motion and calculation of orbitalparameters, Lagrange's equation. Rigid body dynamics including Eulcr's equations, the

Poinsot construction, spin stabilization, the rotation matrix. Vibrations of coupledsystems, orthogonality relationships, generalized co-ordinates and system parameters.

542. Astrodynamics I. Prerequisite: Aero. Eng. 441. I. (3).The study of motion of spacecraft in a vacuum and in the atmosphere with emphasison preliminary mission planning. Analysis of trajectories in suborbtial, orbital, lunar,and interplanetary operations. Aerodynamic forces and heating characteristics and

their effect on the selection of flight paths during entry into planetary atmospheres.

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543. Structural Dynamics. Prerequisite: Aero. Eng. 414 or 540. (3).Natural frequencies and mode shapes of elastic bodies. Nonconservative elastic sys

tems. Structural viscous damping. Influence coefficient methods for typical flight structures. Response of structures to random and shock loads. Lab demonstration.

544. Aeroelasticity. Prerequisite: Aero. Eng. 414 or 540. (3).An introduction to aeroelasticity. Vibration and flutter of elastic bodies exposed to

fluid flow. Static divergence and flutter of airplane wings. Flutter of flat plates andthin walled cylinders at supersonic speeds. Oscillations of structures due to vortex

shedding.

549(Eng. Mech. 549) (Mech. Eng. 549). Random Vibrations of Mechanical Systems.

Prerequisite: Eng. Mech. 340 or Eng. Mech. 343. II. (3).Random mechanical inputs: wind buffeting; earthquakes; surface irregularities.Engineering applications include response of a linear spring-mass system and an

elastic beam to single and multiple random loading. Failure theories. Necessary

concepts such as ensemble averages, correlation functions, stationary and ergodicrandom processes, power spectra, are developed heuristically.

590. Directed Study. (To be arranged).Individual study of specialized aspects of aerospace engineering. Primarily for graduates.

5%. Aurora and Airglow. Prerequisite: permission of instructor. II. (3).Morphology and physics of the aurora and airglow. Emission spectra in the auroraand their atomic and molecular origin; proton aurora; metastable excitation; calculation of emission profiles. Night- and day-glow; pre-dawn and post-twilight enhancements; mid-latitude red arc; excitation mechanisms.

610. Energy Theorems and Matrix Methods in Structural Mechanics II. Prerequisite:Aero. Eng. 310. (3).

Application of energy methods and matrix methods to shells, built-up shell-type structures, and problems in three-dimensional elasticity. Nonlinear problems in structuralmechanics that arise from large amplitude deformations. Static and dynamic problems.

620. Dynamics of Viscous Fluids. Prerequisite: Aero. Eng. 320. (3).Navier-Stokes equations; low Reynolds number flows; incompressible and compressiblelaminar boundary layers; boundary layer stability and transition to turbulence;

turbulent boundary layers, wakes, and jets.

621. Dynamics of Compressible Fluids. Prerequisite: Aero. Eng. 520. (3).Theory of characteristics; shock-wave phenomena; interaction problems; hodographtransformation; transonic flow.

622. Hypersonic Aerodynamics. Prerequisite: Aero. Eng. 520. (3).Inviscid flow past thin bodies at high Mach number; blunt-body methods; blastwavetheory; viscous interaction, nonequilibrium flows.

624. Linearized Aerodynamic Theory. Prerequisite: Aero. Eng. 520. (3).Application of conformal mapping in the study of thin airfoils; three dimensionalsubsonic and supersonic wing theory; forces acting on oscillating wings; slender-bodytheory; higher approximations.

625. Methods of Theoretical Aerodynamics. Prerequisite: Aero. Eng. 520. (3).Application of methods for solving partial differential equations which arise in aero

dynamics problems. Subsonic and supersonic wing theory, sound waves, viscous flows,

boundary-layer theory, shock waves. Emphasis on the use of fundamental solutionsand superposition in linear problems and asymptotic methods in nonlinear problems.

Similarity solutions, characteristics.

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627. Continuum Theory of Fluids. Prerequisite: Aero. Eng. 520. (3).Physical concepts underlying the flow of fluids acted upon by stresses arising fromviscosity and from electromagnetic and gravity fields. Invariant analysis of stress-strainrelations. Maxwell's equations, analysis of electromagnetic stresses and energy dissipation in moving media, the equations of motion and energy in a moving fluid, and some

solutions of the complete equations.

628. Statistical Theory of Fluids. Prerequisite: Aero. Eng. 532. (3).A study of the flows of neutral and charged particles from the .viewpoint of kinetictheory; Chapman-Enskog theory of transport phenomena, dynamics of rarefied gases,plasma kinetics without external magnetic field, plasma oscillations and Landaudamping, micro-instabilities, plasma interactions.

632. Gas Flows with Chemical Reactions. Prerequisite: Aero. Eng. 532, 620. (3).Thermodynamics of gas mixtures, chemical kinetics, conservation equations formulti-component reacting gas mixtures. Deflagration and detonation waves. Nozzleflows and boundary layers with reaction and diffusion.

640. Space Dynamics II. Prerequisite: Aero. Eng. 540. II. (2).Hamilton's equations, canonical transformations, and Hamilton-Jacobi theory. Applications to orbital problems. General perturbation theory. Introduction to specialrelativity.

642. Astrodynamics II. Prerequisite: Aero. Eng. 542. II. (3).Orbit determination. Systems of canonical equations. Perturbation theory with applications to the motion of an artificial satellite. Lunar and planetary theories.

650. Computational Methods for Flight Simulation. Prerequisite: Aero. Eng. 540, andC.I.C.E. 482 or Elect. Eng. 365. (2).

Equations of motion for aircraft and aerospace vehicles. Axis systems and axis transformations including body, stability, flight-path, navigational, and inertial axes. Eulerangles, direction cosines, and quaternions. Simulation of flat earth trajectories, low-eccentricity orbits, lunar and planetary trajectories. Use of conservation laws and constraint methods. Mechanization in six degrees of freedom using analog, hybrid, anddigital computers.

651. Computation of Aerospace Trajectories. Prerequisite: Aero. Eng. 640. (2).Error analysis of numerical integration methods. Comparison of Cowell's method,Enkc's method and variation-of-parameters in ternis of accuracy and convenience.FORTRAN programming of integration methods. Student programming and solutionof trajectory problems.

670. Guidance and Navigation of Aerospace Vehicles. Prerequisite: a course in feedback control. II. (3).

Principles of space vehicle, homing and ballistic missile guidance systems in two andthree dimensions. Explicit, linear perturbation, and velocity-to-be gained guidancemodes. Mechanization by inertial and other means, including strapped-down and stable-platform inertial systems. Celestial navigation procedures with deterministic and redundant measurements. Application of Kalman filtering to recursive navigation theory.

671. Guidance and Control Laboratory. Prerequisite: preceded or accompanied byAero. Eng. 670 and Aero. Eng. 674. (2).

Simulation of aircraft, missile, and space vehicle autopilot systems on analog andhybrid computer systems. Digital and analog solution of missile and space vehicleguidance problems.

674. Control of Aircraft, Missiles, and Space Vehicles. Prerequisite: C.I.C.E. 550. (2).Analysis and synthesis of autopilots for aircraft and cruise-type missiles. Design ofthrust-vector control systems including effects of elastic structures and fuel sloshing.Attitude control systems for space vehicles; mechanization using jet thrusters andinertia wheels; gravity gradient moments.

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675. Optimization of Space Trajectories. Prerequisite: permission of instructor. II. (3).Necessary and sufficient conditions for ordinary extremum and variational problems,with emphasis on the problem of Bolza. Applications of the calculus of variations to

optimal space trajectories. Problems with control and state variable inequality con

straints. Iterative computational methods for two-point boundary-value problems, including the gradient method, Newton's method, and quasilinearization.

676. Optimal Guidance. Prerequisite: Aero. Eng. 675 or C.I.C.E. 540. (3).Optimum guidance modes, including the path-adaptive mode, iterative guidance mode,and neighboring optimum guidance. The effect of normality and conjugate points inguidance analysis. Applications to space missions involving high thrust, low thrust,

impulsive thrust and re-entry. Necessary conditions for singular guidance problems.Future needs in guidance theory.

721. Turbulence. Prerequisite: Aero. Eng. 620. (3).Physical and mathematical description of turbulence in boundary layers, wakes, jets,and behind grids; turbulent fields; theories for turbulent mass, momentum, heat, andparticle diffusion.

726. Introduction to Plasma Dynamics. Prerequisite: permission of instructor. (3).Physical properties of a plasma; particle orbit theory; collective phenomena in a

plasma; kinetic equations for a plasma; instabilities; transport phenomena and derivation of the magneton ydrodynamic equations.

729. Special Topics in Gasdynamics. Prerequisite: permission of instructor. (To be

arranged).Advanced topics of current interest.

730. Energy Transfer in High Temperature Gas Flows. Prerequisite: Aero. Eng. 532

and 620. (3).Energy transfer processes as related to high temperature gas flows; unsteady heatconduction, convection in non-reactive and reactive flows, transport properties, ablation and gaseous radiation.


810. Seminar in Structures. (To be arranged.)





880. Seminar in Space Technology. Prerequisite: permission of instructor. (To be ar

ranged ).

882. Seminar in Guided Missiles. Prerequisite: permission of instructor. (To be ar

ranged ).Primarily for military officers.

895(Elec Eng. 895). Seminar in Space Research. Prerequisite: permission of instructor.

(To be arranged).Detailed analyses of objectives, procedures, and results of research being carried outat The University of Michigan. Topics will include the following: structure of the

upper atmosphere; measurement of temperature, pressure, density, composition, andwinds. The ionosphere; measurement of ion and electron density and temperature.Investigation of radio waves incident on the earth at frequencies absorbed by the

ionosphere by means of instrumented satellites. Interpretation of infrared data from

meteorological satellites. Research in attitude control of multistage sounding rockets.

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120 / BIOENGINEERING

900. Research. (To be arranged).Specialized individual or group problems of research or design nature supervised by

a member of the staff.

Bioengineering

Office: 207 West EngineeringSee Page 112 for statement on Course Equivalence.

434(Chem. Eng. 434) (Civ. Eng. 580) (Microb. 434). Microbiology for Engineers. Pre

requisite: Math. 316, Chem. 225, and senior standing. I. (3).Principles and techniques of microbiology with an introduction to their applicationin the several fields of engineering. Lectures and laboratory.

471(Elec. Eng. 471). Electrical Biophysics. Prerequisite: Elec. Eng. 311 or 314 or 215.

Electrical biophysics of muscle, nerve and synapse. Hodgkin-Huxley equation, electrical conduction in excitable tissue, phase plane analysis and modeling of neural ele

ments, semiconductor characteristics of biological membranes, biopotential mappingand biological noise.

516(Chem. Eng. 516). Dynamics of Biochemical Systems. Prerequisite: a course in

physical chemistry, a course in biology. (3).Colloidal phenomena in biological systems, mechanisms of transport through mem

branes, physical chemical properties of biological materials, kinetics of growth processes, enzyme catalysis, natural control mechanisms, engineering applications of biochemical phenomena.

525(Psych. 525) (Com. Comm. Sri. 550). Information Processing in Behavioral Systems.

Prerequisite: enrollment in Bioengineering Program or permission of instructor.I. (3).

Surveys four areas of experimental and mathematical psychology, such as sensory,

learning, skilled performance and thinking and reasoning with emphasis on the relations between empirical data and logical, mathematical, or computer simulation modelsof underlying processes.

534(Ind. Eng. 534). Biomechanics and Physiology of Work. Prerequisite: Ind. Eng. 333.

II. (3).Limitations of the human body in coping with stressful situations. Concepts to be included are: skeletal muscle physiology and mechanics, skeletal articulation and mechanics, circulatory and pulmonary system function and limitations, and nervous sys

tem control and limitations.

546(Mech. Eng. 546). Biomechanics L Prerequisite: Mech. Eng. 340 or Mech. Eng. 540.

1.(3).Statics, kinematics, and dynamics of body motions; study of body motion response to

various dynamic load inputs utilizing lumped parameter methods; properties of biological materials; tolerance of man to adverse environments including impact, vibration, weightlessness; appropriate physiological failure criteria.

571(Elec Eng. 571). Introduction to Neurophysiological Systems. Prerequisite: Elec.Eng. 350 or C.I.C.E. 450. I, II and IIIa. (3).

Application of systems theory to neurophysiology; a theoretical and experimental studyof the application of linear and nonlinear systems theory, state-space concepts, and

stability criteria to several neurophysiological systems; neuromuscular systems, pupillarycontrol, eye tracking, temperature regulation, and central nervous system function.

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advanced level course relative to his current status if the other prerequisites are

satisfied. If the difference in standing level is greater than one academic year, it

is usually not wise to elect an advanced level course without first consulting the

department or the instructor offering the course.



200. General Aeronautics and Astronautics. Prerequisite: Physics 140. I and II. (2).Introduction to aerospace engineering. Elementary problems designed to orient tbe


current state of aerospace developments and the role of the engineer. Recitations and

demonstrations.

201. Conquest of Air and Space. II. (2).An introduction to the physical principles of flight within the atmosphere and in

space, to the major historical developments in the conquest of air and space, and to

the current state of aerospace developments and their role in national and worldaffairs. Not open to students enrolled in the College of Engineering.

20S(A.S. 403). Pilot Ground School. I and II. (1).Lecture/practicum, 3 hours a week for 9 weeks, by arrangement. Preflight, meteorology,Federal Aviation Regulations, flight computer, navigation, radio navigation. Open to

all University students with approval of instructor.

301. Laboratory L Prerequisite: preceded or accompanied by Elec.-Comp. Eng. 314.

(2).Comprehensive series of lectures and experiments designed to introduce the student to

basic principles of electronics, circuit analysis, transducers, modem laboratory instrumentation, experimental methods, and data analysis. Experiments involve simplemeasurement and instrumentation problems.

302. Laboratory n. Prerequisite: Aero. Eng. 301. (2).Continuation of the material in Aero. Eng. 301.

314(Eng. Mech. 314). Structural Mechanics I. Prerequisite: Eng. Mech. 211. II. (4).Review of plane states of stress and strain. Basic equations of plane elasticity and

selected problems; failure criteria and applications; energy principles of structuraltheory; thin -walled beam theory.

320. Aerodynamics I. Prerequisite: preceded or accompanied by Eng. Mech. 240 and

Math. 450. I and II. (4).Development of the fundamentals of aerodynamics which form the basis for the study

of modern aircraft. Calculation of the forces and moments acting on wings and bodiesin incompressible inviscid flow and comparison with experiment.

330. Propulsion I. Prerequisite: Mech. Eng. 335, Aero. Eng. 320 or Mech. Eng. 336. 1

and II. (3).Introduction to aerothermodynamics and applications to problems in flight propulsion.Discussion of the momentum theorem, one dimensional flow systems with heataddition, shock waves, diffusers, compressors, and turbines.

350. Aerospace Engineering Analysis. Prerequisite: Math. 216. (3).Formulation and solution of some of the elementary initial- and boundary-valueproblems relevant to aerospace engineering. Application of Fourier series, separation of

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variables, and vector analysis to problems of forced oscillations, wave motion, diffusion,

elasticity, and perfect-fluid theory.

390. Undergraduate Seminar. Prerequisite: Junior standing. I and II. (1).A series of seminars by noted outside speakers designed to acquaint undergraduateswith both current problems and state of the art of the aerospace industry. Will involvea short term project or paper pertinent to one of the seminar topics.

414(Eng. Mech. 414). Structural Mechanics II. Prerequisite: Aero. Eng. 314. I and II.(3 or 4).

Introduction to plate theory. Stability of structural elements; columns and beam

columns; plates in compression and shear; secondary instability of columns. Introduction to matrix methods of deformation analysis; structural dynamics. Lectures and

laboratory.

415. Principles of Structural Mechanics. Prerequisite: Eng. Mech. 211 or 319. I. (3).An accelerated coverage of the material in Aero. Eng. 314 and 414 designed primarilyfor graduate students. Not open to students who have elected Aero. Eng. 314 or 414.

420. Aerodynamics n. Prerequisite: Aero. Eng. 320, and preceded or accompanied byAero. Eng. 330. I and II. (3 or 4).

Continuation of Aerodynamics I. Viscous and compressible fluid theory applied to the

calculation of the forces and moments on wings and bodies and comparison with

experiment. Loads on an airplane. Lectures and laboratory.

421. Topics in Fluid Mechanics. Prerequisite: Aero. Eng. 420. (3).Topics include free surface phenomena, flow separation, flow in tubes, lubrication, flowin a gravity-free environment. The objective of the course is to extend the student's

background in gas dynamics to the fundamental aspects of other fluid phenomena ofimportance in aerospace and other industrial applications. Lectures and demonstrations.

423. Aero-Acoustics. Prerequisite: Aero. Eng. 420 or a course in compressible flow. (3).Principles of generation, perception, and abatement of sound generated by fluid flows.

Elementary acoustics; acoustical response of the human ear. Theory and results ofmeasurement of sound generated by explosions, sonic booms, jets, boundary layers andflow excited structural vibrations. Qualitative assessment of techniques and effec

tiveness of noise abatement procedures.

424. Laminar and Turbulent Transport Processes. Prerequisite: Aero. Eng. 420 or an

introductory course in viscous flow. (3).Turbulent transport processes are important in fluid flows in nature and technology.Elementary statistical concepts; nature of turbulent flow in boundary layers, wakes,

jets, and plumes. Turbulent transport of mass, momentum, and heat in above flows

and comparison with laminar transport processes. Eddy viscosity and diffusivity of heat

and mass. Qualitative description of turbulent buffeting.


430. Propulsion n. Prerequisite: Aero. Eng. 330. I and II. (3 or 4).Performance and analysis of flight-propulsion systems including the reciprocatingengine-propeller, turboprop, ramjet, pulsejet, and rocket. Lectures and laboratory.

432. Advanced Propulsion Concepts. Prerequisite: Aero. Eng. 430 or an introductorycourse in jet propulsion. I and II. (3).

Advanced turbojet analysis including compressor and turbine performance, equilibii-

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455. Priawrpiei of PropaHuaB. P'rrrciuu.'r Kffli £ag. WJ- '?'-An accelerated coverage of the sstatenal in Aero. Ear J?0 and 4W descord pnmaru'iiii tj*f.u*vt students. Not open to tt orients who hare elected .Vtol Eng. 5M or 4M.

4M. Aircraft Pmuwaiiiw Laboratory Prerequisite: preceded by Aero. Emg. 330. <2i,

Vrie» of experiments dettsmed to illustrate the general principles of propuisaao and to

introduce the student to certain experimental techniques in the stncfc of actual

propulsive devices, using full-tcale or reduced saodels of Che po.hr jet. rarbojet. ramk-tand rocket aaoiors.

44$. Vehicle Sincisu Performance. Prerequisite: potior stsstdmg. II. /Jkfc'/le of performance in svstems analvsis; mathematical modeling; identification ofconstraints, performance parameters, and performance indices. The aircraft performance problem: Sight envelope, aerodynamic approximations, available propulsionsysiems; take-off, landing, climb, and range performance. Modern perfonnance optimi7*1 urn techniques. Applications to automobile, high-speed train, and space vehicle

performance analysis.

+41. Mechanic! of flight. Prerequisite: Aero. Eng. 320. 1 and II. (4).Mechanics of a particle applied to the analysis of vehicle flight paths. Orbits, ballistictrajectories, and trajectories of vehicles in the atmosphere. Rigid body mechanicsapplied to translational and rotational vehicle motion. Analysis of vehicle motion and

static and dynamic stability using perturbation theory. Control characteristics.

+47. Flight Tevting. Prerequisite: Aero. Eng. 441. (2).Theory and practice of obtaining flight-test data on perfonnance and stability of

airplanes from actual flight tests. No laboratory fee will be charged, but a depositcovering student insurance and operating expense of the airplane will be required.

.449. Principles of Vertical Take-off and Landing Aircraft. Prerequisite: Aero. Eng. 420

Lifting rotor and propellor analysis in vertical and forward flight; ducted fan analysis:helicopter performance analysis; transitional flight problems of VTOL aircraft; stability and control problems of helicopters and VTOL aircraft.

.460. Aerophysics I. Prerequisite: Physics 240, Math. 216. L (3).Lagrangian and Hamillonian concepts applied to aerospace engineering problems:principles of optics related to aeronautical measurements; electromagnetic forces in

moving media; radiation processes in gases.

44il. Afrophysics II. Prerequisite: Aero. Eng. 460 or Aero. Eng. 464. II. (3).Quantum mechanical concepts in gas dynamics; principles of atomic and molecularspectra, and diagnostics of high energy flows; spectroscopy and application to ionuedgases in the laboratory, upper atmosphere, and interplanetary space; radiative transfer.

rh

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464(Meteor.-Ocean. 464). Upper Atmospheric Science. Prerequisite: senior or graduatestanding in a physical science or engineering. I. (3).

An introduction to physical processes in the upper atmosphere; density, temperature,composition, and winds; atmospheric radiation transfer processes and heat balance;

the ionosphere; rocket and satellite measurement techniques.

465. Principles of Atmospheric Measurement. Prerequisite: preceded or accompaniedby Aero. Eng. 464 or Elec.-Comp. Eng. 495. II. (3).

Physical observations related to the upper atmosphere: scanning, filtering, detecting,sensitivity. Apparatus design: ideal and practical. Experiment design: modeling, errors-

statistical and experimental. Data retrieval and presentation. Details of illustrative

experiments using remote and in situ sensors on aerospace vehicles.

466. Atmospheric Measurements Laboratory. Prerequisite: preceded or accompanied byAero. Eng. 465. (2).

Measurement projects in gas dynamics and in radiation phenomena in all parts of the

electromagnetic spectrum of significance to atmospheric and space research. Emphasisis placed on ground based techniques which yield useful aeronomical data.

467. Aerodynamic Topics in Atmospheric Environment. Prerequisite: Aero. Eng. 420 or

Eng. Mech. 422. (2).Physical and chemical nature of the atmosphere. Gravitational and coriolis force effects

on air flow. Aerodynamic elements in the weather forecasting problem. Hydrodynamicvortex and atmospheric tornado. Free convection and hot plumes. Suspension and

dispersion of aerosols in the atmosphere. Free air turbulence.

471. Automatic Control Systems. Prerequisite: Aero. Eng. 441. I and II. (3 or 4).Transient and steady-state analysis of linear control systems; transfer functions,

stability analysis, and synthesis methods; airplane transfer functions and synthesis of

autopilot and powerplant control systems; use of analog computer in the laboratory forsimulation. Lectures and laboratory.


calculation of preliminary performance, stability, and control characteristics. Designprocedure, including layouts and preliminary structural design. Subsonic and supersonic designs. Emphasis on design techniques and systems approach. Lectures andlaboratory.

482. Design of Rocket- and Air-Borne Remote Sensing Probes. Prerequisite: Aero. Eng.314 and 441. I and II. (4).

Design techniques and projects for geophysical, environmental, and earth resources

surveys. Aircraft, sounding rocket, and balloon instruments and payloads as well as

vehicle characteristics and performance are considered. Student projects bring togetherin a unified concept components for sensing (remote and in situ), telemetering,tracking, performance, safety, and data processing.

483. Aerospace System Design. Prerequisite: Aero. Eng. 314 and 441 and preceded oraccompanied by Aero. Eng. 430. I and II. (4).

Aerospace system design, analysis and integration. Consideration of launch facilities,booster systems, spacecraft systems, communications, data processing and projectmanagement. Lectures and laboratory.

485. Aerospace Communication Systems. Prerequisite: Math. 450, Elec.-Comp. Eng.314. (3).

Introduction to the design of space communications and tracking systems for the

aerospace system designer. Basic principles in the design of space communications and

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f.j^r^r.u ,^ ar.alyut of sr.'iacri.r'"i. Ir.e '. ^ >-i p"jies erf various shapes, load me. a&iiMrS.an vitS..-fx.y r?.rxzy of in-pUne V-ni.~T s&eiis of rrsohajoo. ofcadrical sbefls.

)rrS..z.% iryi mrrirxirj- u**k-*y; pLaaic ana.yas of structures beams, frames, plates:

y -rt" aAUrxr- mffUnimi. AppiicatK-x-.s of aerospace interest.

S I V tj^, Kccfc. 51?). Foundation* of Stnsciural Meihanes SI P-rreewue: Aero. f-*Cill I3,

fVr.avior ,A structuret in a tbrrraal environment, heal conduction.

hr»ttn% of hijrii speed vehicles, thermal stresses and deflections, thermalrti«u»K* of material properties at elevaied temperatures. Elements oflircar viscoelasticity.

*2#. '-wItrumi,, L peerequisite: Aero. Eng. 420 or 425. (J>fxa«Unamics at an intermediate level: Thermodynamics; the conservation equations:vortwity theorems; unweady one-dimensional flow, the method of chars•Jaitonary and moving shock waves; two-dimensional steady flow including method ot•fin II perturbations.

521. Experimental Gasdynamics. Prerequisite: Aero. Eng. 330 and 420. (3).Experimental methods in modem gasdvnamics; physical principles and interpretation.Shop practice and theory of instrument design: mechanics, electronics, and optics.Measurement of velocity, pressure, density, temperature, composition, energy and masstransfer in fluids and plasmas. Transducers and laboratory instrumentation in gasdynarnic research.

Vtt. Catdvnamio II. Prerequisite: Aern. Eng. 520. (3).Similarity laws for two- and three-dimensional high speed flows; two-dimensionalincompressible flows by conformal mapping; examples of flows with viscosity , includingsimple ratet of compressible boundary layer flow; introduction to electromagnetictheory, and the equations for magnetohydrodynamic flow.

52S. Aerodynamic of High-Speed Flight. Prerequisite: Aero. Eng. 420 or 425. (3).Treatment of problems in the aerodynamics of flight at supersonic and hypersonicvelocities; linearized theory of wings with arbitrary planform and bodies of revolution;wing-body interference; hypersonic aerodynamics, aerodynamic heating, real gas effects.

M0. Propulsion III. Prerequisite: Aero. Eng. 430. (3.)Continuation of Aero. Eng. 430. further treatment of aircraft engine performance,including off design operation, and study of selected problems in the field of propul•ion.

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AEROSPACE ENGINEERlNG / 127

532. Introduction to Gaskinetics and Real Gas Effects. Prerequisite: Aero. Eng. 420.

(3).A study of some modern topics of flow problems not covered in the traditionalgasdynamics of ideal gases: concepts of gaskinetics, aerodynamics of free molecules,

shock transition layer, real gas effects, high temperature effects, multicomponent flows,

etc.

535. Rocket Propulsion. Prerequisite: Aero. Eng. 430 or 435. (3).Analysis and performance of liquid and solid propellant rocket powerplants; propel-lant thermochemistry, heat, transfer, system considerations, advanced rocket propulsiontechniques.

540. Space Dynamics I. Prerequisite: Eng. Mech. 240. (4).Kinematics of motion, particle dynamics, orbital motion and calculation of orbitalparameters, Lagrange's equation. Rigid body dynamics including Euler's equations, the

Poinsot construction, spin stabilization, the rotation matrix. Vibrations of coupledsystems, orthogonality relationships, generalized co-ordinates and system parameters.

542. Astrodynamics L Prerequisite: Aero. Eng. 441. I. (3).The study of motion of spacecraft in a vacuum and in the atmosphere with emphasison preliminary mission planning. Analysis of trajectories in suborbital, orbital, lunar,and interplanetary operations. Aerodynamic forces and heating characteristics and theireffect on the selection of flight paths during entry into planetary atmospheres.

543. Structural Dynamics. Prerequisite: Aero. Eng. 414 or 540. (3).Natural frequencies and mode shapes of elastic bodies. Nonconservativc clastic systems.Structural viscous damping. Influence coefficient methods for typical flight structures.Response of structures to random and shock loads. Lab demonstration.

544. Aeroelasticity. Prerequisite: Aero. Eng. 414 or 540. (3).An introduction to aeroelasticity. Vibration and flutter of elastic bodies exposed to

fluid flow. Static divergence and flutter of airplane wings. Flutter of flat plates and thinwalled cylinders at supersonic speeds. Oscillations of structures due to vortex shedding.

549(Eng. Mech. 549) (Mech. Eng. 549). Random Vibrations of Mechanical Systems.

Prerequisite: Eng. Mech. 240 or Eng. Mech. 343. II. (3).Random mechanical inputs: wind buffeting; earthquakes; surface irregularities. Engineering applications include response of a linear spring-mass system and an elasticbeam to single and multiple random loading. Failure theories. Necessary concepts such

as ensemble averages, correlation functions, stationary and ergodic random processes,power spectra, are developed heuristically.


596. Aurora and Airglow. Prerequisite: permission of instructor. II. (3).Morphology and physics of the aurora and airglow. Emission spectra in the aurora and

their atomic and molecular origin; proton aurora; metastable excitation; calculation ofemission profiles. Night- and day-glow; pre-dawn and post-twilight enhancements;

mid-latitude red arc; excitation mechanisms.


Application of energy methods and matrix methods to shells, built-up shell-typestructures, and problems in three-dimensional elasticity. Nonlinear problems in struc

tural mechanics that arise from large amplitude deformations. Static and dynamicproblems.

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620. Dynamics of Viscous Fluids. Prerequisite: Aero. Eng. 520. (J).Navier-Stokes equations; low Reynolds number flows; incompressible and compressiblelaminar boundary layers; boundary layer stability and transition to turbulence;



622. Hypersonic Aerodynamics. Prerequisite: Aero. Eng. 520. (3).Inviscid flow past thin bodies at high Mach number; blunt-body methods; blastwave

theory; viscous interaction nonequilibrium flows.

624. Linearized Aerodynamic Theory. Prerequisite: Aero. Eng. 520. (3).Application of conformal mapping in the study of thin airfoils; three dimensional

subsonic and supersonic wing theory; forces acting on oscillating wings; slender-bodytheory; higher approximations.

625. Methods of Theoretical Aerodynamics. Prerequisite: Aero. Eng. 520. (3).Application of methods for solving partial differential equations which arise in

aerodynamics problems. Subsonic and supersonic wing theory, sound waves, viscous

flows, boundary-layer theory, shock waves. Emphasis on the use of fundamentalsolutions and superposition in linear problems and asymptotic methods in nonlinearproblems. Similarity solutions, characteristics.

627. Continuum Theory of Fluids. Prerequisite: Aero. Eng. 520. (3).Physical concepts underlying the flow of fluids acted upon by stresses arising from

viscosity and from electromagnetic and gravity fields. Invariant analysis of stress-strain

relations. Maxwell's equations, analysis of electromagnetic stresses and energy dissipation in moving media, the equations of motion and energy in a moving fluid, and somesolutions of the complete equations.

628. Statistical Theory of Fluids. Prerequisite: Aero. Eng. 532. (3).A study of the flows of neutral and charged particles from the viewpoint of kinetictheory; Chapman-Enskog theory of transport phenomena, dynamics of rarefied gases,

plasma kinetics without external magnetic field, plasma oscillations and Landaudamping, micro-instabilities, plasma interactions.

632. Gas Flows with Chemical Reactions. Prerequisite: Aero. Eng. 532, 620. (3).Thermodynamics of gas mixtures, chemical kinetics, conservation equations for multi-component reacting gas mixtures. Deflagration and detonation waves. Nozzle flows and

boundary layers with reaction and diffusion.

640. Space Dynamics n. Prerequisite: Aero. Eng. 540. (1).Hamilton's equations, canonical transformations, and Hamilton-Jacobi theory. Applications to orbital problems. General perturbation theory. Introduction to special relativity.


650. Computational Methods of Flight Simulation. Prerequisite: Aero. Eng. 540, andC.1.CE. 482 or Elec.-Comp. Eng. 365. (2).

Equations of motion for aircraft and aerospace vehicles. Axis systems and axistransformations including body, stability, flight-path, navigational, and inertial axes,

Euler angles, direction cosines, and quaternions. Simulation of flat earth trajectories,

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low-eccentricity orbits, lunar and planetary trajectories. Use of conservation laws and

constraint methods. Mechanization of six degrees of freedom using analog, hybrid, and

digital computers.

651. Computation of Aerospace Trajectories. Prerequisite: Aero. Eng. 640. (2).Error analysis of numerical integration methods. Comparison of Cowell's method,

Enke's method and variation-of-parameters in terms of accuracy and convenience.

FORTRAN programming of integration methods. Student programming and solution

of trajectory problems.

670. Guidance and Navigation of Aerospace Vehicles. Prerequisite: a course in feed

back control. II. (3).Principles of space vehicle, homing and ballistic missile guidance systems in two and

three dimensions. Explicit, linear perturbation, and velocity- to-be gained guidancemodes. Mechanization by inertial and other means, including strapped-down and

stable-platform inertial systems. Celestial navigation procedures with deterministic and

redundant measurements. Application of Kalman filtering to recursive navigation

theory.

671. Guidance and Control Laboratory. Prerequisite: preceded or accompanied by-

Aero. Eng. 670 and Aero. Eng. 674. (2).Simulation of aircraft, missile, and space vehicle autopilot systems on analog and

hybrid computer systems. Digital and analog solution of missile and space vehicle

guidance problems.

674. Control of Aircraft, Missiles, and Space Vehicles. Prerequisite: C.I.C.E. 550. (2).Analysis and synthesis of autopilots for aircraft and cruise-type missiles. Design of

thrust-vector control systems including effects of elastic structures and fuel sloshing.Attitude control systems for space vehicles; mechanization using jet thrusters andinertia wheels; gravity gradient moments.

675. Optimization of Space Trajectories. Prerequisite: permission of instructor. II. (3).

Necessary and sufficient conditions for ordinary extremum and variational problems,with emphasis on the problem of Bolza. Applications of the calculus of variations to

optimal space trajectories. Problems with control and state variable inequality constraints. Iterative computational methods for two-point boundary-value problems,including the gradient method, Newton's method, and quasilinearization.

676. Optimal Guidance. Prerequisite: Aero. Eng. 675 or C.l.C.E. 540. (3).Optimum guidance modes, including the path-adaptive mode, iterative guidance mode,and neighboring optimum guidance. The effect of normality and conjugate points inguidance analysis. Applications to space missions involving high thrust, low thrust,


721. Turbulence. Prerequisite: Aero. Eng. 620. (3).Physical and mathematical description of turbulence in boundary layers, wakes, jets,anil behind grids, turbulent fields; theories for turbulent mass, momentum, heat, andparticle diffusion.

726. Introduction to Plasma Dynamics. Prerequisite: permission of instructor. (3).

Physical properties of a plasma; particle orbit theory; collective phenomena in a

plasma; kinetic equations for a plasma; instabilities; transport phenomena and derivation of the magnetohydrodynamic equations.



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130 / BIOENGINEERING

730. Energy Transfer in High Temperature Gas Flows. Prerequisite: Aero. Eng. 5)?

and 620. (3).Energy transfer processes as related to high temperature gas flows; unsteady heat

conduction, convection in non-reactive and reactive flows, transport properties, ablationand gaseous radiation.







880. Seminar in Space Technology. Prerequisite: permission of instructor. (To be

arranged).


arranged ).

Primarily for military officers.

895(Elec-Comp. Eng. 895). Seminar in Space Research. Prerequisite: permission ofinstructor. (To be arranged).

Detailed analyses of objectives, procedures, and results of research being carried out at

The University of Michigan. Topics will include the following: structure of the upperatmosphere; measurement of temperature, pressure, density, composition, and winds.The ionosphere; measurement of ion and electron density and temperature. Investigation of radio waves incident on the earth at frequencies absorbed by the ionosphere bymeans of instrumented satellites. Interpretation of infrared data from meteorologicalsatellites. Research in attitude control of multistage sounding rockets.

900. Research. (To be arranged).Specialized individual or group problems of research or design nature supervised by a

member of the staff.

Bioengineering

Office: 207 West EngineeringSee Page 121 for statement on Course Equivalence.

434(Chem. Eng. 434) (Civ. Eng. 580) (Microb. 434). Microbiology for Engineers.Prerequisite: Chem. 225. I and II. (3).

Principles and techniques of microbiology with an introduction to their application in

the several fields of engineering. Lectures and laboratory.

464(Elec-Comp. Eng. 464). Computer Techniques for Bioelcctrical Signal Analysis.Prerequisite: Eng. 102 and Elec.-Comp. Eng. 430. II. (3).

Analysis of techniques used in computer processing of bioelectrical signals. Analog to

digital conversion. Digital filtering and averaging techniques. Signal recognition in thetime and frequency domain. Time series analysis of pulse trains.

47I(Elec-Comp. Eng. 471). Electrical Biophysics. Prerequisite: Elec.-Comp. Eng. 311 or314 or 215. (3).

Electrical biophysics of muscle, nerve and synapse. Hodgkin-Huxley equation, electricalconduction in excitable tissue, phase plane analysis and modeling of neural elements.

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Unless a phrase such as "Junior Standing", "Senior Standing" or "GraduateStanding" is part of the list of prerequisites for a course, a student may elect an






Department Office: 302 Aerospace Engineering BuildingSee Page 123 for statement on Course Equivalence.

100. Introduction to Flight. (2).An introduction to the physical principles of flight within the atmosphere and in

space, to the major historical developments in the conquest of air and space, and to

the current state of aerospace developments and their role in national and worldaffairs.

200. General Aeronautics and Astronautics. Prerequisite: Physics 140. I and II. (2).Introduction to aerospace engineering. Elementary problems designed to orient the


current state of aerospace developments and the role of the engineer. Recitations and

demonstrations.

203(A.S. 403). Pilot Ground School. I and II. (1).

Lecture/ practicum, 3 hours a week for 9 weeks, by arrangement. Preflight, meteorology.Federal Aviation Regulations, flight computer, navigation, radio navigation. Open to

all University students with approval of instructor.

301. Laboratory L Prerequisite: preceded or accompanied by Elec.-Comp. Eng. 314.

(2)-Comprehensive series of lectures and experiments designed to introduce the student to

basic principles of electronics, circuit analysis, transducers, modern laboratory instrumentation, experimental methods, and data analysis. Experiments involve simplemeasurement and instrumentation problems.

302. Laboratory II. Prerequisite: Aero. Eng. 301. (2).Continuation of the material in Aero. Eng. 301.

314(Eng. Mech. 314). Structural Mechanics I. Prerequisite: Eng. Mech. 211. (4).Review of plane states of stress and strain. Basic equations of plane elasticity and

selected problems; failure criteria and applications; energy principles of structural

theory; thin-walled beam theory.

320. Compressible Flow and Propulsion I. Prerequisite: Mech. Eng. 335; preceded or

accompanied by Aero. Eng. 350. I and II. (4).First part of an aerodynamics sequence designed to study the fundamental principlesand their applications; physical nature of fluids, conservation laws: nozzles and dif-fusers; shock waves; combustion; applications to jet propulsion and other problems.

330. Aerodynamics II. Prerequisite: Aero. Eng. 320. I and II. (3).Second part of an aerodynamics sequence designed to study the fundamental principlesand their applications; viscous effects in laminar and turbulent flows; boundary layertheory; concepts of instability and transition to turbulent flow; flows under the influence of gravitational and electromagnetic forces.

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350(Math. 310). Aerospace Engineering Analysis. Prerequisite: Math. 216. (3).Formulation and solution of some of the elementary initial- and boundary-valueproblems relevant to aerospace engineering. Application of Fourier series, separation ofvariables, and vector analysis to problems of forced oscillations, wave motion, diffusion,


380. Undergraduate Seminar. Prerequisite: Junior standing. II. (/).A series of seminars by noted outside speakers designed to acquaint undergraduateswith both current problems and state of the art of the aerospace industry. Will involvea short term project or paper pertinent to one of the seminar topics.

390. Directed Study. (To be arranged).Individual study of specialized aspects of aerospace engineering.

414(Eng. Mech. 414). Structural Mechanics II. Prerequisite: Aero. Eng. 314. (3).Introduction to plate theory. Stability of structural elements; columns and beam

columns; plates in compression and shear; secondary instability of columns. Introduction to matrix methods of deformation analysis; structural dynamics.

415. Principles of Structural Mechanics. Prerequisite: Eng. Mech. 211 or 319. 1. (3).An accelerated coverage of the material in Aero. Eng. 314 and 414 designed primarilyfor graduate students. Not open to students who have elected Aero. Eng. 314 or 414.

420. Aerodynamics III. Prerequisite: Aero. Eng. 320. I and II. (3).Third part of an aerodynamics sequence designed to study the fundamental principlesand their applications; inviscid flows and fundamentals of field theory; generationof airfoil lift; thin airfoil theory; induced drag and finite wings; wave kinematics; twodimensional compressible flow.

421. Topics in Fluid Mechanics. Prerequisite: Aero. Eng. 420. (3).Topics include free surface phenomena, flow separation, flow in tubes, lubrication, flowin a gravity-free environment. The objective of the course is to extend the student'sbackground in gas dynamics to the fundamental aspects of other fluid phenomena ofimportance in aerospace and other industrial applications. Lectures and demonstrations.

423. Aero-Acoustics. Prerequisite: Aero. Eng. 420 or a course in compressible flow. (3).Principles of generation, perception, and abatement of sound generated by fluid flows.

Elementary acoustics; acoustical response of the human ear. Theory and results ofmeasurement of sound generated by explosions, sonic booms, jets, boundary layers andflow excited structural vibrations. Qualitative assessment of techniques and effectiveness of noise abatement procedures.

424. Laminar and Turbulent Transport Processes. Prerequisite: Aero. Eng. 420 or anintroductory course in viscous flow. (3).

Turbulent transport processes are important in fluid flows in nature and technology.Elementary statistical concepts; nature of turbulent flow in boundary layers, wakes,

jets, and plumes. Turbulent transport of mass, momentum, and heat in above flowsand comparison with laminar transport processes. Eddy viscosity and diffusivity of heatand mass. Qualitative description of turbulent buffeting.


430. Fundamentals of Propulsion. Prerequisite: Aero. Eng. 320. I and II. (3).Performance and analysis of flight-propulsion systems including the reciprocatingengine-propeller, turboprop, ramjet, pulsejet, and rocket.

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126 / AEROSPACE ENGlSEERING

432. Advanced Propulsion Concepts. Prerequisite: Aero. Eng. 430 or an introductorycourse in jet propulsion. (3).

Advanced turbojet analysis including compressor and turbine performance, equilibrium running of turbojet engine, dynamics of turbojet engine considered as a quasrstaticsystem, afterburners, fan jets; design of solid propellent rocket engines; underwater

propulsion, including underwater ramjet. Use of the computer in design and per

formance analysis will be emphasized.

433. Combustion Processes. Prerequisite: Aero. Eng. 330. (3).Study of combustion processes with appropriate consideration of the fluid mechanics(aero-thermo-chemistry); emphasis placed on the physical understanding, applications,performance, pollution aspects, experimental techniques, and commonality between jet

propulsion combustors, internal combustion engines, and stationary power plants:includes equilibrium constants, chemical kinetics, flames, explosions, liquid drops,particulate formation.


439. Aircraft Propulsion Laboratory. Prerequisite: preceded by Aero. Eng. 330. (2).Series of experiments designed to illustrate the general principles of propulsion and to

introduce the student to certain experimental techniques in the study of actualpropulsive devices, using full-scale or reduced models of the pulsejet, turbojet, ramjet,and rocket motors.

440. Vehicle Systems Performance. Prerequisite: junior standing. (3).Role of performance in systems analysis; mathematical modeling; identification ofconstraints, performance parameters, and performance indices. The aircraft performance problem: flight envelope, aerodynamic approximations, available propulsionsystems; take-off, landing, climb, and range performance. Modem performance optimization techniques. Applications to automobile, high-speed train, and space vehicleperformance analysis.

441. Mechanics of Flight. Prerequisite: Aero. Eng. 320. I and II. (4).Mechanics of a particle applied to the analysis of vehicle flight paths. Orbits, ballistictrajectories, and trajectories of vehicles in the atmosphere. Rigid body mechanicsapplied to translational and rotational vehicle motion. Analysis of vehicle motion andstatic and dynamic stability using perturbation theory. Control characteristics.

447. Flight Testing. Prerequisite: Aero. Eng. 441. (2).Theory and practice of obtaining flight-test data on performance and stability ofairplanes from actual flight tests. No laboratory fee will be charged, but a depositcovering student insurance and operating expense of the airplane will be required.

449. Principles of Vertical Take-off and Landing Aircraft. Prerequisite: Aero. Eng. 420.

(3).Lifting rotor and propellor analysis in vertical and forward flight; ducted fan analysis;helicopter performance analysis; transitional flight problems of VTOL aircraft; stability and control problems of helicopters and VTOL aircraft.

452(C.I.CE. 412) (Elec.-Comp. Eng. 412). Engineering Probability and Statistic*.Prerequisite: Math. 216. I and II. (3).

Basic concepts of probability theory: random variables, probability distributions,averages, moments, characteristic functions, independence. Binomial. Poisson. andGaussian distributions. Introduction to statistical inference and its applications inengineering; statistics of measurements; confidence intervals; least square fitting ofdata.

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453(C.I.C.E. 460) (Elec.-Comp. Eng. 460). Digital Computers and Computation. I and

II. (4).An introduction to the important hardware and software concepts of digital com

putation. The laboratory which is part of the course involves programming and

logical design. Students who have taken Elec.-Comp. Eng. 365, Elec.-Comp. Eng. 366

and Com. Comm. Sci. 473 or some equivalent sequence should not elect this course.

454(C.I.CE. 482) (Elec.-Comp. Eng. 482). Applications of the Analog Computer.

Prerequisite: Math. 216, or Math. 404. I, II, and IIIa. (3).Basic theory and principles of operation of analog computers. Applications to one

and two degree-of-freedom vibration problems, automatic control systems, heat-flow,

eigenvalue problems, nonlinear vibration problems, and other selected topics. Lecture

and laboratory. Laboratory consists of the solution of problems on the analog com

puter.

455(CI.CE. 465) (Elec.-Comp. Eng. 465). Computer Graphics Applications. Prerequisite:

Elec.-Comp. Eng. 270. II. (3).Application of several software packages and display devices for engineering problemsolving and production of computer animated films. Use of Computek, Tektronix, andPDP graphics terminals for electrical circuit design, interactive data smoothing,production of engineering graphs, etc. POLYGRAPHICS and BEFLIX computeranimation packages and their use in MTS. Production of 2 or 3 films using graphicsterminals.

460. Aerophysics I. Prerequisite: Physics 240, Math. 216. 1. (3).Lagrangian and Hamiltonian concepts applied to aerospace engineering problems;principles of optics related to aeronautical measurements; electromagnetic forces in


461. Aerophysics II. Prerequisite: Aero. Eng. 460 or Aero. Eng. 464. II. (3).

Quantum mechanical concepts in gas dynamics; principles of atomic and molecular

spectra, and diagnostics of high energy flows; spectroscopy and application to ionized

gases in the laboratory, upper atmosphere, and interplanetary space; radiative transfer.

464(AAO. Sci. 464). Upper Atmospheric Science. Prerequisite: Senior or graduatestanding in a physical science or engineering. I. (3).



465. Principles of Atmospheric Measurement. Prerequisite: preceded or accompaniedby Aero. Eng. 464 or Elec.-Comp. Eng. 495. II. (3).

Physical observations related to the upper atmosphere: scanning, filtering, detecting,sensitivity. Apparatus design: ideal and practical. Experiment design: modeling, errors-statistical and experimental. Data retrieval and presentation. Details of illustrativeexperiments using remote and in situ sensors on aerospace vehicles.


Measurement projects in gas kinetics and in radiation phenomena in several parts of the

electromagnetic spectrum of significance to atmospheric and space research. Emphasisis placed on ground based techniques which yield useful atmospheric data.

467. Aerodynamic Topics in Atmospheric Environment Prerequisite: Aero. Eng. 420 orEng. Mech. 422. (2).

Physical and chemical nature of the atmosphere. Gravitational and coriolis force effects

on air flow. Aerodynamic elements in the weather forecasting problem. Hydrodynamic

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vortex and atmospheric tornado. Free convection and hot plumes. Suspension and

dispersion of aerosols in the atmosphere. Free air turbulence.

471. Automatic Control Systems. Prerequisite: Aero. Eng. 441. I and II. (3).Transient and steady-state analysis of linear control systems; transfer functions,

stability analysis, and synthesis methods; airplane transfer functions and synthesis of

autopilot and powerplant control systems; use of analog computer in the laboratory for

simulation.

472(C.I.C.E. 450) (Elec.-Comp. Eng. 450). Fundamentals of Control Systems.

Prerequisite: preceded or accompanied by Elec.-Comp. Eng. 300 or Math. 44S.

I, II, and IIIa. (3).The concept and advantages of feedback control. Transient and steady state analysis:block diagram; signal flow graphs; transfer functions; state variables; stability; sensi

tivity. Design philosophies and criteria. Use of Nyquist, Bode and root-locus methodsfor analysis and synthesis. Not open to students with credit for Mech. Eng. 461 orAero. Eng. 471.

473(CI.C.E. 451) (Elec-Comp. Eng. 451). Feedback Control Laboratory I. Prerequisitepreceded or accompanied by C.I.C.E. 450. I and II. (2).

Introduction to control system simulation and design. Experiments with physicalsystems. IIlustration of basic control principles. Design examples and the use of com

puter design aids. Not open to students with credit for Mech. Eng. 461, Aero. Eng.471, or equivalent.

475(C.I.C.E. 453) (Elec-Comp. Eng. 453). Feedback Control Laboratory II. Prerequisite:C.I.C.E. 451. II. (1).

Project experiments in automatic control to be selected in conjunction with facultvadviser.


calculation of preliminary performance, stability, and control characteristics. Designprocedure, including layouts and preliminary structural design. Subsonic and supersonic designs. Emphasis on design techniques and systems approach. Lectures and

laboratory.

482. Design of Rocket- and Air-Borne Remote Sensing Probes. Prerequisite: Aero. Eng.314 and 441. I and II. (4).

Design techniques and projects for geophysical, environmental, and earth resourcessurveys. Aircraft, sounding rocket, and balloon instruments and payloads as well as

vehicle characteristics and performance are considered. Student projects bring togetherin a unified concept components for sensing (remote and in situ), telemeteringtracking, performance, safety, and data processing.

483. Aerospace System Design. Prerequisite: Aero. Eng. 314 and 441 and preceded oraccompanied by Aero. Eng. 430. I and II. (4).

Aerospace system design, analysis and integration. Consideration of launch facilities,booster systems, spacecraft systems, communications, data processing and projec:management. Lectures and laboratory.

485. Aerospace Communication Systems. Prerequisite: Math. 450, Elec.-Comp. Eng314. (3).

Introduction to the design of space communications and tracking systems for theaerospace system designer. Basic principles in the design of space communications andtracking systems, including modulation-demodulation techniques, frequency and timedivision multiplexing, methods of data storage, system gain considerations, power

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sources, antennas, propagation and tracking methods. Application to system problemsemphasized.

490. Directed Study. (To be arranged).Individual study of specialized aspects of aerospace engineering. Primarily for under

graduates.

510. Energy Theorems and Matrix Methods in Structural Mechanics I. Prerequisite:Aero. Eng. 414 or Eng. Mech. 411 or 510. (3).

The principle of virtual work and the theorems of minimum potential and minimum

complementary energy. Variational calculus, the Rayleigh-Ritz method, Galerkin'smethod. Solution by finite differences. The matrix force and displacement methods.

Applications to simple structures and structural elements such as beams, frames, and

plates. Static and dynamic problems.

514(Eng. Mech. 511). Foundations of Structural Mechanics I. Prerequisite: Aero. Eng.414. (3).

Elements of the analysis of structures. Includes plates of various shapes, loading, and

boundary conditions, effects of in-plane loading; shells of revolution, cylindrical shells,

bending and membrane theories; plastic analysis of structures beams, frames, plates;

plastic collapse mechanism. Applications of aerospace interest.

515(Eng. Mech. 512). Foundations of Structural Mechanics II. Prerequisite: Aero. Eng.514. (3).

Behavior of structures in a thermal environment, heat conduction, aerodynamicheating of high speed vehicles, thermal stresses and deflections, thermal instabilities,

discussion of material properties at elevated temperatures. Elements of the theory oflinear viscoelasticity.

520. Gasdynamics I. Prerequisite: Aero. Eng. 420 or 425. (3).Gasdynamics at an intermediate level: Thermodynamics; the conservation equations;vorticity theorems; unsteady one-dimensional flow; the method of characteristics;

stationary and moving shock waves; two-dimensional steady flow including method of. small perturbations.

521. Experimental Gasdynamics. Prerequisite: Aero. Eng. 330 and 420. (3).Experimental methods in modern gasdynamics; physical principles and interpretation.Shop practice and theory of instrument design: mechanics, electronics, and optics.Measurement of velocity, pressure, density, temperature, composition, energy and mass

f transfer in fluids and plasmas. Transducers and laboratory instrumentation in gasdy-namic research.

522. Gasdynamics II. Prerequisite: Aero. Eng. 520. (3).Similarity laws for two- and three-dimensional high speed flows; two-dimensionalincompressible flows by conformal mapping; examples of flows with viscosity, includingsimple cases of compressible boundary layer flow; introduction to electromagnetictheory, and the equations for magnetohydrodynamic flow.

530. Propulsion III. Prerequisite: Aero. Eng. 430. (3.)Continuation of Aero. Eng. 4S0. Further treatment of aircraft engine performance,including off-design operation, and study of selected problems in the field of propulsion.


(J).' A study of some modern topics of flow problems not covered in the traditionalgasdynamics of ideal gases: concepts of gaskinetics, aerodynamics of free molecules,

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IS0 / AEROSPACE ENGINEERING

shock transition layer, real gas effects, high temperature effects, multicomponent flowi

etc

535. Rocket Propulsion. Prerequisite: Aero. Eng. 430 or 435. (3).

Analysis and performance of liquid and solid propellant rocket powerplants; propel-

lant thermochemistry, heat transfer, system considerations, advanced rocket propulsion

techniques.

540. Space Dynamics L Prerequisite: Eng. Mech. 240. (4).Kinematics of motion, particle dynamics, orbital motion and calculation of orbital

parameters, Lagrange's equation. Rigid body dynamics including Euler's equations, the

Poinsot construction, spin stabilization, the rotation matrix. Vibrations of coupled

systems, orthogonality relationships, generalized co-ordinates and system parameters.

542. Astrodynamics I. Prerequisite: Aero. Eng. 441. I. (3).The study of motion of spacecraft in a vacuum and in the atmosphere with emphasis

on preliminary mission planning. Analysis of trajectories in suborbital, orbital, lunar,

and interplanetary operations. Aerodynamic forces and heating characteristics and their

effect on the selection of flight paths during entry into planetary atmospheres.

543. Structural Dynamics. Prerequisite: Aero. Eng. 414 or 540. (3).Natural frequencies and mode shapes of elastic bodies. Nonconservative elastic systems

Structural and viscous damping. Influence coefficient methods for typical flight struc

tures. Response of structures to random and shock loads. Lab demonstration.

544. Aeroelasticity. Prerequisite: Aero. Eng. 414 or 540. (3).An introduction to aeroelasticity. Vibration and flutter of elastic bodies exposed lo

fluid flow. Static divergence and flutter of airplane wings. Flutter of flat plates and thin

walled cylinders at supersonic speeds. Oscillations of structures due to vortex shedding.

549(Eng. Mech. 549) (Mech. Eng. 549). Random Vibrations of Mechanical Systems.Prerequisite: Eng. Mech. 240 or Eng. Mech. 343. II. (3).

Random mechanical inputs: wind buffeting; earthquakes; surface irregularities. Engineering applications include response of a linear spring-mass system and an elastic

beam to single and multiple random loading. Failure theories. Necessary concepts such

as ensemble averages, correlation functions, stationary and ergodic random processes,power spectra, are developed heuristically.


596. Aurora and Airglow. Prerequisite: permission of instructor. II. (3).Morphology and physics of the aurora and airglow. Emission spectra in the aurora andtheir atomic and molecular origin; proton aurora; metastable excitation; calculation of

emission profiles. Night- and day-glow; pre-dawn and post-twilight enhancements:mid-latitude red arc; excitation mechanisms.

610. Energy Theorems and Matrix Methods in Structural Mechanics II. Prerequisite-Aero. Eng. 510. (3).

Application of energy methods and matrix methods to shells, built-up shell-typestructures, and problems in three-dimensional elasticity. Nonlinear problems in structural mechanics that arise from large amplitude deformations. Static and dynamicproblems.

620. Dynamics of Viscous Fluids. Prerequisite: Aero. Eng. 520. (3).Navier-Stokes equations; low Reynolds number flows; incompressible and compressible

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laminar boundary layers; boundary layer stability and transition to turbulence;


621. Dynamics of Compressible Fluids. Prerequisite: Aero. Eng. 520. (3).

Theory of characteristics; shock-wave phenomena; interaction problems; hodographtransformation; transonic flow.

625. Methods of Theoretical Aerodynamics. Prerequisite: Aero. Eng. 520. (3).Application of methods for solving partial differential equations which arise in


flows, boundary-layer theory, shock waves. Emphasis on the use of fundamentalsolutions and superposition in linear problems and asymptotic methods in nonlinear

problems. Similarity solutions, characteristics.

627. Continuum Theory of Fluids. Prerequisite: Aero. Eng. i20. (3).Physical concepts underlying the flow of fluids acted upon by stresses arising from


relations. Maxwell's equations, analysis of electromagnetic stresses and energy dissipation in moving media, the equations of motion and energy in a moving fluid, and some




632. Gas Flows with Chemical Reactions. Prerequisite: Aero. Eng. 532, 620. (3).Thermodynamics of gas mixtures, chemical kinetics, conservation equations for multi-component reacting gas mixtures. Deflagration and detonation waves. Nozzle flows andboundary layers with reaction and diffusion.

640. Space Dynamics n. Prerequisite: Aero. Eng. 540. (3).Hamilton's equations, canonical transformations, and Hamilton-Jacobi theory. Applications to orbital problems. General perturbation theory. Introduction to special relativ

ity.

642. Astrodynamics II. Prerequisite: Aero. Eng. 542. II. (J).Orbit determination. Systems of canonical equations. Perturbation theory with applications to the motion of an artificial satellite. Lunar and planetary theories.

650. Computational Methods of Flight Simulation. Prerequisite: Aero. Eng. 540, andC.I.C.E. 482 or Elec. Comp. Eng. 365. (2).

Equations of motion for aircraft and aerospace vehicles. Axis systems and axistransformations including body, stability, flight-path, navigational, and inertial axes.

Euler angles, direction cosines, and quaternions. Simulation of flat earth trajectories,low-eccentricity orbits, lunar and planetary trajectories. Use of conservation laws and

constraint methods. Mechanization of six degrees of freedom using analog, hybrid, anddigital computers.

651. Computation of Aerospace Trajectories. Prerequisite: Aero. Eng. 640. (2).Error analysis of numerical integration methods. Comparison of Co well's method,

Enke's method and variation-of-parameters in terms of accuracy and convenience.FORTRAN programming of integration methods. Student programming and solutionof trajectory problems.

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670. Guidance and Navigation of Aerospace Vehicles. Prerequisite: a course in feedback control. II. (3).

Principles of space vehicle, homing and ballistic missile guidance systems in two and

three dimensions. Explicit, linear perturbation, and velocity-to-be gained guidancemodes. Mechanization by inertial and other means, including strapped-down and

stable-platform inertial systems. Celestial navigation procedures with deterministic and

redundant measurements. Application of Kalman filtering to recursive navigation

theory.

671. Guidance and Control Laboratory. Prerequisite: preceded or accompanied by

Aero. Eng. 670 and Aero. Eng. 674. (2).Simulation of aircraft, missile, and space vehicle autopilot systems on analog and

hybrid computer systems. Digital and analog solution of missile and space vehicle

guidance problems.

674. Control of Aircraft, Missiles, and Space Vehicles. Prerequisite: C.I.C.E. 550. (2).Analysis and synthesis of autopilots for aircraft and cruise-type missiles. Design of

thrust-vector control systems including effects of elastic structures and fuel sloshing.Attitude control systems for space vehicles; mechanization using jet thrusters and

inertia wheels: gravity gradient moments.

675. Optimization of Space Trajectories. Prerequisite: permission of instructor. II. (3y

Necessary and sufficient conditions for ordinary extremum and variational problems,with emphasis on the problem of Bolza. Applications of the calculus of variations to


straints. Iterative computational methods for two-point boundary-value problems,including the gradient method, Newton's method, and quasilinearization.

676. Optimal Guidance. Prerequisite: Aero. Eng. 675 or C.I.C.E. 540. (3).Optimum guidance modes, including the path-adaptive mode, iterative guidance mode,

and neighboring optimum guidance. The effect of normality and conjugate points in

guidance analysis. Applications to space missions involving high thrust, low thrust,

impulsive thrust and re-entry. Necessary conditions for singular guidance problem*.Future needs in guidance theory.

721. Turbulence. Prerequisite: Aero. Eng. 620. (3).Physical and mathematical description of turbulence in boundary layers, wakes, jets,and behind grids, turbulent fields; theories for turbulent mass, momentum, heat, andparticle diffusion.


plasma; kinetic equations for a plasma; instabilities; transport phenomena and derivation of the magnetohydrodynamic equations.




and 620. (3).Energy transfer processes as related to high temperature gas flows; unsteady healconduction, convection in non-reactive and reactive flows, transport properties, ablationand gaseous radiation.



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ATMOSPHERIC AND OCEANIC SCIENCE / 133






arranged).





The University of Michigan. Topics will include the following: structure of the upperatmosphere; measurement of temperature, pressure, density, composition, and winds.The ionosphere; measurement of ion and electron density and temperature. Investigation of radio waves incident on the earth at frequencies absorbed by the ionosphere by

means of instrumented satellites. Interpretation of infrared data from meteorologicalsatellites. Research in attitude control of multistage sounding rockets.

990. Dissertation/Pre-Candidate. I and II (2-8); IIIa and III6 (1-4).Election for dissertation work by doctoral student not yet admitted to status as a

Candidate.

995. Dissertation/Candidate. Prerequisite: Graduate School authorization for admissionas a doctoral candidate. I and II (8); IIIa and III6 (4).

Election for dissertation work by doctoral student who has been admitted to status as

a Candidate.

Atmospheric and Oceanic Science


202. Weather and Climate. I and II. (3). Not open to meteorology majors.Elementary description of the atmosphere: its motion systems, thermal characteristics,clouds and precipitation; weather map interpretation and analysis; climates of the

United States.

203. The Oceans. I and II. (3).Elementary descriptions of the oceans, their characteristics, and behavior; the sea as a

world resource and as an influence on civilizations.

300. The Atmosphere. Prerequisite: Math. 215, Chem. 113 or 114, Physics 140. II. (3).Technical survey of atmospheric science designed especially for students studyingscience and/or engineering. Atmospheric structure and circulation; composition andcontrolling processes; determinants of climate and climatic change; topics related to

human influences on the atmosphere and atmospheric influences on human activities.

304. Atmospheric and Oceanic Sciences I. Prerequisite: Physics 140. I and II. (3).The various aspects of meteorology and oceanography. Emphasis is placed on the

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l26 / AEROSPACE ENGISEERING

Unless a phrase such as "Junior Standing", "Senior Standing" or "GraduateStanding" is part of the list of prerequisites for a course, a student may elect an






Department Office: 302 Aerospace Engineering BuildingSec Page l25 for statement on Course Equivalence.

I00. Introduction to Flight. (2).An introduction to the physical principles of flight within the atmosphere and inspace, to the major historical developments in the conquest of air and space, and to

the current state of aerospace developments and their role in national and worldaffairs.

200. General Aeronautics and Astronautics. Prerequisite: Physics I40. I and II. (2).Introduction to aerospace engineering. Elementary problems designed to orient thestudent in the program of aerospace engineering, together with a discussion of the

current state of aerospace developments and the role of the engineer. Recitations anddemonstrations.

203(A.S. 403) (N.S. 303). Pilot Ground School. Prerequisite: permission of instructor.I and II. (2).

Lecture/practicum, 3 hours a week for l6 weeks. Aerodynamics for aviators, meteorology, air traffic control, Federal Aviation Regulations, flight computers, navigation,radio navigation, flight physiology, and accident prevention. Open to all Universitystudents.

300. Elements of Space Science and Technology. Prerequisite: Math. 2l6; Physics 240.

I and II. (3).Scientific and technological aspects of current space flights, mission goals, the spaceenvironment, vehicle characteristics, performance and flight paths. Mission support:communications, power, computers, etc. Open to all University students.

30l. Laboratory I. Prerequisite: preceded or accompanied by Elec.-Comp. Eng. 3I4.

(2).Comprehensive series of lectures and experiments designed to introduce the student tobasic principles of electronics, circuit analysis, transducers, modern laboratory instrumentation, experimental methods, and data analysis. Experiments involve simplemeasurement and instrumentation problems.

302. Laboratory II. Prerequisite: Aero. Eng. 30l. (2).Continuation of the material in Aero. Eng. 30l.

3l4(AppL Mech. 3I4). Structural Mechanics I. Prerequisite: Appl. Mech. 2ll. (4).Review of plane states of stress and strain. Basic equations of plane elasticity andselected problems; failure criteria and applications; energy principles of structuraltheory; thin-walled beam theory.

320. Compressible Flow and Propulsion I. Prerequisite: Mech. Eng. 33}. I and II. (4).First part of an aerodynamics sequence designed to study the fundamental principlesand their applications; physical nature of fluids, conservation laws; nozzles and diffuse! s; shock waves; combustion; applications to jet propulsion and other problems.

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AEROSPACE ENGINEERING / l27

330. Aerodynamics II. Prerequisite: Aero. Eng. 320 or introductory course in fluidmechanics. I and II. (3).

Second part of an aerodynamics sequence designed to study the fundamental principlesand their applications; viscous effects in laminar and turbulent flows; boundary layertheory; concepts of instability and transition to turbulent flow; flows under the influence of gravitational and electromagnetic forces.

340. Mechanics of Flight. Prerequisite: Appl. Mech. 240. II. (4).Mechanics of a particle applied to the analysis of vehicle flight paths. Rigid bodymechanics applied to translational and rotational vehicle motion. Analysis of vehiclemotion and static and dynamic stability using perturbation theory. Introduction to

feedback control and autopilot design; the root-locus method.

350(Math. 3l0). Aerospace Engineering Analysis. Prerequisite: Math. 2t6. (3).Formulation and solution of some of the elementary initial- and boundary-valueproblems relevant to aerospace engineering. Application of Fourier series, separation ofvariables, and vector analysis to problems of forced oscillations, wave motion, diffusion,


380. Undergraduate Seminar. Prerequisite: Junior standing. II. (t).A series of seminars by noted outside speakers designed to acquaint undergraduateswith both current problems and state of the art of the aerospace industry. Will involvea short term project or paper pertinent to one of the seminar topics.


4l4. (Appl. Mech. 4l4). Structural Mechanics II. Prerequisite: Aero. Eng. 3l4. (3).Introduction to plate theory. Stability of structural elements; columns and beamcolumns; plates in compression and shear; secondary instability of columns. Introduction to matrix methods of deformation analysis; structural dynamics.

4l5. Principles of Structural Mechanics. Prerequisite: Appl. Mech. 2tt or 3t9. I. (3).An accelerated coverage of the material in Aero. Eng. 3l4 and 4l4 designed primarilyfor graduate students. Not open to students who have elected Aero. Eng. 3l4 or 4l4.

420. Aerodynamics III. Prerequisite: Aero. Eng. 320, and Aero. Eng. 350 or Math. 450.

I and II. (3).Third part of an aerodynamics sequence designed to study the fundamental principlesand their applications; inviscid flows and fundamentals of Held theory; generationof airfoil lift; thin airfoil theory; induced drag and finite wings; wave kinematics: two

dimensional compressible flow.

42I. Topics in Fluid Mechanics. Prerequisite: Aero. Eng. 330. (3).Topics include free surface phenomena, flow separation, flow in tubes, lubrication, flow

in a gravity-free environment. The objective of the course is to extend the student's

background in gas dynamics to the fundamental aspects of other fluid phenomena of

importance in aerospace and other industrial applications. Lectures and demonstrations.

423. Aero-Acoustics. Prerequisite: Aero. Eng. 320 or a course in compressible flow. (3).

Principles of generation, perception, and abatement of sound generated by fluid flows.

Elementary acoustics; acoustical response of the human ear. Theory and results ofmeasurement of sound generated by explosions, sonic booms, jets, boundary layers and

flow excited structural vibrations. Qualitative assessment of techniques and effec

tiveness of noise abatement procedures.

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l28 / AEROSPACE ENGINEERING

424. Laminar and Turbulent Transport Processes. Prerequisite: Aero. Eng. 330 or an

introductory course in viscous flow. (3).Turbulent transport processes are important in fluid flows in nature and technology.Elementary statistical concepts; nature of turbulent flow in boundary layers, wakes,

jets, and plumes. Turbulent transport of mass, momentum, and heat in above flows

and comparison with laminar transport processes. Eddy viscosity and diffusivity of heat

and mass. Qualitative description of turbulent buffeting.

425. Principles of Aerodynamics. Prerequisite: Appl. Mech. 324. (3).An accelerated coverage of the material in Aero. Eng. 320 and 420 designed primarilyfor graduate students. Not open to students who have elected Aero. Eng. 320 or 420.

430. Fundamentals of Propulsion. Prerequisite: Aero. Eng. 320. (3).Performance and analysis of flight-propulsion systems including the reciprocatingengine-propeller, turbojet, turboprop, ramjet, and rocket.


Advanced turbojet analysis including compressor and turbine performance, equilibrium running of turbojet engine, dynamics of turbojet engine considered as a quasistaticsystem, afterburners, fan jets; design of solid propellent rocket engines; underwaterpropulsion, including underwater ramjet. Use of the computer in design and performance analysis will be emphasized.

433. Combustion Processes. Prerequisite: Aero. Eng. 320. (3).Study of combustion processes with appropriate consideration of the fluid mechanics

(aero-thermo chemistry); emphasis placed on the physical understanding, applications,performance, pollution aspects, experimental techniques, and commonality between jetpropulsion combustors, internal combustion engines, and stationary power plants;includes equilibrium constants, chemical kinetics, flames, explosions, liquid drops,particulate formation.


439. Aircraft Propulsion Laboratory. Prerequisite: Aero. Eng. 320. (2).Scries of experiments designed to illustrate the general principles of propulsion and tointroduce the student to certain experimental techniques in the study of actualpropulsive devices, using full-scale or reduced models of the pulsejet, turbojet, ramjet,and rocket motors.

440. 'Vehicle Systems Performance. Prerequisite: junior standing. (3).Role of performance in systems analysis; mathematical modeling; identification ofconstraints, performance parameters, and performance indices. The aircraft performance problem: flight envelope, aerodynamic approximations, available propulsionsystems; take-off, landing, climb, and range performance. Modem performance optimization techniques. Applications to automobile, high-speed train, and space vehicleperformance analysis.

447. Flight Testing. Prerequisite: Aero. Eng. 44t. (2).Theory and practice of obtaining flight-test data on performance and stability ofairplanes from actual flight tests. No laboratory fee will be charged, but a depositcovering student insurance and operating expense of the airplane will be required.

449. Principles of Vertical Take-off and Landing Aircraft. Prerequisite: Aero. Eng. 420.

(3)-Lifting rotor and propellor analysis in vertical and forward flight; ducted fan analysis;

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AEROSPACE ENGINEERING / l29

helicopter performance analysis; transitional flight problems of VTOL aircraft; stability and control problems of helicopters and VTOL aircraft.

452(CI.CE. 4I2) (Elec.-Comp. Eng. 4I2). Engineering Probability and Statistics.

Prerequisite: Math. 2l6. I and II. (3).Basic concepts of probability theory: random variables, probability distributions,

averages, moments, characteristic functions, independence. Binomial, Poisson, and

Gaussian distributions. Introduction to statistical inference and its applications inengineering; statistics of measurements; confidence intervals; least square fitting ofdata. CJ.C.E. students may not receive graduate credit for both CJ.C.E. 4l2 andC.I.C.E. 5l2.

454(CLCE. 482) (Elec.-Comp. Eng. 482). Analog Computation. Prerequisite: Math.2l6. I and D. (3).

Basic theory of analog computers. Analog devices: operational amplifiers, multipliers,function generators. Analog simulation of linear and nonlinear dynamic systems, in

cluding ordinary and partial differential equations. Lecture and laboratory.

455(CLCE. 465) (Elec-Comp. Eng. 465). Computer Graphics Applications. Prerequisite:Elec.-Comp. Eng. 270, I.&O.E. 473, Comp. & Comm. Sci. 473 or C.I.C£. 46l. (3).

Application of several software packages and display devices for engineering problemsolving and production of computer animated films. Use of Gomputek, Tektronix, and

PDP graphics terminals for electrical circuit design, interactive data smoothing,production of engineering graphs, etc. POLYGRAPHICS and BEFLIX computeranimation packages and their use in MTS. Production of 2 or 3 films using graphicsterminals.

460. Aerophysics L Prerequisite: Physics 240, Math. 2l6. I. (3).LagTangian and Hamiltonian concepts applied to aerospace engineering problems:principles of optics related to aeronautical measurements; electromagnetic forces in


46I. Aerophysics II. Prerequisite: Aero. Eng. 460 or Aero. Eng. 464. II. (3).

Quantum mechanical concepts in gas dynamics; principles of atomic and molecularspectra, and diagnostics of high energy flows; spectroscopy and application to ionizedgases in the laboratory, upper atmosphere, and interplanetary space; radiative transfer.

464(AAO. Sci. 464). Upper Atmospheric Science. Prerequisite: Senior or graduatestanding in a physical science or engineering. I. (3).



465(AJcO. Sci. 465). Atmospheric Measurements and Data Analysis. Prerequisite:Senior or graduate standing in a physical science or engineering. II. (3).

Introduction to operational and experimental measurements of atmospheric parameters. Instrumentation for "in-situ" measurements at the surface and from aerospacevehicles. Remote sensing using electromagnetic radiation and acoustical waves withboth passive and active systems. Analysis of data, error theory, the use of least

squares methods and empirical orthogonal functions, the information content of

experimental data.


Measurement projects in gas kinetics and in radiation phenomena in several parts of the

electromagnetic spectrum of significance to atmospheric and space research. Emphasisis placed on ground based techniques which yield useful atmospheric data.

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13O / AEROSPACE ENGINEERING

467. Aerodynamic Topics in Atmospheric Environment. Prerequisite: Aero Eng. 330 orAppl. Mech. 422. (2).

Physical and chemical nature of the atmosphere. Gravitational and coriolis force effectson air flow. Aerodynamic elements in the weather forecasting problem. Hydrodynamicvortex and atmospheric tornado. Free convection and hot plumes. Suspension anddispersion of aerosols in the atmosphere. Free air turbulence.

471. Automatic Control Systems. Prerequisite: Math. 216. I. (3).Transient and steady-state analysis of linear control systems; transfer function andstate-space description of control systems; stability analysis and synthesis methods;application to the design of autopilots and other modern control systems; introductionto nonlinear control systems and phase plane analysis.

472(CI.C.E. 450) (Elec.-Comp. Eng. 450). Fundamentals of Control Systems: Prerequisite:Elec.-Comp. Eng. 300 or Math. 448, and senior standing. I and II. (3).

Concept and importance of control systems. Control system descriptions: state variableand transfer function representations. System performance and design criteria: stability,sensitivity, time response. Concept of feedback. Time response of linear control systems.Use of Hurwitz, root-locus, Nyquist, and Bode methods for analysis and synthesis oflinear control systems. Not open to students with credit for Mech. Eng. 461 or Aero.Eng. 471.

473(CI.C.E. 451) (Elec.-Comp. Eng. 451). Control Systems Laboratory. Prerequisite:CJ.CE. 450 or Aero. Eng. 471. I and II. (2).

Introduction to control system simulation and design. Experiments with physicalsystems. IIlustration of basic control principles. Design examples and the use of com

puter design aids.

481. Airplane Design. Prerequisite: senior standing. (4).Power-required anil power-available characteristics of aircraft on a comparative basis,calculation of preliminary performance, stability, and control characteristics. Designprocedure, including layouts and preliminary structural design. Subsonic and supersonic designs. Emphasis on design techniques and systems approach. Lectures andlaboratory.

482. Design of Rocket- and Air-Borne Remote Sensing Probes. Prerequisite: seniorstanding. (4).

Design techniques and projects for geophysical, environmental, and earth resourcessurveys. Aircraft, sounding rocket, and balloon instruments and payloads as well asvehicle characteristics and performance are considered. Student projects bring togetherin a unified concept components for sensing (remote and in situ), telemetering,tracking, performance, safety, and data processing.

483. Aerospace System Design. Prerequisite: senior standing. (4).Aerospace system design, analysis and integration. Consideration of launch facilities,booster systems, spacecraft systems, communications, data processing and projectmanagement. Lectures and laboratory.

485. Aerospace Communication Systems. Prerequisite: Math. 450 or Aero. Eng. 350,

Elec.-Comp. Eng. 314. (3).Introduction to the design of space communications and tracking systems for theaerospace system designer. Basic principles in the design of space communications andtracking systems, including modulation-demodulation techniques, frequency and timedivision multiplexing, methods of data storage, system gain considerations, powersources, antennas, propagation and tracking methods. Application to system problemsemphasized.

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AEROSPACE ESC.INEERING / 131


510(Mech. Eng. 557). Energy Theorems and Matrix Methods in Structural MechanicsL Prerequisite: Aero. Eng. 414 or Mech. Eng. 362. I. (3).

The principle of virtual work and theorems of minimum potential and minimumcomplementary energy. Development of finite element method. Application to lineelements, beams, plane-stress, plane strain and plate bending. Static and dynamicproblems. Computer-oriented approach with several computer problems assigned.

5l4(Appl. Mech. 511). Foundations of Structural Mechanics I. Prerequisite: Aero. Eng.414. (3).

Elements of the analysis of structures. Includes plates of various shapes, loading, and


bending and membrane theories; plastic analysis of structures beams, frames, plates;


515(Appl. Mech. 512). Foundations of Structural Mechanics II. Prerequisite: Aero. Eng.514. (3).

Behavior of structures in a thermal environment, heat conduction, aerodynamicheating of high speed vehicles, thermal stresses and deflections, thermal instabilities,

discussion of material properties at elevated temperatures. Elements of the theory oflinear viscoelaslicity.

520. Gasdynamics I. Prerequisite: Aero. Eng. 420 or 425. (3).Gasdynamics at an intermediate level: Thermodynamics; the conservation equations;Tonicity theorems; unsteady one-dimensional flow; the method of characteristics;

stationary and moving shock waves; two-dimensional steady flow including method ofsmall perturbations.

521. Experimental Gasdynamics. Prerequisite: Aero. Eng. 330 and 420. (3).Experimental methods in modem gasdynamics; physical principles and interpretation.Shop practice and theory of instrument design: mechanics, electronics, and optics.

Measurement of velocity, pressure, density, temperature, composition, energy and mass

transfer in fluids and plasmas. Transducers and laboratory instrumentation in gasdy-

namic research.

522. Gasdynamics II. Prerequisite: Aero. Eng. 520.(3).Similarity laws for two- and three-dimensional high speed flows; two-dimensional

incompressible flows by conformal mapping; examples of flows with viscosity, including

simple cases of compressible boundary layer flow; introduction to electromagnetic

theory, and the equations for magnetohydrodynamic flow.

530. Propulsion III. Prerequisite: Aero. Eng. 430. (3.)Continuation of Aero. Eng. 430. Further treatment of aircraft engine performance,

including off-design operation, and study of selected problems in the field of propul

sion.


A study of some modern topics of flow problems not covered in the traditional

^dynamics of ideal gases: concepts of gaskinetics. aerodynamics of free molecules,

diock transition layer, real gas effects, high temperature effects, multicomponent flows,

etc

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535. Rocket Propulsion. Prerequisite: Aero. Eng. 430 or 435. (3).

Analysis and performance of liquid and solid propellant rocket powerplants; propel-lant thermochemistry, heat transfer, system considerations, advanced rocket propulsiontechniques.

540. Space Dynamics I. Prerequisite: Appl. Mech. 240. (4).Kinematics of motion, particle dynamics, orbital motion and calculation of orbital

parameters, Lagrange's equation. Rigid body dynamics including Euler's equations, thePoinsot construction, spin stabilization, the rotation matrix. Vibrations of coupledsystems, orthogonality relationships, generalized co-ordinates and system parameters.

542. Astrodynamics I. Prerequisite: Aero. Eng. 441. I. (3).The study of motion of spacecraft in a vacuum and in the atmosphere with emphasison preliminary mission planning. Analysis of trajectories in suborbital, orbital, lunar,and interplanetary operations. Aerodynamic forces and heating characteristics and theireffect on the selection of flight paths during entry into planetary atmospheres.

543. Structural Dynamics. Prerequisite: Aero. Eng. 414 or 540. (3).Natural frequencies and mode shapes of elastic bodies. Nonconservative elastic systems.Structural and viscous damping. Influence coefficient methods for typical flight structures. Response of structures to random and shock loads. Lab demonstration.

544. Aeroelasticity. Prerequisite: Aero. Eng. 414 or 540. (3).An introduction to aeroelasticity. Vibration and flutter of elastic bodies exposed tofluid flow. Static divergence and flutter of airplane wings. Flutter of flat plates and thinwalled cylinders at supersonic speeds. Oscillations of structures due to vortex shedding.

549.(Appl. Mech. 549) (Mech. Eng. 549). Random Vibrations of Mechanical Systems.Prerequisite: Appl. Mech. 204 or Appl. Mech. 343. II. (3).

Random mechanical inputs: wind buffeting; earthquakes; surface irregularities. Engineering applications include response of a linear spring-mass system and an elasticbeam to single and multiple random loading. Failure theories. Necessary concepts suchas ensemble averages, correlation functions, stationary and ergodic random processes,power spectra, are developed heuristically.

570. Guidance and Navigation of Aerospace Vehicles. Prerequisite: a course in feedback control. I. (3).

Principles of space vehicle, homing and ballistic missiles guidance systems in two andthree dimensions. Explicit, linear perturbation, and velocity-to-be gained guidancemodes. Mechanization by incrtial and other means, including strapped-down and stable-platform inertial systems. Celestial navigation procedures with deterministic andredundant measurements. Application of Kalman filtering to recursive navigationtheory.

574. Control of Aircraft, Missiles, and Space Vehicles. Prerequisite: preceded or ac

companied by C.I.C.E. 550. II. (2).Analysis and synthesis of autopilots for aircraft and cruise-type missiles. Design ofthrust-vector control systems including effects of elastic structures and fuel sloshing.Attitude control systems for space vehicles; mechanization using jet thrusters andinertia wheels; gravity gradient moments.

575. Optimization of Space Trajectories. Prerequisite: permission of instructor. II. (3).Necessary and sufficient conditions for ordinary extremum and variational problems,with emphasis on the problem of Bolza. Applications of the calculus of variations to


straints. Iterative computational methods for two-point boundary-value problems,including the gradient method, Newton's method, and quasilinearization.

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590. Directed Study. (To be arranged).Individual study of specialized aspects of aerospace engineering. Primarily for gradu-

596. Aurora and Airflow. Prerequisite: permission of instructor. II. (3).Morphology and physics of the aurora and airglow. Emission spectra in the aurora andtheir atomic and molecular origin; proton aurora; metastable excitation; calculation ofemission profiles. Night- and day-glow; pre-dawn and post-twilight enhancements;

mid-latitude red arc; excitation mechanisms.


Application of energy methods and matrix methods to shells, built-up shell-typestructures, and problems in three-dimensional elasticity. Nonlinear problems in structural mechanics that arise from large amplitude deformations. Static and dynamicproblems.

620. Dynamics of Viscous Fluids. Prerequisite: Aero. Eng. 520. (3).Xav ier-Stokes equations; low Reynolds number flows; incompressible and compressiblelaminar boundary layers; boundary layer stability and transition to turbulence;



625. Methods of Theoretical Aerodynamics. Prerequisite: Aero. Eng. 520. (3 ).

Application of methods for solving partial differential equations which arise in


flows, boundary-layer theory, shock waves. Emphasis on the use of fundamentalsolutions and superposition in linear problems and asymptotic methods in nonlinearproblems. Similarity solutions, characteristics.

627. Continuum Theory of Fluids. Prerequisite: Aero. Eng. >20.(3).Physical concepts underlying the flow of fluids acted upon by stresses arising from


relations. Maxwell's equations, analysis of electromagnetic stresses and energy dissipa

tion in moving media, the equations of motion and energy in a moving fluid, and some




632. Gas Flows with Chemical Reactions. Prerequisite: Aero. Eng. 532, 620. (3).Thermodynamics of gas mixtures, chemical kinetics, conservation equations for multi-

component reacting gas mixtures. Deflagration and detonation waves. Nozzle flows and


HO. Space Dynamics II. Prerequisite: Aero. Eng. 540. (3).

Himilton's equations, canonical transformations, and Hamilton-Jacobi theory. Applica

tions to orbital problems. General perturbation theory. Introduction to special relativ

ity.

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650. Computational Methods of Flight Simulation. Prerequisite: Aero. Eng. 540, andC.I.C.E. 482 or Elec.Comp. Eng. 365. (2).

Equations of motion for aircraft and aerospace vehicles. Axis systems and axistransformations including body, stability, flight-path, navigational, and inertial axes.Euler angles, direction cosines, and quaternions. Simulation of flat earth trajectories,low-eccentricity orbits, lunar and planetary trajectories. Use of conservation laws andconstraint methods. Mechanization of six degrees of freedom using analog, hybrid, anddigital computers.

651. Computation of Aerospace Trajectories. Prerequisite: Aero. Eng. 640. (2).Error analysis of numerical integration methods. Comparison of Cowell's method,

Enke's method and variation-of-parametcrs in terms of accuracy and convenience.FORTRAN programming of integration methods. Student programming and solutionof trajectory problems.

671. Guidance and Control Laboratory. Prerequisite: preceded or accompanied byAero. Eng. 670 and Aero. Eng. 674. (2).

Simulation of aircraft, missile, and space vehicle autopilot systems on analog andhybrid computer systems. Digital and analog solution of missile and space vehicleguidance problems.

676. Optimal Guidance. Prerequisite: Aero. Eng. 675 or C.I.C.E. 540. (3).Optimum guidance modes, including the path-adaptive mode, iterative guidance mode,and neighboring optimum guidance. The effect of normality and conjugate points inguidance analysis. Applications to space missions involving high thrust, low thrust,


721. Turbulence. Prerequisite: Aero. Eng. 620. (3).Physical and mathematical description of turbulence in boundary layers, wakes, jets,and behind grids, turbulent fields; theories for turbulent mass, momentum, heat, and

particle diffusion.


plasma; kinetic equations for a plasma; instabilities; transport phenomena and deriva

tion of the magnetohydrodynamic equations.




and 620. (3).Energy transfer processes as related to high temperature gas flows; unsteady heat

conduction, convection in non-reactive and reactive flows, transport properties, ablationand gaseous radiation.




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APPLIED MECHANICS AND ENGINEERING SCIENCE / l35





arranged).





The University of Michigan. Topics will include the following: structure of the upperatmosphere; measurement of temperature, pressure, density, composition, and winds.The ionosphere; measurement of ion and electron density and temperature. Investigation of radio waves incident on the earth at frequencies absorbed by the ionosphere by

means of instrumented satellites. Interpretation of infrared data from meteorologicalsatellites. Research in attitude control of multistage sounding rockets.

990. Dissertation/Pre-Candidate. I and II (2-8); IIia and III6 (t-4).Election for dissertation work by doctoral student not yet admitted to status as a

Candidate.

995. Dissertation/Candidate. Prerequisite: Graduate School authorization for admissionas a doctoral candidate. I and II (8); 11ia and III6 (4).

Election for dissertation work by docioral student who has been admitted to status as

a Candidate.

Applied Mechanics and Engineering Science

Department office: 20l West EngineeringSee Page l25 for statement on Course Equivalence.

2ll. Introduction to Solid Mechanics. Prerequisite: Physics l40, Math. It6. I. II,IIIa and III6. (4). Open to juniors and seniors with permission of instructor.

Principles of statics including equilibrium and static equivalence. Determination of

moment and force resultants in slender members. Introduction to mechanics of

deformable bodies; concepts of stress and strain, classification of material behavior,

stress-strain relations and generalized Hooke's law. Application to engineering problems

involving members under axial load, torsion of circular rods and tubes, bending and

shear stresses in beams, combined stresses, deflection of beams. Three lectures and two

hours of recitation-demonstration.

2l8. Vector Mechanics of a Particle and a System of Particles. Prerequisite: Physicst40 and Math. tt6. I. (3).

Review of scalars. matrices, vectors. Cartesian tensors. Transformation, rotation, angu

lar velocity. Idealization and concept of a model. Newtonian mechanics. Dynamics of a

particle. Momentum and energy levels. Trajectories, propulsion, impact, harmonicoscillator, orbits. Relative motion and geophysical examples. Systems. Statics: equilibrium, vector systems, virtual work, stability.

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100. Introduction to Flight. (2).An introduction to the physical principles of flight within the atmosphere and in space, tothe major historical developments in the conquest of air and space, and to the current state

of aerospace developments and their role in national and world affairs.

200. General Aeronautics and Astronautics. Prerequisite: Physics 140. I and II. (2).Introduction to aerospace engineering. Elementary problems designed to orient the studentin the program of aerospace engineering, together with a discussion of the current state ofaerospace developments and the role of the engineer. Recitations and demonstrations.

203/A.S. 403) (N.S. 303). Pilot Ground School. Prerequisite: permission of instructor. 1 and

11.(2)..Lecture/practicum, 3 hours a week for 16 weeks. Aerodynamics for aviators, meteorology,air traffic control, Federal Aviation Regulations, flight computers, navigation, radio navigation, flight physiology, and accident prevention. Open to a

ll University students.

300. Elements of Space Science and Technology. Prerequisite: Math. 216; Physics 240. (3).Scientific and technological aspects of current space flights, mission goals, the spaceenvironment, vehicle characteristics, performance, and flight paths. Mission support: communications, power, computers, etc. Open to all University students.

301. Laboratory I. Prerequisite: preceded or accompanied by Elec.-Comp. Eng. 314. (2).Comprehensive series of lectures and experiments designed to introduce the student tobasic principles of electronics, circuit analysis, transducers, modern laboratory instrumentation, experimental methods, and data analysis. Experiments involve simple measurementand instrumentation problems.


314(Appl. Mech. 314). Structural Mechanics I. Prerequisite: Appl. Mech. 211. (3).Review of plane states of stress and strain. Basic equations of plane elasticity and selectedproblems; failure criteria and applications; energy principles of structural theory; thin-walled beam theory.

320. Compressible Flow and Propulsion I. Prerequisite: Mech. Eng. 235. I and II. (3).First part of an aerodynamics sequence designed to study the fundamental principles andtheir applications; physical nature of fluids, conservation laws; nozzles and diffuse rs;shock waves; applications to jet propulsion and other problems.

330. Aerodynamics D. Prerequisite: Aero. Eng. 320 or introductory course in fluid mechanics. I and II. (3).

Second part of an aerodynamics sequence designed to study the fundamental principlesand their applications; viscous effects in laminar and turbulent flows; boundary layertheory; concepts of instability and transition to turbulent flow; flows under the influence ofgravitational and electromagnetic forces.

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AEROSPACE ENGINEERING I 127

340. Mechanics of Flight. Prerequisite: Appl. Mech. 240. II. (3).Mechanics of a particle applied to the analysis of vehicle flight paths. Rigid body mechan

ics applied to translational and rotational vehicle motion. Analysis of vehicle motion and

static and dynamic stability using perturbation theory.

350tMath. 350). Aerospace Engineering Analysis. Prerequisite: Math. 216. (3).Formulation and solution of some of the elementary initial- and boundary-value problemsrelevant to aerospace engineering. Application of Fourier series, separation of variables,

and vector analysis to problems of forced oscillations, wave motion, diffusion, elasticity,and perfect-fluid theory.

380. Undergraduate Seminar. Prerequisite: junior standing. II. (1).A series of seminars by noted outside speakers designed to acquaint undergraduates withboth current problems and state of the art of the aerospace industry. Will involve a short

term project or paper pertinent to one of the seminar topics.


41 1(Appl. Mech. 411) (Civ. Eng. 411) (Nav. Arch. 411). Finite Element Applications.Prerequisite: Eng. 102. Appl. Mech. 211. I. (3).

The course consists of user oriented application of existing finite element computerprograms for solving practical structural mechanics problems of frames, 2-D and 3-Dsolids, plates, shells, etc. Students will leam to prepare input data and how to interpretresults. A short introduction of underlying theory and its application to field equations willalso be presented.

414(Appl. Mech. 414). Structural Mechanics II. Prerequisite: Aero. Eng. 314. (3).Introduction to plate theory. Stability of structural elements; columns and beam columns;

plate in compression and shear; secondary instability of columns. Introduction to matrixmethods of deformation analysis; structural dynamics.

415. Principles of Structural Mechanics. Prerequisite: Appl. Mech. 21 1 or 319. I. (3).An accelerated coverage of the material in Aero Eng. 314 and 414 designed primarily forgraduate students. Not open to students who have elected Aero. Eng. 314 or 414.

420. Aerodynamics III. Prerequisite: Aero. Eng. 320, and Aero. Eng. 350 or Math. 450. I

and II. (3).Third part of an aerodynamic sequence designed to study the fundamental principles and

their applications; inviscid flows and fundamentals of field theory; generation of airfoil lift;thin airfoil theory; induced drag and finite wings; wave kinematics; two dimensionalcompressible flow.

421. Topics in Fluid Mechanics. Prerequisite: Aero. Eng. 330. (3).Topics include free surface phenomena, flow separation, flow in tubes, lubrication, flow in

a gravity-free environment. The objective of the course is to extend the student's background in gas dynamics to the fundamental aspects of other fluid phenomena of importancein aerospace and other industrial applications. Lectures and demonstrations.

423. Aero-Acoustics. Prerequisite: Aero. Eng. 320 or a course in compressible flow. (3).

Principles of generation, perception, and abatement of sound generated by fluid flows.

Elementary acoustics; acoustical response of the human ear. Theory and results of mea

surement of sound generated by explosions, sonic booms, jets, boundary layers, and flow

excited structural vibrations. Qualitative assessment of techniques and effectiveness ofnoise abatement procedures.

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424. Laminar and Turbulent Transport Processes. Prerequisite: Aero. Eng. 330 or anintroductory course in viscous flow. (3).

Turbulent transport processes are important in fluid flows in nature and technology.Elementary statistical concepts; nature of turbulent flow in boundary layers; wakes, jets,and plumes. Turbulent transport of mass, momentum, and heat in above flows and

comparison with laminar transport processes. Eddy viscosity and diffusivity of heat and

mass. Qualitative description of turbulent buffeting.

425. Principles of Aerodynamics. Prerequisite: Appl. Mech. 324. (3).An accelerated coverage of the material in Aero. Eng. 320 and 420 designed primarily forgraduate students. Not open to students who have elected Aero. Eng. 320 or 420.

430. Propulsion D. Prerequisite: Aero. Eng. 320. (3).Performance and analysis of flight-propulsion systems including the reciprocating engine-

propeller, turbojet, turboprop, ramjet, and rocket.


Advanced turbojet analysis including compressor and turbine performance, equilibriumrunning of turbojet engine, dynamics of turbojet engine considered as a quasistatic system,afterburners, fan jets; design of solid propellent rocket engines; underwater propulsion,including underwater ramjet. Use of the computer in design and performance analysis willbe emphasized.

433. Combustion Processes. Prerequisite: Aero. Eng. 320. (3).Study of combustion processes with appropriate consideration of the fluid mechanics(aero-thermo-chemistry); emphasis placed on the physical understanding, applications,performance, pollution aspects, experimental techniques, and commonality between jetpropulsion combustors, internal combustion engines, and stationary power plants; includesequilibrium constants, chemical kinetics, flames, explosions, liquid drops, particulate formation.

435. Principles of Propulsion. Prerequisite: Mech. Eng. 235. (3).An accelerated coverage of the material in Aero. Eng. 330 and 430 designed primarily forgraduate students. Not open to students who have elected Aero. Eng. 330 or 430.

439. Aircraft Propulsion Laboratory. Prerequisite: Aero. Eng. 320. (2).Series of experiments designed to illustrate the general principles of propulsion and to

introduce the student to certain experimental techniques in the study of actual propulsivedevices, using full-scale or reduced models of the pulsejet, turbojet, ramjet, and rocketmotors.

440. Vehicle Systems Performance. Prerequisite: junior standing. (3).Role of performance in systems analysis; mathematical modeling; identification of constraints, performance parameters, and performance indices. The aircraft performanceproblem: flight envelope, aerodynamic approximations, available propulsion systems; takeoff, landing, climb, and range performance. Modem performance optimization techniques.Applications to automobile, high-speed train, and space vehicle performance analysis.

447. Flight Testing. Prerequisite: Aero. Eng. 340. (2).Theory and practice of obtaining flight-test data on performance and stability of airplanesfrom actual flight tests. No laboratory fee will be charged, but a deposit covering studentinsurance and operating expense of the airplane will be required.

449. Principles of Vertical Take-off and Landing Aircraft. Prerequisite: Aero. Eng. 420. (3).Lifting rotor and propellor analysis in vertical and forward flight; ducted fan analysis;helicopter performance analysis: transitional flight problems of VTOL aircraft: stabilityand control problems of helicopters and VTOL aircraft.

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AEROSPACE ENGINEERING I l29

452(C.I.C.E. 4I2) (Elec.-Comp. Eng. 4I2). Engineering Probability and Statistics.

Prerequisite: Math. 2l5. I and II. (3).Basic concepts of probability theory: random variables, probability distributions, averages,

moments, characteristic functions, independence. Binomial, Poisson, and Gaussian distributions. Introduction to statistical inference and its applications in engineering, statistics ofmeasurements, confidence intervals, least square fitting of data. C.I.C.E. students may not

receive graduate credit for both C.I.C.E. 4l2 and C.I.C.E. 5l2.

454(C.I.C.E. 482) (Elec.-Comp. Eng. 482). Analog Computation. Prerequisite: Math. 2l6. I

and 11.(3).Basic theory of analog computers. Analog devices: operational amplifiers, multipliers,function generators. Analog simulation of linear and nonlinear dynamic systems, includingordinary and partial differential equations. Lecture and laboratory.

455(C.I.C.E. 465) (Elec.-Comp. Eng. 465). Computer Graphics Applications. Prerequisite:

Elec.-Comp. Eng. 270. I.&O.E. 473, Comp. & Comm. Sci. 473 or C.I.C.E. 46l. (3).

Application of several software packages and display devices for engineering problemsolving and production of computer animated films. Use of Computek, Tektronix, and PDPgraphics terminals for electrical circuit design, interactive data smoothing, production ofengineering graphs, etc. POLYGRAPHICS and BEFLIX computer animation packages

and their use in MTS. Production of 2 or 3 films using graphics terminals.

460. Aerophysics. I. Prerequisite: Physics 240, Math. 2l6. I. (3).Lagrangian and Hamiltonian concepts applied to aerospace engineering problems; princi

ples of optics related to aeronautical measurements, electromagnetic forces in movingmedia, radiation processes in gases.

46I. Aerophysics D. Prerequisite: Aero. Eng. 460 or Aero. Eng. 464. II. (3).

Quantum mechanical concepts in gas dynamics; principles of atomic and molecular spec

tra, and diagnostics of high energy flows; spectroscopy and application to ionized gases in

the laboratory, upper atomosphere, and interplanetary space; radiative transfer.

464(A.&O. Sci. 464). Upper Atmospheric Science. Prerequisite: senior or graduate standing

in a physical science or engineering. I. (3).An introduction to physical processes in the upper atmosphere; density, temperature,

composition, and winds; atmospheric radiation transfer processes and heat balance; the

ionosphere; rocket and satellite measurement techniques.

465(A.&O. Sci. 465). Atmospheric Measurements and Data Analysis. Prerequisite: senior or

graduate standing in a physical science or engineering. II. (3).

Introduction to operational and experimental measurements of atmospheric parameters.

Instrumentation for "in-situ" measurements at the surface and from aerospace vehicles.

Remote sensing using electromagnetic radiation and acoustical waves with both passiveand active systems. Analysis of data, error theory, the use of least squares methods and

empirical orthogonal functions, the information content of experimental data.

466. Atmospheric Measurements Laboratory. Prerequisite: preceded or accompanied by

Aero. Eng. 465. (2).Measurement projects in gas kinetics and in radiation phenomena in several parts of the

electromagnetic spectrum of significance to atmospheric and space research. Emphasis is

placed on ground based techniques which yield useful atmospheric data.

467. Aerodynamic Topics in Atmospheric Environment. Prerequisite: Aero. Eng. 330 or

Appl. Mech.422. (2).Physical and chemical nature of the atmosphere. Gravitational and coriolis force effects on

air flow. Aerodynamic elements in the weather forecasting problem. Hydrodynamic vortex

and atmospheric tornado. Free convection and hot plumes. Suspension and dispersion ofaerosols in the atmosphere. Free air turbulence.

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47l. Automatic Control Systems. Prerequisite: Math. 2l6. I. (3).Transient and steady-state analysis of linear control systems; transfer function and state-

space description of control systems; stability analysis and synthesis methods; applicationto the design of autopilots and other modern control systems; introduction to nonlinearcontrol systems and phase plane analysis.

472(C.I.C.E. 450) (Elec.-Comp. Eng. 450). Fundamentals of Control Systems. Prerequisite:Appl. Mech. 240, Elec.-Comp. Eng. 3l0, or Elec.-Comp. Eng. 355, and senior standing. I, II and IIia. (3).

Concept and importance of control systems. Control system descriptions: state variableand transfer function representations. System performance and design criteria: stability,sensitivity, time response. Concept of feedback. Time response of linear control systems.Use of Hurwitz, root-locus. Nyquist and Bode methods for analysis and synthesis of linearcontrol systems. Not open to students with credit for Aero. Eng. 47l.

473(C.I.C.E. 45I) (Elec.-Comp. Eng. 45I). Control Systems Laboratory. Prerequisite:C.I.C.E. 450 or Aero. Eng. 47l. I and II. (2).

Introduction to control system simulation and design. Experiments with physical systems.Illustration of basic control principles. Design examples and the use of computer designaids.

48l. Airplane Design. Prerequisite: senior standing. (4).Power-required and power-available characteristics of aircraft on a comparative basis,calculation of preliminary performance, stability, and control characteristics. Designprocedure, including layouts and preliminary structural design. Subsonic and supersonicdesigns. Emphasis on design techniques and systems approach. Lectures and laboratory.

482. Design of Rocket- and Air-Borne Remote Sensing Probes. Prerequisite: senior standing.(4).

Design techniques and projects for geophysical, environmental, and earth resourcessurveys. Aircraft, sounding rocket, and balloon instruments and payloads as well as

vehicle characteristics and performance are considered. Student projects bring together in

a unified concept components for sensing (remote and in situ), telemetering, tracking,performance, safety, and data processing.

483. Aerospace System Design. Prerequisite: senior standing. (4).Aerospace system design, analysis and integration. Consideration of launch facilities,booster systems, spacecraft systems, communications, data processing, and project man

agement. Lectures and laboratory.

485(C.I.C.E. 435)(Elec.-Comp. Eng. 435). Aerospace Communication Systems. Prerequisite:Math. 450 or Aero. Eng. 350. Elec.-Comp. Eng. 3l4. (3).

Introduction to the design of space communications and tracking systems for the aerospace system designer. Basic principles in the design of space communications and tracking systems, including modulation-demodulation techniques, frequency and time divisionmultiplexing, methods of data storage, system gain considerations, power sources, antennas, propagation, and tracking methods. Application to system problems emphasized.

490. Directed Study. (To he arranged).Individual study of specialized aspects of aerospace engineering. Primarily for undergraduates.

5l0(Appl. Mech. 5l0) (Mech. Eng. 557). Finite Element Methods in Mechanics I.Prerequisite: Aero. Eng. 4l4{Appl. Mech. 4l4) or Mech. Eng. 362. I. (3).

Development of the finite element method with emphasis on energy principles. Virtual

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AEROSPACE ENGINEERING I l3l

work. Potential energy. Application to line elements, beams, plane stress, plane strain, and

three-dimensional stress. Several computer problems assigned.

5I<KAppl. Mech. 5I4). Foundations of Structural Mechanics I. Prerequisite: Aero. Eng. 4l4.

(3).Elements of the analysis of structures. Includes plates of various shapes, loading and


bending and membrane theories; plastic analysis of structures, beams, frames, plates;


5I5(Appl. Mech. 5I5). Foundations of Structural Mechanics D. Prerequisite: Aero. Eng.5l4. (3).

Behavior of structures in a thermal environment, heat conduction, aerodynamic heating ofhigh speed vehicles, thermal stresses and deflections, thermal instabilities, discussion ofmaterial properties at elevated temperature. Elements of the theory of linear viscoelastic-ity.

520. Gasdynamics I. Prerequisite: Aero. Eng. 420 or 425. (3).Gasdynamics at an intermediate level: Thermodynamics; the conservation equations; vor-ticity theorems; unsteady one-dimensional flow; the method of characteristics; stationaryand moving shock waves; two-dimensional steady flow including method of small perturbations.

52l. Experimental Gasdynamics. Prerequisite: Aero. Eng. 330 and 420. (3).Experimental methods in modem gasdynamics; physical principles and interpretation.Shop practice and theory of instrument design: mechanics, electronics, and optics. Measurement of velocity, pressure, density, temperature, composition, energy and mass trans

fer in fluids and plasmas. Transducers and laboratory instrumentation in gasdynamicresearch.

522. Gasdynamics II. Prerequisite: Aero. Eng. 520. (3).The Navier-Stokes equations, including elementary discussion of tensors; exact solutions.Laminar boundary-layer theory; asymptotic concepts; solutions for incompressible boundary layers. Compressible boundary layers; special solutions; transformation of equations;heat transfer in forced and free convection. Introduction to the mechanics of turbulence;

Reynolds stresses; turbulent boundary layers.

530. Propulsion III. Prerequisite: Aero. Eng. 430. (3).Continuation of Aero. Eng. 430. Further treatment of aircraft engine performance, including off-design operation, and study of selected problems in the field of propulsion.

532. Introduction to Gaskinetks and Real Gas Effects. Prerequisite: Aero. Eng. 420. (3).A study of some modern topics of flow problems not covered in the traditional gasdynamics of ideal gases: concepts of gaskinetics, aerodynamics of free molecules, shock transi

tion layer, real gas effects, high temperature effects, multicomponent flows, etc.

535. Rocket Propulsion. Prerequisite: Aero. Eng. 430 or 435. (3).Analysis and performance of liquid and solid propellant rocket powerplants; propellantthermochemistry, heat transfer, system considerations, advanced rocket propulsion tech

niques.

540. Space Dynamics I. Prerequisite: Appl. Mech. 240. (4).Kinematics of motion, particle dynamics, orbital motion and calculation of orbital parameters, Lagrange's equation. Rigid body dynamics including Euler's equations, the Poinsotconstruction, spin stabilization, the rotation matrix. Vibrations of coupled systems, orthogonality relationships, generalized co-ordinates and system parameters.

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542. Astrodynamics I. Prerequisite: Aero. Eng. 340. I. (3).The study of motion of spacecraft in a vacuum and in the atmosphere with emphasis onpreliminary mission planning. Analysis of trajectories in suborbital, orbital, lunar, andinterplanetary operations. Aerodynamic forces and heating characteristics and their effecton the selection of flight paths during entry into planetary atmospheres.

543. Structural Dynamics. Prerequisite .-Aero. Eng. 414 or 540. (3).Natural frequencies and mode shapes of elastic bodies. Nonconservative elastic systems.Structural and viscous damping. Influence coefficient methods for typical flight structures.Response of structures to random and shock loads. Lab demonstration.

544. Aeroelasticity. Prerequisite: Aero. Eng. 414 or 540. (3).An introduction to aeroelasticity. Vibration and flutter of elastic bodies exposed to fluidflow. Static divergence and flutter of airplane wings. Flutter of flat plates and thin walledcylinders at supersonic speeds. Oscillations of structures due to vortex shedding.

546. Space Dynamics n. Prerequisite: Aero. Eng. 540. (3).Hamilton's equations, canonical transformations, and Hamilton-Jacobi theory. Applications to orbital problems. General perturbation theory. Introduction to special relativity.

548. Astrodynamics EL Prerequisite: Aero. Eng. 542. (3).Orbit determination. Systems of canonical equations. Perturbation theory with applicationsto the motion of an artificial satellite. Lunar and planetary theories.

549(Appl. Mech. 549) (Mech. Eng. 549). Random Vibrations of Mechanical Systems.

Prerequisite: Appl. Mech. 240 or Appl. Mech. 343. II. (3).Random mechanical inputs; wind buffeting; earthquakes; surface irregularities. Engineering applications include response of a linear spring-mass system and an elastic beam tosingle and multiple random loading. Failure theories. Necessary concepts such as ensemble averages, correlation functions, stationary and ergodic random processes, power spectra, are developed heuristically.

570. Guidance and Navigation of Aerospace Vehicles. Prerequisite: a course in feedbackcontrol. I. (3).

Principles of space vehicle, homing and ballistic missiles guidance systems in two andthree dimensions. Explicit, linear perturbation, and velocity-to-be gained guidance modes.Mechanization by inertial and other means, including strapped-down and stable-platforminertial systems. Celestial navigation procedures with deterministic and redundant measurements. Application of Kalman filtering to recursive navigation theory.

574. Control of Aircraft, Missiles, and Space Vehicles. Prerequisite: preceded or accompanied by C. I. C.E. 550. U.(2).

Analysis and synthesis of autopilots for aircraft and cruise-type missiles. Design of thrust-vector control systems including effects of elastic structures and fuel sloshing. Attitudecontrol systems for space vehicles; mechanization using jet thrusters and inertia wheels;gravity gradient moments.

575. Optimization of Space Trajectories. Prerequisite: permission of instructor. II. (3).Necessary and sufficient conditions for ordinary extremum and variational problems, withemphasis on the problem of Bolza. Applications of the calculus of variations to optimalspace trajectories. Problems with control and state variable inequality constraints. Iterative computational methods for two-point boundary-value problems, including the gradientmethod. Newton's method, and quasilinearization.


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596. Aurora and Airglow. Prerequisite: permission of instructor. II. (3).Morphology and physics of the aurora and airglow. Emission spectra in the aurora and

their atomic and molecular origin; proton aurora; metastable excitation; calculation ofemission profiles. Night- and day-glow; pre-dawn and post-twilight enhancements; mid-latitude red arc; excitation mechanisms.

6I0(Appl. Mech. 6I0). Finite Element Methods in Mechanics II. Prerequisite: Aero. Eng.5l0(Appl. Mech. 5l0) (Mech. Eng. 557). II. (3).

Advanced topics in finite element theory. Plates, shells, large deflections, stability, plasticity, dynamics. Iterative methods for nonlinear problems. Solution of field problems forfluid flow and electric potential. Survey of software available.

620. Dynamics of Viscous Fluids. Prerequisite: Aero. Eng. 520. (3).Navier-Stokes equations; low Reynolds number flows; incompressible and compressiblelaminar boundary layers; boundary layer stability and transition to turbulence; turbulentboundary layers, wakes, and jets.

62I. Dynamics of Compressible Fluids. Prerequisite: Aero. Eng. 520. (3).Theory of characteristics; shock-wave phenomena; interaction problems; hodograph transformation; transonic flow.

625. Methods of Theoretical Aerodynamics. Prerequisite: Aero. Eng. 520. (3).Application of methods for solving partial differential equations which arise in aerodynamics problems. Subsonic and supersonic wing theory, sound waves, viscous flows,boundary-layer theory, shock waves. Emphasis on the use of fundamental solutions and

superposition in linear problems and asymptotic methods in nonlinear problems. Similaritysolutions, characteristics.

627. Continuum Theory of Fluids. Prerequisite: Aero. Eng. 520. (3).Physical concepts underlying the flow of fluids acted upon by stresses arising fromviscosity and from electromagnetic and gravity fields. Invariant analysis of stress-strainrelations. Maxwell's equations, analysis of electromagnetic stresses and energy dissipationin moving media, the equations of motion and energy in a moving fluid, and some solutionsof the complete equations.

628. Statistical Theory of Fluids. Prerequisite: Aero. Eng. 532. (3).A study of the flows of neutral and charged particles from the viewpoint of kinetic theory;Chapman-Enskog theory of transport phenomena, dynamics of rarefied gases, plasma

kinetics without external magnetic field, plasma oscillations and Landau damping, micro-instabilities, plasma interactions.

632. Gas Flows with Chemical Reactions. Prerequisite: Aero. Eng. 532, 620. (3).Thermodynamics of gas mixtures, chemical kinetics, conservation equations for multi-component reacting gas mixtures. Deflagration and detonation waves. Nozzle flows and


650. Computational Methods of Flight Simulation. Prerequisite: Aero. Eng. 540, andC.I.C.E. 482 or Elec.-Comp. Eng. 365. (2).

Equations of motion for aircraft and aerospace vehicles. Axis systems and axis transformations including body, stability, flight-path, navigational, and inertial axes. Euler angles,direction cosines, and quaternions. Simulation of flat earth trajectories, low-eccentricityorbits, lunar and planetary trajectories. Use of conservation laws and constraint methods.

Mechanization in six degrees of freedom using analog, hybrid, and digital computers.

65I. Computation of Aerospace Trajectories. Prerequisite: Aero. Eng. 546. (2).Error analysis of numerical integration methods. Comparison of Cowell's method, Enke'smethod and variation-of-parameters in terms of accuracy and convenience. FORTRAN

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programming of integration methods. Student programming and solution of trajectoryproblems.

671. Guidance and Control Laboratory. Prerequisite: preceded or accompanied by Aero.Eng. 570 and Aero. Eng. 574. (2).

Simulation of aircraft, missile, and space vehicle autopilot systems on analog and hybridcomputer systems. Digital and analog solution of missile and space vehicle guidanceproblems.

676. Optimal Guidance. Prerequisite: Aero. Eng. 575 or C.I.C.E. 540. (3).Optimum guidance modes, including the path-adaptive mode, iterative guidance mode, andneighboring optimum guidance. The effect of normality and conjugate points in guidanceanalysis. Applications to space missions involving high thrust, low thrust, impulsive thrustand re-entry. Necessary conditions for singular guidance problems. Future needs in guidance theory.

721. Turbulence. Prerequisite: Aero. Eng. 620. (3).Physical and mathematical description of turbulence in boundary layers, wakes, jets, andbehind grids, turbulent fields; theories for turbulent mass, momentum, heat, and particlediffusion.

726. Introduction to Plasma Dynamics. Prerequisite: permission of instructor. (3).Physical properties of a plasma; particle orbit theory; collective phenomena in a plasma;kinetic equations for a plasma; instabilities; transport phenomena and derivation of themagnetohydrodynamic equations.

729. Special Topics in Gasdynamics. Prerequisite: permission of instructor. (To be arranged).


730. Energy Transfer in High Temperature Gas Flows. Prerequisite: Aero Eng. 532 and620. (3).

Energy transfer processes as related to high temperature gas flows; unsteady heat conduction, convection in non-reactive and reactive flows, transport properties, ablation andgaseous radiation.








arranged).

882. Seminar in Guided Missiles. Prerequisite: permission of instructor. (To be arranged).Primarily for military officers.

895(Elec.-Comp. Eng. 895). Seminar in Space Research. Prerequisite: permission of instructor. (To be arranged).


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APPLIED MECHANICS AND ENGINEERING SCIENCE I 135

The University of Michigan. Topics will include the following: structure of the upperatmosphere; measurement of temperature, pressure, density, composition, and winds. Theionosphere; measurement of ion and electron density and temperature. Investigation ofradio waves incident on the earth at frequencies absorbed by the ionosphere by means ofinstrumented satellites. Interpretation of infrared data from meteorological satellites. Re

search in attitude control of multistage sounding rockets.

990. Dissertation/ Pre-Candidate. I and II (2-8); 11la and III* (1-4).Election for dissertation work by doctoral student not yet admitted to status as a Candidate.

995. Dissertation/Candidate. Prerequisite: Graduate School authorization for admission as

a doctoral candidate. I and II (8): IIIa and III* (4).Election for dissertation work by doctoral student who has been admitted to status as a

Candidate.

Applied Mechanics and Engineering Science

Department office: 201 West EngineeringSee Page 125 for statement on Course Equivalence.

211. Introduction to Solid Mechanics. Prerequisite: Physics 140, Math. 116. I, II, IIIa and

IIU». (4). Open to juniors and seniors with permission of instructor.Principles of statics including equilibrium and static equivalence. Determination of moment

and force resultants in slender members. Introduction to mechanics of deformable bodies;

concepts of stress and strain, classification of material behavior, stress-strain relations and

generalized Hooke's law. Application to engineering problems involving members underaxial load, torsion of circular rods and tubes, bending and shear stresses in beams,

combined stresses, deflection of beams. Three lectures and two hours of recitation-demonstration.

218. Vector Mechanics of a Particle and a System of Particles. Prerequisite: Phvsics 140 andMath. 116. I. (3).

Review of scalars, matrices, vectors, Cartesian tensors. Transformation, rotation, angularvelocity. Idealization and concept of a model. Newtonian mechanics. Dynamics of a

particle. Momentum and energy levels. Trajectories, propulsion, impact, harmonic oscillator, orbits. Relative motion and geophysical examples. Systems. Statics: equilibrium,vector systems, virtual work, stability.

240. Introduction to Dynamics. Prerequisite: Physics 140 and preceded or accompanied by

Math. 216. I, II, IIk and III*. (4).Vector description of force, position, velocity and acceleration in fixed and movingreference frames. Force and couple resolution, and equilibrium concepts. Kinetics ofparticles, assemblies of particles and of rigid bodies, energy and momentum concepts.Euler's equations. Keplerian motion. Moment of inertia properties. The simple oscillatorand its applications.

245. Vector Mechanics of a Rigid Body and Analytical Mechanics. Prerequisite: Appl. Mech.218, preceded or accompanied by Math. 216. II. (3).

Review of algebraic equations. Eigenvalues and eigenvectors of a symmetric matrix.Dynamics of a rigid body. Plane motion, balancing, the rigid rotor, oscillation, stability ofspin. Analytical mechanics: degrees of freedom and constraints. Hamilton's principle,Lagrange's equations. Coupled systems and normal modes of oscillation. Extension to the

vibrating string.

314(Aero. Eng. 314). Structural Mechanics I. Prerequisite: Appl. Mech. 211. II. (3).Review of plane states of stress and strain; basic equations of plane elasticity and selected

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100. Introduction to FUght. (2).An introduction to the physical principles of flight within the atmosphere and in space, to the

major historical developments in the conquest of air and space, and to the current state ofaerospace developments and their role in national and world affairs.

200. General Aeronautics and Astronautics. Prerequisite: Physics 140. I and II. (2).Introduction to aerospace engineering. Elementary problems designed to orient the student in

the program of aerospace engineering, together with a discussion of the current state ofaerospace developments and the role of the engineer. Recitations and demonstrations.

203(A.S.403) (N.S. 303). Pilot Ground School. Prerequisite: permission ofinstructor. I and II.(2).

Lecture/practicum, 3 hours a week for 16 weeks. Aerodynamics for aviators, meteorology,air traffic control. Federal Aviation Regulations, flight computers, navigation, radio navigation, flight physiology, and accident prevention. Open to all University students.

300. Elements of Space Science and Technology. Prerequisite: Math. 216; Physics 240. (3).Scientific and technological aspects of current space flights, mission goals, the space environment, vehicle characteristics, performance, and flight paths. Mission support: communications, power, computers, etc. Open to all University students.

301. Laboratory I. Prerequisite: preceded or accompanied by Elec.-Comp. Eng. 314. (2).Comprehensive series of lectures and experiments designed to introduce the student to basicprinciples of electronics, circuit analysis, transducers, modern laboratory instrumentation,experimental methods, and data analysis. Experiments involve simple measurement and

instrumentation problems.


314(Appl. Mech. 314). Structural Mechanics I. Prerequisite: Appl. Mech. 211. (3).Review of plane states of stress and strain. Basic equations of plane elasticity and selected

problems; failure criteria and applications; energy principles of structural theory; thin-walledbeam theory.

320. Compressible Flow and Propulsion I. Prerequisite: Mech. Eng. 235. I and II. (3).First part of an aerodynamics sequence designed to study the fundamental principles and theirapplications; physical nature of fluids, conservation laws; nozzles and diffusers; shockwaves; applications to jet propulsion and other problems.


Second part of an aerodynamics sequence designed to study the fundamental principles and

their applications: viscous effects in laminar and turbulent flows; boundary layer theory;concepts of instability and transition to turbulent flow; flows under the influence of gravitational and electromagnetic forces.

340. Mechanics of Flight. Prerequisite: Appl. Mech. 240. (3).Mechanics of a particle applied to the analysis of vehicle flight paths. Rigid body mechanicsapplied to translational and rotational vehicle motion. Analysis of vehicle motion and static

and dynamic stability using perturbation theory.

350(Math. 350). Aerospace Engineering Analysis. Prerequisite: Math. 216. (3).Formulation and solution of some of the elementary initial- and boundary-value problemsrelevant to aerospace engineering. Application of Fourier series, separation of variables, andvector analysis to problems of forced oscillations, wave motion, diffusion, elasticity, andperfect-fluid theory.

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380. Undergraduate Seminar. Prerequisite: junior standing. 11.(l).A series of seminars by noted outside speakers designed to acquaint undergraduates with both

current problems and state of the art of the aerospace industry. Will involve a short termproject or paper pertinent to one of the seminar topics.


4ll(Appl. Mech. 4II) (Civ. Eng. 4II) (Nav. Arch. 4lI). Finite Element Applications.Prerequisite: Eng. l02, Appl. Mech. 2ll . I. (3).

The course consists of user oriented application of existing finite element computer programs

for solving practical structural mechanics problems of frames, 2-D and 3-D solids, plates,shells, etc. Students will learn to prepare input data and how to interpret results. A short

introduction of underlying theory and its application to field equations will also be presented.

4I4(Appl. Mech. 4I4). Structural Mechanics D. Prerequisite: Aero. Eng. 3l4. (3).Introduction to plate theory. Stability of structural elements; columns and beam columns;plate in compression and shear; secondary instability of columns. Introduction to matrix

methods of deformation analysis; structural dynamics.

420. Aerodynamics III. Prerequisite: Aero. Eng. 320, and Aero. Eng. 350or Math. 450. land11.(3).

Third part ofan aerodynamic sequence designed to study the fundamental principles and theirapplications; inviscid flows and fundamentals of field theory; generation of airfoil lift; thinairfoil theory; induced drag and finite wings; wave kinematics; two dimensional compressibleflow.

423. Aero-Acoustics. Prerequisite: Aero. Eng. 320 or a course in compressible flow. (3).Principles of generation, perception, and abatement of sound generated by fluid flows.Elementary acoustics; acoustical response of the human ear. Theory and results of measure

ment of sound generated by explosions, sonic booms, jets, boundary layers, and flow excitedstructural vibrations. Qualitative assessment of techniques and effectiveness of noise abate

ment procedures.

424. Laminar and Turbulent Transport Processes. Prerequisite: Aero. Eng. 330 or an introductory course in viscous flow. (3).

Turbulent transport processes are important in fluid flows in nature and technology. Elementary statistical concepts; nature of turbulent flow in boundary layers; wakes, jets, and plumes.

Turbulent transport of mass, momentum, and heat in above flows and comparison withlaminar transport processes. Eddy viscosity and diffusivity of heat and mass. Qualitativedescription of turbulent buffeting.

430. Propulsion II. Prerequisite: Aero. Eng. 320. (3).Performance and analysis of flight-propulsion systems including the reciprocating engine-propeller, turbojet, turboprop, ramjet, and rocket.

433. Combustion Processes. Prerequisite: Aero. Eng. 320. (3).Study of combustion processes with appropriate consideration of the fluid mechanics (aero-thermo-chemistry); emphasis placed on the physical understanding, applications, performance, pollution aspects, experimental techniques, and commonality between jet propulsioncombustors, internal combustion engines, and stationary power plants; includes equilibriumconstants, chemical kinetics, flames, explosions, liquid drops, particulate formation.



440. Vehicle Systems Performance. Prerequisite: junior standing. (3).Role of performance in systems analysis; mathematical modeling; identification of con

straints, performance parameters, and performance indices. The aircraft performance prob

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lem: flight envelope, aerodynamic approximations, available propulsion systems; takeoff,

landing, climb, and range performance. Modern performance optimization techniques. Applications to automobile, high-speed train, and space vehicle performance analysis.

447. Flight Testing. Prerequisite: Aero. Eng. 340. (2).Theory and practice of obtaining flight-test data on performance and stability of airplanesfrom actual flight tests. No laboratory fee will be charged, but a deposit covering student

insurance and operating expense of the airplane will be required.

449. Principles of Vertical Take-off and Landing Aircraft. Prerequisite: Aero. Eng. 420. (3).Lifting rotor and propellor analysis in vertical and forward flight; ducted fan analysis:helicopter performance analysis; transitional flight problems of VTOL aircraft; stability and

control problems of helicopters and VTOL aircraft.

452(C.I.C.E. 412) (Elec.-Comp. Eng. 412). Engineering Probability and Statistics.Prerequisite: Math. 215. I and II. (3).

Basic concepts of probability theory: random variables, probability distributions, averages,moments, characteristic functions, independence. Binomial, Poisson, and Gaussian distributions. Introduction to statistical inference and its applications in engineering, statistics ofmeasurements, confidence intervals, least square fitting of data. C.I.C.E. students may not

receive graduate credit for both C.I.C.E. 412 and C.I.C.E. 512.

454(C.I.C.E. 482) (Elec.-Comp. Eng. 482). Analog Computation. Prerequisite: Math. 216. I

and II. (3).Basic theory of analog computers. Analog devices: operational amplifiers, multipliers, function generators. Analog simulation of linear and nonlinear dynamic systems, including ordinary and partial differential equations. Lecture and laboratory.

455(C.I.C.E. 465) (Elec.-Comp. Eng. 465). Computer Graphics Applications. Prerequisite:Elec.-Comp. Eng. 270, l.&O.E. 473. Comp. & Comm. Sci. 473 or C.I.C.E. 461. (3).

Application of several software packages and display devices for engineering problem solvingand production of computer animated films. Use of Computek, Tektronix, and PDP graphicsterminals for electrical circuit design, interactive data smoothing, production of engineeringgraphs, etc. POL YGRAPHICS and BEFLIX computer animation packages and their use in

MTS. Production of 2 or 3 films using graphics terminals.

460. Aerophysics I. Prerequisite: Physics 240. Math. 216. I. (3).Lagrangian and Hamiltonian concepts applied to aerospace engineering problems; principlesof optics related to aeronautical measurements, electromagnetic forces in moving media,

radiation processes in gases.

461. Aerophysics D. Prerequisite: Aero. Eng. 460 or Aero. Eng. 464. II. (3).

Quantum mechanical concepts in gas dynamics; principles of atomic and molecular spectra,and diagnostics of high energy flows; spectroscopy and application to ionized gases in the

laboratory, upper atmosphere, and interplanetary space; radiative transfer.

464(A.&O. Sci. 464). Upper Atmospheric Science. Prerequisite: senior or graduate standingin a physical science or engineering. I. (3).

An introduction to physical processes in the upper atmosphere; density, temperature, com

position, and winds; atmospheric radiation transfer processes and heat balance: the ionosphere; rocket and satellite measurement techniques.

465(A.&O. Sci. 465). Atmospheric Measurements and Data Analysis. Prerequisite: senior orgraduate standing in a physical science or engineering. II. (3).

Introduction to operational and experimental measurements of atmospheric parameters.

Instrumentation for "in-situ" measurements at the surface and from aerospace vehicles.Remote sensing using electromagnetic radiation and acoustical waves with both passive and

active systems. Analysis of data, error theory, the use of least squares methods and empiricalorthogonal functions, the information content of experimental data.

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467. Aerodynamic Topics in Atmospheric Environment. Prerequisite: Aero. Eng.330orAppI.Mech. 422. (2).

Physical and chemical nature of the atmosphere. Gravitational and coriolis force effects on airflow. Aerodynamic elements in the weather forecasting problem. Hydrodynamic vortex and

atmospheric tornado. Free convection and hot plumes. Suspension and dispersion of aerosolsin the atmosphere. Free air turbulence.

47I. Automatic Control Systems. Prerequisite: Math. 2l6. (3).Transient and steady-state analysis of linear control systems; transfer function and state-

space description of control systems; stability analysis and synthesis methods; application to

the design of autopilots and other modem control systems; introduction to nonlinear controlsystems and phase plane analysis.

472(C.I.C.E. 450) (Elec.-Comp. Eng. 450). Fundamentals of Control Systems. Prerequisite:Appl. Mech. 240, Elec.-Comp. Eng. 3l0, or Elec.-Comp. Eng. 355, and senior standing.I, II and IIia. (3).

Concept and importance of control systems. Control system descriptions: state variable and

transfer function representations. System performance and design criteria: stability, sensitivity, time response. Concept of feedback. Time response of linear control systems. Use ofHurwitz, root-locus, Nyquist and Bode methods for analysis and synthesis of linear controlsystems. Not open to students with credit for Aero. Eng. 47l.

473(C.I.C.E. 45l) (Elec.-Comp. Eng. 45I). Control Systems Laboratory. Prerequisite:C.I.C.E. 450 or Aero. Eng. 47l. I and II. (2).

Introduction to control system simulation and design. Experiments with physical systems.IIlustration of basic control principles. Design examples and the use of computerdesign aids.

48I. Airplane Design. Prerequisite: senior standing. 1.(4).Power-required and power-available characteristics ofaircraft on a comparative basis, calculation of preliminary performance, stability, and control characteristics. Design procedure,including layouts and preliminary structural design. Subsonic and supersonic designs. Emphasis on design techniques and systems approach. Lectures and laboratory.

482. Design of Rocket- and Air-Borne Remote Sensing Probes. Prerequisite: senior standing.(4).

Design techniques and projects for geophysical, environmental, and earth resources surveys.Aircraft, sounding rocket, and balloon instruments and payloads as well as vehicle characteristics and performance are considered. Student projects bring together in a unified conceptcomponents for sensing (remote and in situ), telemetering, tracking, performance, safety, anddata processing.

483. Aerospace System Design. Prerequisite: senior standing. II. (4).Aerospace system design, analysis and integration. Consideration of launch facilities, boostersystems, spacecraft systems, communications, data processing, and project management.

Lectures and laboratory.

485(C.I.C.E. 435) (Elec.-Comp. Eng. 435). Aerospace Communication Systems. Prerequisite:Math. 450 or Aero. Eng. 350, Elec.-Comp. Eng. 3l4. (3).

Introduction to the design of space communications and tracking systems for the aerospace

system designer. Basic principles in the design of space communications and tracking systems, including modulation-demodulation techniques, frequency and time division multiplexing, methods of data storage, system gain considerations, power sources, antennas, propagation, and tracking methods. Application to system problems emphasized.

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5l0( Appl. Mech. 5l0) (Mech. Eng. 557). Finite Element Methods in Mechanics I. Prerequisite:Aero. Eng. 4l4(Appl. Mech. 4l4) or Mech. Eng. 362. I. (3).

Development of the finite element method with emphasis on energy principles. Virtual work.Potential energy. Application to line elements, beams, plane stress, plane strain, and three-

dimensional stress. Several computer problems assigned.

5I4(Appl. Mech. 5l4). Foundations of Structural Mechanics I. Prerequisite: Aero. Eng. 4l4.

(3).Elements of the analysis of structures. Includes plates of various shapes, loading and boundary conditions, effects of in-plane loading; shells of revolution, cylindrical shells, bending and

membrane theories; plastic analysis of structures, beams, frames, plates; plastic collapsemechanism. Applications of aerospace interest.

5l5(Appl. Mech. 5l5). Foundations of Structural Mechanics II. Prerequisite: Aero. Eng. 5l4.

(3).Behavior of structures in a thermal environment, heat conduction, aerodynamic heating ofhigh speed vehicles, thermal stresses and deflections, thermal instabilities, discussion ofmaterial properties at elevated temperature. Elements of the theory of linear viscoelasticity.

520. Gasdynamics I. Prerequisite: Aero. Eng. 420 or 425. (3).Gasdynamics at an intermediate level: Thermodynamics; the conservation equations; vortic-ity theorems; unsteady one-dimensional flow; the method of characteristics; stationary and

moving shock waves; two-dimensional steady flow including method of small perturbations.

52I. Experimental Gasdynamics. Prerequisite: Aero. Eng. 330 and 420. (3).Experimental methods in modem gasdynamics; physical principles and interpretation. Shoppractice and theory of instrument design: mechanics, electronics, and optics. Measurement ofvelocity, pressure, density, temperature, composition, energy and mass transfer in fluids and

plasmas. Transducers and laboratory instrumentation in gasdynamic research.

522. Gasdynamics II. Prerequisite: Aero. Eng. 520. (3).The Navier- Stokes equations, including elementary discussion of tensors; exact solutions.Laminar boundary-layer theory; asymptotic concepts; solutions for incompressible boundary

layers. Compressible boundary layers; special solutions; transformation of equations; heat

transfer in forced and free convection. Introduction to the mechanics of turbulence; Reynoldsstresses; turbulent boundary layers.

530. Propulsion III. Prerequisite: Aero. Eng. 430. (3).Continuation of Aero. Eng. 430. Further treatment of aircraft engine performance, includingoff-design operation, and study of selected problems in the field of propulsion.

532. Introduction to Gaskinetics and Real Gas Effects. Prerequisite .Aero. Eng. 420. (3).A study of some modern topics of flow problems not covered in the traditional gasdynamics ofideal gases: concepts of gaskinetics, aerodynamics of free molecules, shock transition layer,real gas effects, high temperature effects, multicomponent flows, etc.

535. Rocket Propulsion. Prerequisite: Aero. Eng. 430 or 435. (3).Analysis and performance of liquid and solid propellant rocket powerplants; propellantthermochemistry, heat transfer, system considerations, advanced rocket propulsion tech

niques.

540(Appl. Mech. 540). Intermediate Dynamics. Prerequisite: Appl. Mech. 240. I. (4).Kinematics of motion, particle dynamics, Lagrange's equations. Rigid body dynamics including Euler's equations, the Poinsot construction, spin stabilization, the rotation matrix. Vibrations of coupled systems, orthogonality relationships, generalized co-ordinates andgeneralized system parameters.

542. Astrodynamics I. Prerequisite: Aero. Eng. 340. I. (3).The study of motion of spacecraft in a vacuum and in the atmosphere with emphasis on

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preliminary mission planning. Analysis of trajectories in suborbital, orbital, lunar, and interplanetary operations. Aerodynamic forces and heating characteristics and their effect on the

selection of flight paths during entry into planetary atmospheres.

543. Structural Dynamics. Prerequisite: Aero. Eng. 414 or 540. (3).Natural frequencies and mode shapes of elastic bodies. Nonconservative elastic systems.

Structural and viscous damping. Influence coefficient methods for typical flight structures.Response of structures to random and shock loads. Lab demonstration.

544. Aeroelasticity. Prerequisite: Aero. Eng. 414 or 540. (3).An introduction to aeroelasticity. Vibration and flutter of elastic bodies exposed to fluid flow.Static divergence and flutter of airplane wings. Flutter of flat plates and thin walled cylindersat supersonic speeds. Oscillations of structures due to vortex shedding.

546. Space Dynamics II. Prerequisite: Aero. Eng. 540. (3).Hamilton's equations, canonical transformations, and Hamilton-Jacobi theory. Applicationsto orbital problems. General perturbation theory. Introduction to special relativity.

548. Astrodynamics D. Prerequisite: Aero. Eng. 542. (3).Orbit determination. Systems of canonical equations. Perturbation theory with applicationsto the motion of an artificial satellite. Lunar and planetary theories.


Prerequisite: Appi. Mech. 240. II. (3).Random mechanical inputs; wind buffeting: earthquakes; surface irregularities. Engineeringapplications include response of linear spring-mass system and an elastic beam to single and

multiple random loading. Failure theories. Necessary concepts such as ensemble averages,

correlation functions, stationary and ergodic random processes, power spectra, are de

veloped heuristically.


Principles of space vehicle, homing and ballistic missiles guidance systems in two and three

dimensions. Explicit, linear perturbation, and velocity-to-be gained guidance modes.

Mechanization by inertial and other means, including strapped-down and stable-platforminertial systems. Celestial navigation procedures with deterministic and redundant measure

ments. Application of Kalman filtering to recursive navigation theory.

574. Control of Aircraft, Missiles, and Space Vehicles. Prerequisite: preceded or accompanied by C.I.C.E. 550. II. (2).

Analysis and synthesis of autopilots for aircraft and cruise-type missiles. Design of thrust-vector control systems including effects of elastic structures and fuel sloshing. Attitudecontrol systems for space vehicles; mechanization using jet thrusters and inertia wheels;

gravity gradient moments.

575. Optimization of Space Trajectories. Prerequisite: permission of instructor. 11.(3).Necessary and sufficient conditions for ordinary extremum and variational problems, with

emphasis on the problem of Bolza. Applications of the calculus of variations to optimal space

trajectories. Problems with control and state variable inequality constraints. Iterative compu

tational methods for two-point boundary-value problems, including the gradient method.

Newton's method, and quasilinearization.


596. Aurora and Airglow. Prerequisite: permission of instructor. 11.(3).Morphology and physics of the aurora and airglow. Emission spectra in the aurora and their

atomic and molecular origin; proton aurora; metastable excitation; calculation of emission

profiles. Night- and day-glow; pre-dawn and post-twilight enhancements; mid-latitude red

arc; excitation mechanisms.

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6l0(Appl. Mech. 6l0). Finite Element Methods in Mechanics II. Prerequisite: Aero. Eng.5l0(Appl. Mech. 5l0) (Mech. Eng. 557). II. (3).

Advanced topics in finite element theory. Plates, shells, large deflections, stability, plasticity,dynamics. Iterative methods for nonlinear problems. Solution of field problems for fluid flowand electric potential. Survey of software available.


62l. Dynamics of Compressible Fluids. Prerequisite: Aero. Eng. 520. (3).Theory of characteristics; shock-wave phenomena; interaction problems; hodograph transformation; transonic flow.

625. Methods of Theoretical Aerodynamics. Prerequisite: Aero. Eng. 520. (3).Application of methods for solving partial differential equations which arise in aerodynamicsproblems. Subsonic and supersonic wing theory, soundwaves, viscous flows, boundary -layertheory, shock waves. Emphasis on the use of fundamental solutions and superposition inlinear problems and asymptotic methods in nonlinear problems. Similarity solutions, characteristics.

627. Continuum Theory of Fluids. Prerequisite: Aero. Eng. 520. (3).Physical concepts underlying the flow of fluids acted upon by stresses arising from viscosityand from electromagnetic and gravity fields. Invariant analysis of stress-strain relations.Maxwell's equations, analysis of electromagnetic stresses and energy dissipation in movingmedia, the equations of motion and energy in a moving fluid, and some solutions of thecomplete equations.

628. Statistical Theory of Fluids. Prerequisite: Aero. Eng. 532. (3).A study of the flows of neutral and charged particles from the viewpoint of kinetic theory;Chapman-Enskog theory of transport phenomena, dynamics of rarefied gases, plasma kinetics without external magnetic field, plasma oscillations and Landau damping, microinsta-bilities, plasma interactions.

632. Gas Flows with Chemical Reactions. Prerequisite: Aero. Eng. 532, 620. (3).Thermodynamics of gas mixtures, chemical kinetics, conservation equations for multicom-ponent reacting gas mixtures. Deflagration and detonation waves. Nozzle flows and boundary layers with reaction and diffusion.

65l. Computation of Aerospace Trajectories. Prerequisite: Aero. Eng. 546. (2).Error analysis of numerical integration methods. Comparison of Cowell's method, Enke'smethod and variation-of-parameters in terms of accuracy and convenience. FORTRANprogramming of integration methods. Student programming and solution of trajectory problems.

673(Elec.-Comp. Eng. 673) (Nuc. Eng. 673). Topics in Theoretical Plasma Physics.Prerequisite: Nuc. Eng. 57l or Elec.-Comp. Eng. 580 or Aero. Eng. 726. I and II. (3).This course may be taken for credit more than once.

An advanced course in theoretical plasma physics covering topics of current research interest. Specific content will vary from year to year. Representative topics include: studies ofweakly ionized plasmas with applications to gas lasers; space plasmas; laser fusion plasmas:and nonlinear plasma dynamics and plasma turbulence.

676. Optimal Guidance. Prerequisite: Aero. Eng. 575 or C.I.C.E. 540. (3).Optimum guidance modes, including the path-adaptive mode, iterative guidance mode, andneighboring optimum guidance. The effect of normality and conjugate points in guidanceanalysis. Applications to space missions involving high thrust, low thrust, impulsive thrustand re-entry. Necessary conditions for singular guidance problems. Future needs in guidancetheory.

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APPLIED MECHANICS AND ENGINEERING SCIENCE I 129

721. Turbulence. Prerequisite: Aero. Eng. 620. (3).Physical and mathematical description of turbulence in boundary layers, wakes, jets, and

behind grids, turbulent fields; theories for turbulent mass, momentum, heat, and particlediffusion.




730. Energy Transfer in High Temperature Gas Flows. Prerequisite: Aero. Eng. 532 and 620.

(3).Energy transfer processes as related to high temperature gas flows; unsteady heat conduction,

convection in non-reactive and reactive flows, transport properties, ablation and gaseous

radiation.







880. Seminar in Space Technology. Prerequisite: permission ofinstructor. ( To be arranged).

990. Dissertation/Pre-Candidate. I and II (2-8); 11la and 11lib (1-4).Election for dissertation work by doctoral student not yet admitted to status as a Candidate.


a doctoral candidate. I and II (8): l11a and lUb (4).Election for dissertation work by doctoral student who has been admitted to status as a

Candidate.

Applied Mechanics and Engineering ScienceDepartment office: 201 West EngineeringSee Page 121 for statement on Course Equivalence.

211. Introduction to Solid Mechanics. Prerequisite: Physics 140, Math 116. I, II, IIIa and

Ulb. (4). Open to juniors and seniors with permission of instructor.Principles of statics including equilibrium and static equivalence. Determination of moment

and force resultants in slender members. Introduction to mechanics of deformable bodies;

concepts of stress and strain, classification of material behavior, stress-strain relations and

generalized Hooke's law. Application to engineering problems involving members underaxial load, torsion of circular rods and tubes, bending and shear stresses in beams, combinedstresses, deflection of beams. Three lectures and two hours of recitation-demonstration.

218. Vector Mechanics of a Particle and a System of Particles. Prerequisite: Physics 140 andMath. 116. I. (3).

Review of scalars, matrices, vectors. Cartesian tensors. Transformation, rotation, angular

velocity. Idealization and concept of a model. Newtonian mechanics. Dynamics of a particle.Momentum and energy levels. Trajectories, propulsion, impact, harmonic oscillator, orbits.Relative motion and geophysical examples. Systems. Statics: equilibrium, vector systems,

virtual work, stability.

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Department Office: 302 Aerospace Engineering BuildingSee Page l23 for statement on Course Equivalence.

l00. Introduction to Flight. (2).An introduction to the physical principles of flight within the atmosphere and in space, to tbe

major historical developments in the conquest of air and space, and to the current state of

aerospace developments and their role in national and world affairs.

200. General Aeronautics and Astronautics. Prerequisite: Physics l40. I and II. (2).Introduction to aerospace engineering. Elementary problems designed to orient the student ia

the program of aerospace engineering, together with a discussion of the current state of

aerospace developments and the role of the engineer. Recitations and demonstrations.

203(A.S.403) (N.S. 303). Pilot Ground School. Prerequisite: permission of instructor. (2i.

Lecture/practicum, 3 hours a week for l6 weeks. Aerodynamics for aviators, meteorology,

air traffic control. Federal Aviation Regulations, flight computers, navigation, radio navigation, flight physiology, and accident prevention. Open to all University students.

300. Elements of Space Science and Technology. Prerequisite: Math. 2l6; Physics 240. I3i-

Scientific and technological aspects of current space flights, mission goals, the space envi

ronment, vehicle characteristics, performance, and flight paths. Mission support: communications, power, computers, etc. Open to all University students.

30I. Laboratory I. Prerequisite: preceded or accompanied by Elec.-Comp. Eng. 3l4. Qi.Comprehensive series of lectures and experiments designed to introduce the student to basic

principles of electronics, circuit analysis, transducers, modern laboratory instrumentationexperimental methods, and data analysis. Experiments involve simple measurement and


302. Laboratory II. Prerequisite: Aero. Eng. 30l. (2).

Continuation of the material in Aero. Eng. 30l.

3l4(Appl. Mech. 3I4). Structural Mechanics I. Prerequisite: Appl. Mech. 2ll. (3).Review of plane states of stress and strain. Basic equations of plane elasticity and selected

problems; failure criteria and applications; energy principles of structural theory: thin-walledbeam theory.

320. Compressible Flow and Propulsion I. Prerequisite: Mech. Eng. 235. I and II. (3).First part of an aerodynamics sequence designed to study the fundamental principles and their

applications; physical nature of fluids, conservation laws; nozzles and diffusers: shockwaves; applications to jet propulsion and other problems.



their applications; viscous effects in laminar and turbulent flows; boundary layer theory:

concepts of instability and transition to turbulent flow; flows under the influence of gravitational and electromagnetic forces.

340. Mechanics of Flight. Prerequisite: Appl. Mech. 240. (3).Mechanics of a particle applied to the analysis of vehicle flight paths. Rigid body mechanicsapplied to translational and rotational vehicle motion. Analysis of vehicle motion and static

and dynamic stability using perturbation theory.

350(Math. 350). Aerospace Engineering Analysis. Prerequisite: Math. 2l6. (3).Formulation and solution of some of the elementary initial- and boundary-value problemsrelevant to aerospace engineering. Application of Fourier series, separation of variables, andvector analysis to problems of forced oscillations, wave motion, diffusion, elasticity, andperfect-fluid theory.

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380. Undergraduate Seminar. Prerequisite: junior standing. (1).A series of seminars by noted outside speakers designed to acquaint undergraduates with both

current problems and state of the art of the aerospace industry. Will involve a short term

project or paper pertinent to one of the seminar topics.


411(Appl. Mech. 411) (Civ. Eng. 411) (Nav. Arch. 411). Finite Element Applications. Prerequisite:Eng. 102, Appl. Mech. 211. I. (3).

The application of user oriented finite element computer programs for solving practicalstructural mechanics problems of frames, 2-D and 3-D solids, plates, shells, etc., and

displaying the solutions graphically. Students learn to prepare input data and interpret results.

A short introduction to the underlying theory is also presented.

414(Appl. Mech. 414). Structural Mechanics II. Prerequisite: Aero. Eng. 314. (3).

Introduction to plate theory. Stability of structural elements; columns and beam columns;

plate in compression and shear; secondary instability of columns. Introduction to matrix


420. Aerodynamics III. Prerequisite: Aero. Eng. 320, and Aero. Eng. 350 or Math. 450. landII. (3).

Third part ofan aerodynamic sequence designed to study the fundamental principles and their

applications; inviscid flows and fundamentals of field theory; generation of airfoil lift; thin

airfoil theory; induced drag and finite wings; wave kinematics; two dimensional compressibleflow.



ment procedures.

424. Laminar and Turbulent Transport Processes. Prerequisite: Aero. Eng. 330 or an intro

ductory course in viscous flow. (3).Turbulent transport processes are important in fluid flows in nature and technology. Elemen

tary statistical concepts; nature of turbulent flow in boundary layers; wakes, jets, and plumes.

Turbulent transport of mass, momentum, and heat in above flows and comparison withlaminar transport processes. Eddy viscosity and diffusivity of heat and mass. Qualitativedescription of turbulent buffeting.

430. Propulsion II. Prerequisite: Aero. Eng. 320. (3).Performance and analysis of flight-propulsion systems including the reciprocating engine-


433. Combustion Processes. Prerequisite: Aero. Eng. 320. (3).

Study of combustion processes with appropriate consideration of the fluid mechanics (aero-thermo-chemistry); emphasis placed on the physical understanding, applications, performance, pollution aspects, experimental techniques, and commonality between jet propulsioncombustors, internal combustion engines, and stationary power plants; includes equilibriumconstants, chemical kinetics, flames, explosions, liquid drops, particulate formation.



440. Vehicle Systems Performance. Prerequisite: junior standing. (3).

Role of performance in systems analysis; mathematical modeling; identification of constraints, performance parameters, and performance indices. The aircraft performance prob

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lem: flight envelope, aerodynamic approximations, available propulsion systems; takeoff,

landing, climb, and range performance. Modem performance optimization techniques. Applications to automobile, high-speed train, and space vehicle performance analysis.



449. Principles of Vertical Take-ofT and Landing Aircraft. Prerequisite: Aero. Eng. 420. (3).Lifting rotor and propellor analysis in vertical and forward flight; ducted fan analysis;helicopter performance analysis; transitional flight problems of VTOL aircraft; stability andcontrol problems of helicopters and VTOL aircraft.

452(C.I.C.E. 412) (Elec.-Comp. Eng. 412). Engineering Probability and Statistics.Prerequisite: Math. 215. I and II. (3).

Basic concepts of probability theory: random variables, probability distributions, averages,moments, characteristic functions, independence. Binomial, Poisson, and Gaussian distributions. Introduction to statistical inference and its applications in engineering, statistics ofmeasurements, confidence intervals, least square fitting of data. C.I.C.E. students may not


454(C.I.C.E. 482) (Elec.-Comp. Eng. 482). Analog Computation. Prerequisite: Math. 216. I

and II. (3).Basic theory of analog computers. Analog devices: operational amplifiers, multipliers, function generators. Analog simulation of linear and nonlinear dynamic systems, including ordinary and partial differential equations. Lecture and laboratory.

455(C.I.C.E. 465) (Elec.-Comp. Eng. 465). Computer Graphics Application. Prerequisite:Elec.-Comp. Eng. 270 or I. &O. E. 473 or Comp. & Comm. Sci. 374 or C.I.C.E. 461. (3).

Application of several software packages and display devices for engineering problem solvingand production of computer animated films. Use of Computek, Tektronix, and PDP graphicsterminals for electrical circuit design, interactive data smoothing, production of engineeringgraphs, etc. POLYGRAPH ICS and BEFLIX computer animation packages and their use inMTS. Production of 2 or 3 films using graphics terminals.

460. Aerophysics I. Prerequisite: Physics 240, Math. 216. 1. (3).Lagrangian and Hamiltonian concepts applied to aerospace engineering problems; principlesof optics related to aeronautical measurements, electromagnetic forces in moving media,

radiation processes in gases.

461. Aerophysics II. Prerequisite: Aero. Eng. 460 or Aero. Eng. 464. II. (3).

Quantum mechanical concepts in gas dynamics; principles of atomic and molecular spectra,and diagnostics of high energy flows; spectroscopy and application to ionized gases in thelaboratory, upper atmosphere, and interplanetary space; radiative transfer.


An introduction to physical processes in the upper atmosphere; density, temperature, com

position, and winds; atmospheric radiation transfer processes and heat balance; the ionosphere; rocket and satellite measurement techniques.


Introduction to operational and experimental measurements of atmospheric parameters.Instrumentation for "in-situ" measurements at the surface and from aerospace vehicles.

Remote sensing using electromagnetic radiation and acoustical waves with both passive and

active systems. Analysis of data, error theory, the use of least squares methods and empirical

orthogonal functions, the information content of experimental data.

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467. Aerodynamic Topics in Atmospheric Environment. Prerequisite: Aero. Eng.330orAppl.Mech. 422. (2).


atmospheric tornado. Free convection and hot plumes. Suspension and dispersion of aerosolsin the atmosphere. Free air turbulence.

471. Automatic Control Systems. Prerequisite: Math. 216. (3).Transient and steady-state analysis of linear control systems; transfer function and state-


the design of autopilots and other modern control systems; introduction to nonlinear controlsystems and phase plane analysis.

4724C.I.C.E. 450) (Elec.-Comp. Eng. 450). Fundamentals of Control Systems. Prerequisite:Appl. Mech. 240, Elec.-Comp. Eng. 310. or Elec.-Comp. Eng. 355, and senior standing.I, II and IIIa. (3).


transfer function representations. System performance and design criteria: stability, sensitivity, time response. Concept of feedback. Time response of linear control systems. Use ofHurwitz, root-locus, Nyquist and Bode methods for analysis and synthesis of linear controlsystems. Not open to students with credit for Aero. Eng. 471.

473(C.I.C.E. 451) (Elec.-Comp. Eng. 451). Control Systems Laboratory. Prerequisite:C.I.C.E. 450 or Aero. Eng. 471. I and II. (2).

Introduction to control system simulation and design. Experiments with physical systems.

IIlustration ofbasic control principles. Design examples and the use ofcomputer design aids.

481. Airplane Design. Prerequisite: senior standing. I. (4).Power-required and power-available characteristics of aircraft on a comparative basis, calculation of preliminary performance, stability, and control characteristics. Design procedure,including layouts and preliminary structural design. Subsonic and supersonic designs. Emphasis on design techniques and systems approach. Lectures and laboratory.

482. Design of Rocket- and Air-Borne Remote Sensing Probes. Prerequisite: senior standing.

(4).Design techniques and projects for geophysical, environmental, and earth resources surveys.Aircraft, sounding rocket, and balloon instruments and payloads as well as vehicle characteristics and performance are considered. Student projects bring together in a unified conceptcomponents for sensing (remote and in situ), telemetering, tracking, performance, safety, and

data processing.

483. Aerospace System Design. Prerequisite: senior standing. l1.(4).Aerospace system design, analysis and integration. Consideration of launch facilities, boostersystems, spacecraft systems, communications, data processing, and project management.


485(C.I.C.E. 435) (Elec.-Comp. Eng. 435). Aerospace Communication Systems. Prerequisite:Math. 450 or Aero. Eng. 350, Elec.-Comp. Eng. 314. (3).



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graduates.

5l0(Appl. Mech. 5l0) (Mech. Eng. 557). Finite Element Methods in Mechanics I. Prerequtsiu

Aero. Eng. 4l4(Appl. Mech. 4l4) or Mech. Eng. 362. I. (3).Development of the finite element method with emphasis on energy principles. Virtual work.

Potential energy. Application to line elements, beams, plane stress, plane strain, and thrtt-


5I4(Appl. Mech. 5l4). Foundations of Structural Mechanics I. Prerequisite: Aero. Ene.*U

(3).Elements of the analysis of structures. Includes plates of various shapes, loading and boun

dary conditions, effects of in-plane loading; shells of revolution, cylindrical shells, beninf

and membrane theories; plastic analysis of structures, beams, frames, plates; plastic collar*

mechanism. Applications of aerospace interest.

5I5( Appl. Mech. 5I5). Foundations of Structural Mechanics II. Prerequisite: Aero. Eng. 5!*

(3).Behavior of structures in a thermal environment, heat conduction, aerodynamic heatingof

high speed vehicles, thermal stresses and deflections, thermal instabilities, discussion of

material properties at elevated temperature. Elements of the theory of linear viscoelasticm

520. Gasdynamics I. Prerequisite: Aero. Eng. 420 or 425. (3).Gasdynamics at an intermediate level: Thermodynamics; the conservation equations; vorii-

ity theorems; unsteady one-dimensional flow; the method of characteristics; stationary uimoving shock waves; two-dimensional steady flow including method of small perturbationv

52l. Experimental Gasdynamics. Prerequisite: Aero. Eng. 330 and 420. (3).Experimental methods in modern gasdynamics; physical principles and interpretation. Sbor

practice and theory of instrument design: mechanics, electronics, and optics. Measurement of

velocity, pressure, density, temperature, composition, energy and mass transfer in fluids mi


522. Gasdynamics II. Prerequisite: Aero. Eng. 520. (3).The Navier-Stokes equations, including elementary discussion of tensors; exact solution*

Laminar boundary-layer theory ; asymptotic concepts: solutions for incompressible boundslayers. Compressible boundary layers; special solutions; transformation of equations; he*

transfer in forced and free convection. Introduction to the mechanics of turbulence: Reynold

stresses; turbulent boundary layers.

530. Propulsion III. Prerequisite: Aero. Eng. 430. (3).Continuation of Aero. Eng. 430. Further treatment of aircraft engine performance, includiai

off-design operation, and study of selected problems in the field of propulsion.

532. Introduction to Gaskinetics and Real Gas Effects. Prerequisite.Aero. Eng. 420. (3).

A study of some modern topics of flow problems not covered in the traditional gasdynamicsideal gases: concepts of gaskinetics. aerodynamics of free molecules, shock transition lawreal gas effects, high temperature effects, multicomponent flows, etc.

535. Rocket Propulsion. Prerequisite: Aero. Eng. 430 or 435. (3).Analysis and performance of liquid and solid propellant rocket powerplants: propellani

thermochemistry, heat transfer, system considerations, advanced rocket propulsion tech

niques.

540(Appl. Mech. 540). Intermediate Dynamics. Prerequisite: Appl. Mech. 240. I. (4).Kinematics of motion, particle dynamics, Lagrange's equations. Rigid body dynamics indui

ing Euler's equations, the Poinsot construction, spin stabilization, the rotation matrix. Vibra

tions of coupled systems, orthogonality relationships, generalized co-ordinates ifc

generalized system parameters.

542. Astrodynamics I. Prerequisite: Aero. Eng. 340. I. (3).The study of motion of spacecraft in a vacuum and in the atmosphere with emphasis or

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preliminary mission planning. Analysis of trajectories in suborbital, orbital, lunar, and interplanetary operations. Aerodynamic forces and heating characteristics and their effect on the



Structural and viscous damping. Influence coefficient methods for typical flight structures.

Response of structures to random and shock loads. Lab demonstration.

544. Aeroelasticity. Prerequisite: Aero. Eng. 414 or 540. (3).

An introduction to aeroelasticity. Vibration and flutter of elastic bodies exposed to fluid flow.

Static divergence and flutter of airplane wings. Flutter of flat plates and thin walled cylinders

at supersonic speeds. Oscillations of structures due to vortex shedding.

546. Advanced Dynamics. Prerequisite: Aero. Eng. 540. (3).Hamilton's equations, canonical transformations, and Hamilton-Jacobi theory. Applicationsto orbital problems. General perturbation theory. Introduction to special relativity.

548. Astrodynamics II. Prerequisite: Aero. Eng. 542. (3).Orbit determination. Systems of canonical equations. Perturbation theory with applicationsto the motion of an artificial satellite. Lunar and planetary theories.


Prerequisite: Appl. Mech. 240. II. (3).Random mechanical inputs; wind buffeting; earthquakes; surface irregularities. Engineeringapplications include response of linear spring-mass system and an elastic beam to single and






dimensions. Explicit, linear perturbation, and velocity-to-be gained guidance modes.Mechanization by inert ial and other means, including strapped-down and stable-platforminert ial systems. Celestial navigation procedures with deterministic and redundant measurements. Application of Kalman filtering to recursive navigation theory.



575. Optimization of Space Trajectories. Prerequisite: permission of instructor. 11.(3).Necessary and sufficient conditions for ordinary extremum and variational problems, withemphasis on the problem of Bolza. Applications of the calculus of variations to optimal spacetrajectories. Problems with control and state variable inequality constraints. Iterative computational methods for two-point boundary-value problems, including the gradient method.



5%. Aurora and Airglow. Prerequisite: permission of instructor. II. (3).Morphology and physics of the aurora and airglow. Emission spectra in the aurora and theiratomic and molecular origin; proton aurora; metastable excitation; calculation of emissionprofiles. Night- and day-glow; pre-dawn and post-twilight enhancements; mid-latitude redarc; excitation mechanisms.

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6I0(Appl. Mech. 6l0). Finite Element Methods in Mechanics II. Prerequisite: Aero. En$.5KHAppl. Mech. 5l0) (Mech. Eng. 557). II. (3).

Advanced topics in finite element theory. Plates, shells, large deflections, stability . plasticity,dynamics. Iterative methods for nonlinear problems. Solution of field problems for fluid flowand electric potential. Survey of software available.


62I. Dynamics of Compressible Fluids. Prerequisite: Aero. Eng. 520. (3).Theory of characteristics; shock-wave phenomena: interaction problems; hodograph trans

formation; transonic flow.

625. Methods of Theoretical Aerodynamics. Prerequisite: Aero. Eng. 520. (3).Application of methods for solving partial differential equations which arise in aerodynamicsproblems. Subsonic and supersonic wing theory , sound waves, viscous flows, boundary-layertheory, shock waves. Emphasis on the use of fundamental solutions and superposition in

linear problems and asymptotic methods in nonlinear problems. Similarity solutions, characteristics.

627. Continuum Theory of Fluids. Prerequisite: Aero. Eng. 520. (3).Physical concepts underlying the flow of fluids acted upon by stresses arising from viscosityand from electromagnetic and gravity fields. Invariant analysis of stress-strain relations.Maxwell's equations, analysis of electromagnetic stresses and energy dissipation in movingmedia, the equations of motion and energy in a moving fluid, and some solutions of thecomplete equations.



65l. Computation of Aerospace Trajectories. Prerequisite: Aero. Eng. 546. (2).Error analysis of numerical integration methods. Comparison of Cowell's method, Enke"smethod and variation-of-parameters in terms of accuracy and convenience. FORTRANprogramming of integration methods. Student programming and solution of trajectory problems.

673(Elec.-Comp. Eng. 673) (Nuc. Eng. 673). Topics in Theoretical Plasma Physics.Prerequisite: Nuc. Eng. 57l or Elec.-Comp. Eng. 580 or Aero. Eng. 726. l and II. (3i.This course may be taken for credit more than once.

An advanced course in theoretical plasma physics covering topics of current research interest. Specific content will vary from year to year. Representative topics include: studies ofweakly ionized plasmas with applications to gas lasers; space plasmas; laser fusion plasmas:and nonlinear plasma dynamics and plasma turbulence.

676. Optimal Guidance. Prerequisite: Aero. Eng. 575 or C.I.C.E. 540. (3).Optimum guidance modes, including the path-adaptive mode, iterative guidance mode, andneighboring optimum guidance. The effect of normality and conjugate points in guidanceanalysis. Applications to space missions involving high thrust, low thrust, impulsive thrustand re-entry. Necessary conditions for singular guidance problems. Future needs in guidancetheory.

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721. Turbulence. Prerequisite: Aero. Eng. 620. (3).Physical and mathematical description of turbulence in boundary layers, wakes, jets, and

behind grids, turbulent fields; theories for turbulent mass, momentum, heat, and particlediffusion.




730. Energy Transfer in High Temperature Gas Flows. Prerequisite: Aero. Eng. 532 and 620.

(3).Energy transfer processes as related to high temperature gas flows; unsteady heat conduction,convection in non-reactive and reactive flows, transport properties, ablation and gaseousradiation.







880. Seminar in Space Technology. Prerequisite: permission of instructor. (To be arranged).

990. Dissertation/ Pre-Candidate. I and II (2-8); Ula and III* (1-4).Election for dissertation work by doctoral student not yet admitted to status as a Candidate.


a doctoral candidate. I and II (8); IIIa and IIlfc (4).Election for dissertation work by doctoral student who has been admitted to status as a

Candidate.

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Department Office: 302 Aerospace Engineering Building, phone (313) 764-3310

See Page 125 for statement on Course Equivalence.

100. Introduction to Flight. (2).An introduction to the physical principles of flight within the atmosphere and in space, to the


200. General Aeronautics and Astronautics. Prerequisite: Physics 140. 1 and II. (2).Introduction to aerospace engineering. Elementary problems designed to orient the student in

the program of aerospace engineering, together with a discussion of the current state ofaerospace developments and the role of the engineer. Recitations and demonstrations.

300. Elements of Space Science and Technology. Prerequisite: Math. 216; Physics 240. (3).

Scientific and technological aspects of current space flights, mission goals, the space environment, vehicle characteristics, performance, and flight paths. Mission support: communications, power, computers, etc. Open to all University students.

301. Laboratory I. Prerequisite: preceded or accompanied by Elec.-Comp Eng. 314. 1 and 11.

(2).'

Comprehensive series of lectures and experiments designed to introduce the student to basic

principles of electronics, circuit analysis, transducers, modern laboratory instrumentation,experimental methods, and data analysis. Experiments involve simple measurement and


302. Laboratory II. Prerequisite: Aero. Eng. 301. I and II. (2).Continuation of the material in Aero. Eng. 301.

314(Appl. Mech. 314). Structural Mechanics I. Prerequisite: Appl. Mech. 211. I and II. (3).Review of plane states of stress and strain. Basic equations of plane elasticity and selected

problems; failure criteria and applications; energy principles of structural theory; thin-walledbeam theory.

320. Compressible Flow and Propulsion I. Prerequisite: Mech. Eng. 235. I and II. (3).First part of an aerodynamics sequence designed to study the fundamental principles and theirapplications; physical nature of fluids, conservation laws; nozzles and diffusers; shockwaves; applications to jet propulsion and other problems.


Second part of an aerodynamics sequence designed to study the fundamental principles andtheir applications; viscous effects in laminar and turbulent flows; boundary layer theory;concepts of instability and transition to turbulent flow; flows under the influence of gravitational and electromagnetic forces.

340. Mechanics of Flight. Prerequisite: Appl. Mech. 240. I and II. (3).Mechanics of a particle applied to the analysis of vehicle flight paths. Rigid body mechanicsapplied to translational and rotational vehicle motion. Analysis of vehicle motion and staticand dynamic stability using perturbation theory.

350(Math. 350). Aerospace Engineering Analysis. Prerequisite: Math. 216. I and 11. (3).Formulation and solution of some of the elementary initial- and boundary-value problemsrelevant to aerospace engineering. Application of Fourier series, separation of variables, andvector analysis to problems of forced oscillations, wave motion, diffusion, elasticity, andperfect-fluid theory.

380. Undergraduate Seminar. Prerequisite: junior standing. (1).A series of seminars by noted outside speakers designed to acquaint undergraduates with bothcurrent problems and state of the art of the aerospace industry. Will involve a short termproject or paper pertinent to one of the seminar topics.

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411(Appl. Mech. 411) (Civ. Eng. 411) (Nav. Arch. 411). Finite Element Applications. Prerequisite:Eng. 102, Appl. Mech. 211. I. (3).

The application of user oriented finite element computer programs for solving practicalstructural mechanics problems of frames, 2-D and 3-D solids, plates, shells, etc., and

displaying the solutions graphically. Students learn to prepare input data and interpret results.A short introduction to the underlying theory is also presented.

414(Appl. Mech. 414). Structural Mechanics II. Prerequisite: Aero. Eng. 314. I and II. (3).Introduction to plate theory. Stability of structural elements; columns and beam columns;plate in compression and shear; secondary instability of columns. Introduction to matrix


420. Aerodynamics III. Prerequisite: Aero. Eng. 320. and Aero. Eng. 350 or Math. 450. landII. (3).

Third part of an aerodynamic sequence designed to study the fundamental principles and theirapplications; inviscid flows and fundamentals of field theory; generation of airfoil lift; thinairfoil theory; induced drag and finite wings; wave kinematics; two dimensional compressibleflow.



ment procedures.

424. Laminar and Turbulent Transport Processes. Prerequisite: Aero. Eng. 330 or an introductory course in viscous flow. (3).

Turbulent transport processes are important in fluid flows in nature and technology. Elementary statistical concepts; nature of turbulent flow in boundary layers; wakes, jets, and plumes.Turbulent transport of mass, momentum, and heat in above flows and comparison withlaminar transport processes. Eddy viscosity and diffusivity of heat and mass. Qualitativedescription of turbulent buffeting.

430. Propulsion II. Prerequisite: Aero. Eng. 320. I and II. (3).Performance and analysis of flight-propulsion systems including the reciprocating engine-


433. Combustion Processes. Prerequisite: Aero. Eng. 320. (3).Study of combustion processes with appropriate consideration of the fluid mechanics (aero-thermo-chemistry); emphasis placed on the physical understanding, applications, performance, pollution aspects, experimental techniques, and commonality between jet propulsioncombustors, internal combustion engines, and stationary power plants; includes equilibriumconstants, chemical kinetics, flames, explosions, liquid drops, particulate formation.



440. Vehicle Systems Performance. Prerequisite: junior standing. (3).Role of performance in systems analysis; mathematical modeling; identification of constraints, performance parameters, and performance indices. The aircraft performance problem: flight envelope, aerodynamic approximations, available propulsion systems; takeoff,

landing, climb, and range performance. Modern performance optimization techniques. Applications to automobile, high-speed train, and space vehicle performance analysis.

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128 / AEROSAPCE ENGINEERING



449. Principles of Vertical Take-off and Landing Aircraft. Prerequisite: Aero. Eng. 420. (3).Lifting rotor and propellor analysis in vertical and forward flight; ducted fan analysis;helicopter performance analysis; transitional flight problems of VTOL aircraft; stability and

control problems of helicopters and VTOL aircraft.

452(C.I.C.E. 412) (Elec.-Comp. Eng. 412). Engineering Probability and Statistics. Prerequisite:Math. 215. 1 and II. (3).

Basic concepts of probability theory: random variables, probability distributions, averages,moments, characteristic functions, independence. Binomial, Poisson, and Gaussian distributions. Introduction to statistical inference and its applications in engineering, statistics ofmeasurements, confidence intervals, least square fitting of data. C.I.C.E. students may notreceive graduate credit for both C.I.C.E. 412 and C.I.C.E. 512.

454(C.I.C.E. 482) (Elec.-Comp. Eng. 482). Analog Computation. Prerequisite: Math. 216.

(3).Basic theory of analog computers. Analog devices: operational amplifiers, multipliers, function generators. Analog simulation of linear and nonlinear dynamic systems, including ordinary and partial differential equations. Lecture and laboratory.

455(C.I.C.E. 465) (Elec.-Comp. Eng. 465). Computer Graphics Application. Prerequisite:Elec.-Comp. Eng. 270 or I. &O. E. 473 orComp. & Comm. Sci. 374 or C .1 .C .E.461 .(3).

Application of several software packages and display devices for engineering problem solvingand production of computer animated films. Use of Computek, Tektronix, and PDP graphicsterminals for electrical circuit design, interactive data smoothing, production of engineeringgraphs, etc. POLYGRAPHICS and BEFLIX computer animation packages and their use inMTS. Production of 2 or 3 films using graphics terminals.

460. Aerophysics I. Prerequisite: Physics 240, Math. 216. I. (3).Lagrangian and Hamiltonian concepts applied to aerospace engineering problems; principlesof optics related to aeronautical measurements, electromagnetic forces in moving media,radiation processes in gases.

461. Aerophysics II. Prerequisite: Aero. Eng. 460 or Aero. Eng. 464. II. (3).Quantum mechanical concepts in gas dynamics; principles of atomic and molecular spectra,and diagnostics of high energy flows; spectroscopy and application to ionized gases in thelaboratory, upper atmosphere, and interplanetary space; radiative transfer.


An introduction to physical processes in the upper atmosphere; density, temperature, composition, and winds; atmospheric radiation transfer processes and heat balance; the ionosphere; rocket and satellite measurement techniques.


Introduction to operational and experimental measurements of atmospheric parameters.Instrumentation for "in-situ" measurements at the surface and from aerospace vehicles.Remote sensing using electromagnetic radiation and acoustical waves with both passive and

active systems. Analysis of data, error theory, the use of least squares methods and empiricalorthogonal functions, the information content of experimental data.





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467. Aerodynamic Topics in Atmospheric Environment. Prerequisite: Aero. Eng.330orAppl.Mech. 422. (2).


atmospheric tornado. Free convection and hot plumes. Suspension and dispersion of aerosols

in the atmosphere. Free air turbulence.

471. Automatic Control Systems. Prerequisite: Math. 216. I and II. (3).Transient and steady-state analysis of linear control systems; transfer function and state-


the design of autopilots and other modem control systems; introduction to nonlinear controlsystems and phase plane analysis.

472(C.I.C.E. 450) (Elec.-Comp. Eng. 450). Fundamentals of Control Systems. Prerequisite:Appl. Mech. 240, Elec.-Comp. Eng. 310, or Elec.-Comp. Eng. 355, and senior standing.I and II. (3).


transfer function representations. System performance and design criteria: stability, sensitiv

ity, time response. Concept of feedback. Time response of linear control systems. Use ofHurwitz, root-locus, Nyquist and Bode methods for analysis and synthesis of linear controlsystems. Not open to students with credit for Aero. Eng. 471.

473(C.I.C.E. 451) (Elec.-Comp. Eng. 451). Control Systems Laboratory. Prerequisite:C.I.C.E. 450 or Aero. Eng. 471. (2).

Introduction to control system simulation and design. Experiments with physical systems.

Illustration of basic control principles. Design examples and the use ofcomputer design aids.

481. Airplane Design. Prerequisite: senior standing. 1.(4).Power-required and power-available characteristics of aircraft on a comparative basis, calculation of preliminary performance, stability, and control characteristics. Design procedure,including layouts and preliminary structural design. Subsonic and supersonic designs. Emphasis on design techniques and systems approach. Lectures and laboratory.


(4).Design techniques and projects for geophysical, environmental, and earth resources surveys.

Aircraft, sounding rocket, and balloon instruments and payloads as well as vehicle charac

teristics and performance are considered. Student projects bring together in a unified conceptcomponents for sensing (remote and in situ), telemetering, tracking, performance, safety, and

data processing.

483. Aerospace System Design. Prerequisite: senior standing. II. (4).Aerospace system design, analysis and integration. Consideration of launch facilities, booster

systems, spacecraft systems, communications, data processing, and project management.




system designer. Basic principles in the design of space communications and tracking sys

tems, including modulation-demodulation techniques, frequency and time division multiplexing, methods of data storage, system gain considerations, power sources, antennas, propaga

tion, and tracking methods. Application to system problems emphasized.


510(Appl. Mech. 510) (Mech. Eng. 557). Finite Element Methods in Mechanics I. Prerequisite:Aero. Eng. 414(Appl. Mech. 414) or Mech. Eng. 362. I. (3).



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130 / AEROSAPCE ENGINEERING

514(Appl. Mech. 514). Foundations of Structural Mechanics I. Prerequisite: Aero. Eng. 414.

(3).Elements of the analysis of structures. Includes plates of various shapes, loading and boundary conditions, effects of in-plane loading; shells of revolution, cylindrical shells, bendingand membrane theories; plastic analysis of structures, beams, frames, plates; plastic collapsemechanism. Applications of aerospace interest.

515(Appl. Mech. 515). Foundations of Structural Mechanics II. Prerequisite: Aero. Eng. 514.

(3).Behavior of structures in a thermal environment, heat conduction, aerodynamic heating ofhigh speed vehicles, thermal stresses and deflections, thermal instabilities, discussion ofmaterial properties at elevated temperature. Elements of the theory of linear viscoelasticity .

520. Gasdynamics I. Prerequisite: Aero. Eng. 420 or 425. (3).Gasdynamics at an intermediate level: Thermodynamics; the conservation equations; vortic-ity theorems; unsteady one-dimensional flow; the method of characteristics; stationary andmoving shock waves; two-dimensional steady flow including method of small perturbations.

521. Experimental Gasdynamics. Prerequisite: Aero. Eng. 330 and 420. (3).Experimental methods in modem gasdynamics; physical principles and interpretation. Shoppractice and theory of instrument design: mechanics, electronics, and optics. Measurement ofvelocity, pressure, density, temperature, composition, energy and mass transfer in fluids andplasmas. Transducers and laboratory instrumentation in gasdynamic research.

522. Gasdynamics II. Prerequisite: Aero. Eng. 520. (3).The Navier-Stokes equations, including elementary discussion of tensors; exact solutions.Laminar boundary-layer theory ; asymptotic concepts ; solutions for incompressible boundarylayers. Compressible boundary layers; special solutions; transformation of equations; heat



532. Introduction to Gaskinetics and Real Gas Effects. Prerequisite :Aero. Eng. 420. (3).A study of some modern topics of flow problems not covered in the traditional gasdynamics ofideal gases: concepts of gaskinetics, aerodynamics of free molecules, shock transition layer,real gas effects, high temperature effects, multicomponent flows, etc.

535. Rocket Propulsion. Prerequisite: Aero. Eng. 430 or 435. (3).Analysis and performance of liquid and solid propellant rocket powerplants; propellantthermochemistry, heat transfer, system considerations, advanced rocket propulsion techniques.

540(Appl. Mech. 540). Intermediate Dynamics. Prerequisite: Appl. Mech. 240. I. (4).Kinematics of motion, particle dynamics, Lagrange's equations. Rigid body dynamics including Euler's equations, the Poinsot construction, spin stabilization, the rotation matrix. Vibrations of coupled systems, orthogonality relationships, generalized co-ordinates andgeneralized system parameters.

542. Astrodynamics I. Prerequisite: Aero. Eng. 340. I. (3).The study of motion of spacecraft in a vacuum and in the atmosphere with emphasis onpreliminary mission planning. Analysis of trajectories in suborbital, orbital, lunar, and interplanetary operations. Aerodynamic forces and heating characteristics and their effect on the


543. Structural Dynamics. Prerequisite: Aero. Eng. 414 or 540. (3).Natural frequencies and mode shapes of elastic bodies. Nonconservative elastic systems.Structural and viscous damping. Influence coefficient methods for typical flight structures.Response of structures to random and shock loads. Lab demonstration.

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544. Aeroelasticity. Prerequisite: Aero. Eng. 414 or 540. (3).An introduction to aeroelastidty . Vibration and flutter of elastic bodies exposed to fluid flow.Static divergence and flutter of airplane wings. Flutter of flat plates and thin walled cylindersat supersonic speeds. Oscillations of structures due to vortex shedding.


548. Astrodynamics D. Prerequisite: Aero. Eng. 542. (3).Orbit determination. Systems of canonical equations. Perturbation theory with applicationsto the motion of an artificial satellite. Lunar and planetary theories.


Prerequisite: Appl. Mech. 240. (3).Random mechanical inputs; wind buffeting; earthquakes; surface irregularities. Engineeringapplications include response of linear spring-mass system and an elastic beam to single and





Principles of space vehicle, homing and ballistic missiles guidance systems in two and threedimensions. Explicit, linear perturbation, and velocity-to-be gained guidance modes.Mechanization by inertial and other means, including strapped-down and stable-platforminertial systems. Celestial navigation procedures with deterministic and redundant measure

ments. Application of Kalman filtering to recursive navigation theory.



575. Optimization of Space Trajectories. Prerequisite: permission of instructor. II. (i).Necessary and sufficient conditions for ordinary extremum and variational problems, withemphasis on the problem of Bolza. Applications of the calculus of variations to optimal space

trajectories. Problems with control and state variable inequality constraints. Iterative computational methods for two-point boundary-value problems, including the gradient method.



5%. Aurora and Airglow. Prerequisite: permission of instructor. II.fi).Morphology and physics of the aurora and airglow. Emission spectra in the aurora and theiratomic and molecular origin; proton aurora; metastable excitation; calculation of emissionprofiles. Night- and day-glow; pre-dawn and post-twilight enhancements; mid-latitude red

arc; excitation mechanisms.

610(Appl. Mech. 610). Finite Element Methods in Mechanics II. Prerequisite: Aero. Eng.510(Appl. Mech. 510) (Mech. Eng. 557). II. (3).



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621. Dynamics of Compressible Fluids. Prerequisite: Aero. Eng. 520. (3).Theory of characteristics; shock-wave phenomena; interaction problems; hodograph trans

formation; transonic flow.

625. Methods of Theoretical Aerodynamics. Prerequisite: Aero. Eng. 520. (3).Application of methods for solving partial differential equations which arise in aerodynamicsproblems. Subsonic and supersonic wing theory, sound waves, viscous flows, boundary-layertheory, shock waves. Emphasis on the use of fundamental solutions and superposition in

linear problems and asymptotic methods in nonlinear problems. Similarity solutions, characteristics.

627. Continuum Theory of Fluids. Prerequisite: Aero. Eng. 520. (3).Physical concepts underlying the flow of fluids acted upon by stresses arising from viscosityand from electromagnetic and gravity fields. Invariant analysis of stress-strain relations.Maxwell's equations, analysis of electromagnetic stresses and energy dissipation in movingmedia, the equations of motion and energy in a moving fluid, and some solutions of the

complete equations.



651. Computation of Aerospace Trajectories. Prerequisite: Aero. Eng. 546. (2).Error analysis of numerical integration methods. Comparison of Cowell's method, Enke'smethod and variation-of-parameters in terms of accuracy and convenience. FORTRANprogramming of integration methods. Student programming and solution of trajectory problems.

673(Elec.-Comp. Eng. 673) (Nuc. Eng. 673). Topics in Theoretical Plasma Physics.Prerequisite: Nuc. Eng. 571 or Elec.-Comp. Eng. 580 or Aero. Eng. 726. I and II. (3).This course may be taken for credit more than once.

An advanced course in theoretical plasma physics covering topics of current research interest. Specific content will vary from year to year. Representative topics include: studies ofweakly ionized plasmas with applications to gas lasers; space plasmas; laser fusion plasmas;and nonlinear plasma dynamics and plasma turbulence.

676. Optimal Guidance. Prerequisite: Aero. Eng. 575 or C.I.C.E. 540. (3).Optimum guidance modes, including the path-adaptive mode, iterative guidance mode, andneighboring optimum guidance. The effect of normality and conjugate points in guidanceanalysis. Applications to space missions involving high thrust, low thrust, impulsive thrustand re-entry . Necessary conditions for singular guidance problems. Future needs in guidancetheory.

721. Turbulence. Prerequisite: Aero. Eng. 620. (3).Physical and mathematical description of turbulence in boundary layers, wakes, jets, andbehind grids, turbulent fields; theories for turbulent mass, momentum, heat, and particlediffusion.

726. Introduction to Plasma Dynamics. Prerequisite: permission of instructor. (3).Physical properties of a plasma; particle orbit theory; collective phenomena in a plasma;kinetic equations for a plasma; instabilities; transport phenomena and derivation of the

magnetohydrodynamic equations.



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730. Energy Transfer tn High Temperature Gas Flows. Prerequisite: A ero. Eng. 532 and 620.

(3).Energy transfer processes as related to high temperature gas flows; unsteady heat conduction,convection in non-reactive and reactive flows, transport properties, ablation and gaseous

radiation.








990. Dissertation/Pre-Candidate. I and II (2-8); IIia and 1116 (1-4).Election for dissertation work by doctoral student not yet admitted to status as a Candidate.


a doctoral candidate. I and II (8); IIia and 1Mb (4).Election for dissertation work by doctoral student who has been admitted to status as a

Candidate.

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A erospace Engineering

Department Office: 302 Aerospace Engineering Building, phone (313) 764-3310

See Page 121 for statement on Course Equivalence.

100. Introduction to Flight. (2).An introduction to the physical principles of flight within the atmosphere and in space, to the


200. General Aeronautics and Astronautics. Prerequisite: Physics 140. I and II. (2).Introduction to aerospace engineering. Elementary problems designed to orient the student in

the program of aerospace engineering, together with a discussion of the current state of aerospace developments and the role of the engineer. Recitations and demonstrations.

300. Elements of Space Science and Technology. Prerequisite: Math. 216: Physics 240. (3).Scientific and technological aspects of current space flights, mission goals, the space environment, vehicle characteristics, performance, and flight paths. Mission support: communications, power, computers, etc. Open to all University students.

301. Laboratory I. Prerequisite: preceded or accompanied by Elec.-Comp. Eng. 314. landII. (2).

Comprehensive series of lectures and experiments designed to introduce the student to basic

principles of electronics, circuit analysis, transducers, modern laboratory instrumentation,experimental methods, and data analysis. Experiments involve simple measurement and instrumentation problems.

302. Laboratory II. Prerequisite: Aero. Eng. 301. I and II. (2).Continuation of the material in Aero. Eng. 301.

314(Appl. Mech. 314). Structural Mechanics I. Prerequisite: Appl. Mech. 211. I and II. (3).Review of plane states of stress and strain. Basic equations of plane elasticity and selected

problems; failure criteria and applications; energy principles of structural theory; thin- walledbeam theory.

320. Compressible Flow and Propulsion I. Prerequisite: Mech. Eng. 235. I and II. (3).First part ofan aerodynamics sequence designed to study the fundamental principles and theirapplications; physical nature of fluids, conservation laws; nozzles and diffusers; shock waves;

applications to jet propulsion and other problems.

330. Aerodynamics II. Prerequisite: Aero. Eng. 320 or introductory course in fluidmechanics. 1 and II. (3).


their applications; viscous effects in laminar and turbulent flows; boundary layer theory; con

cepts of instability and transition to turbulent flow; flows under the influence of gravitationaland electromagnetic forces.

340. Mechanics of Flight. Prerequisite: Appl. Mech. 240. I and II. (3).Mechanics of a particle applied to the analysis of vehicle flight paths. Rigid body mechanics

applied to translational and rotational vehicle motion. Analysis of vehicle motion and staticand dynamic stability using perturbation theory.

350(Math. 350). Aerospace Engineering Analysis. Prerequisite: Math. 216. I and II. (3).Formulation and solution of some of the elementary initial- and boundary-value problemsrelevant to aerospace engineering. Application of Fourier series, separation of variables, andvector analysis to problems of forced oscillations, wave motion, diffusion, elasticity, and

perfect-fluid theory.

380. Undergraduate Seminar. Prerequisite: junior standing. (1).A series of seminars by noted outside speakers designed to acquaint undergraduates with bothcurrent problems and state of the art of the aerospace industry. Will involve a short term project or paper pertinent to one of the seminar topics.

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390. Directed Study. {To be arranged).Individual study of specialized aspects of aerospace engineering.

411(Appl. Mecb. 411) (Civ. Eng. 411) (Nav. Arch. 411). Finite Element Applications. Prerequisite:Eng. 102. Appl. Mech. 211. I. (3).

The application of user oriented finite element computer programs for solving practical struc

tural mechanics problems of frames. 2-D and 3-D solids, plates, shells, etc.. and displayingthe solutions graphically. Students learn to prepare input data and interpret results. A short in

troduction to the underlying theory is also presented.

414(Appl. Mech. 414). Structural Mechanics II. Prerequisite. Aero. Eng. 3 14. 1 and 11.(3).Introduction to plate theory. Stability of structural elements; columns and beam columns;plate in compression and shear; secondary instability of columns. Introduction to matrix


420. Aerodynamics III. Prerequisite: Aero. Eng. 320. and Aero. Eng. 350 or Math. 450. landII. (3).

Third part of an aerodynamic sequence designed to study the fundamental principles and theirapplications; inviscid flows and fundamentals of field theory; generation of airfoil lift; thin airfoil theory; induced drag and finite wings; wave kinematics; two dimensional compressibleflow.

423. Aero-Acoustics. Prerequisite: Aero. Eng. 320 or a course in compressible flow. (3).Principles of generation, perception, and abatement of sound generated by fluid flows.Elementary acoustics; acoustical response of the human ear. Theory and results of measurement of sound generated by explosions, sonic booms, jets, boundary layers, and flow excited

structural vibrations. Qualitative assessment of techniques and effectiveness of noise abatement procedures.

430. Propulsion II. Prerequisite: Aero. Eng. 320. I and II. (3).Performance and analysis of flight-propulsion systems including the reciprocating engine-propeller, turbojet, turboprop, ramjet, and rocket.

433. Combustion Processes. Prerequisite: Aero. Eng. 320. (3).Study of combustion processes with appropriate consideration of the fluid mechanics (aero-thermo-chemistry); emphasis placed on the physical understanding, applications, performance, pollution aspects, experimental techniques, and commonality between jet propulsioncombustors. internal combustion engines, and stationary power plants; includes equilibriumconstants, chemical kinetics, flames, explosions, liquid drops, particulate formation.

439. Aircraft Propulsion Laboratory. Prerequisite: Aero. Eng. 320. (2).Series of experiments designed to illustrate the general principles of propulsion and to introduce the student to certain experimental techniques in the study of actual propulsive devices,using full-scale or reduced models of the pulsejet, turbojet, ramjet, and rocket motors.

440. Vehicle Systems Performance. Prerequisite: junior standing. (3).Role of performance in systems analysis; mathematical modeling; identification of constraints, performance parameters, and performance indices. The aircraft performance problem: flight envelope, aerodynamic approximations, available propulsion systems; takeoff,landing, climb, and range performance. Modern performance optimization techniques. Applications to automobile, high-speed train, and space vehicle performance analysis.

447. Flight Testing. Prerequisite: Aero. Eng. 340. (2).Theory and practice of obtaining flight-test data on performance and stability of airplanesfrom actual flight tests. No laboratory fee will be charged, but a deposit covering student in

surance and operating expense of the airplane will be required.

449. Principles of Vertical Take-off and Landing Aircraft. Prerequisite: Aero. Eng. 420. (3).Lifting rotor and propellor analysis in vertical and forward flight; ducted fan analysis; helicopter performance analysis; transitional flight problems of VTOL aircraft; stability and controlproblems of helicopters and VTOL aircraft.

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124 IAEROSPACE ENGINEERING

452(C.I.C.E. 412) (Elec.-Comp. Eng. 412). Engineering Probability and Statistics. Prerequisite:Math. 215. 1 and II.fi).

Basic concepts of probability theory: random variables, probability distributions, averages,moments, characteristic functions, independence. Binomial. Poisson. and Gaussian distributions. Introduction to statistical inference and its applications in engineering, statistics ofmeasurements, confidence intervals, least square fitting of data. C.I.C.E. students may not


454(C.I.C.E. 482) (Elec.-Comp. Eng. 482). Analog Computation. Prerequisite: Math. 216. (3).Basic theory of analog computers. Analog devices: operational amplifiers, multipliers, function generators. Analog simulation of linear and nonlinear dynamic systems, including ordinary and partial differential equations. Lecture and laboratory.

455(C.I.C.E. 465) (Elec.-Comp. Eng. 465). Computer Graphics Application. Prerequisite:Elec.-Comp. Eng. 270 or l.&O.E. 473 or Comp.& Comm. Sci. 374 or C.I.C.E. 461. (3).

Application of several software packages and display devices for engineering problem solvingand production of computer animated films. Use of Computek, Tektronix, and PDP graphicsterminals for electrical circuit design, interactive data smoothing, production of engineering

graphs, etc. POLYGRAPH ICS and BEFLIX computer animation packages and their use in

MTS. Production of 2 or 3 films using graphics terminals.

464(A.&O.Sci. 464). Upper Atmospheric Science. Prerequisite: senior or graduate standing ina physical science or engineering. I. (3).

An introduction to physical processes in the upper atmosphere: density , temperature, composition, and winds; atmospheric radiation transfer processes and heat balance; the ionosphere:rocket and satellite measurement techniques.


Introduction to operational and experimental measurements of atmospheric parameters. Instrumentation for "in-situ" measurements at the surface and from aerospace vehicles. Remote sensing using electromagnetic radiation and acoustical waves with both passive and ac

tive systems. Analysis of data, error theory, the use of least squares methods and empirical orthogonal functions, the information content of experimental data.

471. Automatic Control Systems. Prerequisite: Math. 216. I and II. (3).Transient and steady-state analysis of linear control systems; transfer function and state-


the design of autopilots and other modern control systems; introduction to nonlinear controlsystems and phase plane analysis.

472(C.I.C.E. 450) (Elec.-Comp. Eng. 450). Fundamentals of Control Systems. Prerequisite:Appl. Mech. 240. Elec. -Comp. Eng. 310. or Elec-Comp. Eng. 355. and senior standing.I and II. (3).


transfer function representations. System performance and design criteria: stability, sensitiv

ity, time response. Concept of feedback. Time response of linear control systems. Use ofHurwitz. root-locus, Nyquist and Bode methods for analysis and synthesis of linear controlsystems. Not open to students with credit for Aero. Eng. 471.

473(C.I.C.E. 451) (Elec.-Comp. Eng. 451). Control Systems Laboratory. Prerequisite:C.I.C.E. 450 or Aero. Eng. 471. (2).

Introduction to control system simulation and design. Experiments with physical systems. Illustration of basic control principles. Design examples and the use ofcomputer design aids.

481. Airplane Design. Prerequisite: senior standing. l.(4).Power-required and power-available characteristics of aircraft on a comparative basis, calcu

lation of preliminary performance, stability, and control characteristics. Design procedure,including layouts and preliminary structural design. Subsonic and supersonic designs. Emphasis on design techniques and systems approach. Lectures and laboratory.

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(4).Design techniques and projects for geophysical, environmental, and earth resources surveys.Aircraft, sounding rocket, and balloon instruments and payloads as well as vehicle charac

teristics and performance are considered. Student projects bring together in a unified conceptcomponents for sensing (remote and in situ), telemetering, tracking, performance, safety, and

data processing.

483. Aerospace System Design. Prerequisite: senior standing. II. (4).Aerospace system design, analysis and integration. Consideration of launch facilities, boostersystems, spacecraft systems, communications, data processing, and project management.






graduates.

510(Appl. Mech. 510) (Mech. Eng. 557). Finite Element Methods in Mechanics I. Prerequisite:Aero. Eng. 414(Appl. Mech. 414) or Mech. Eng. 362. I. (3).



514(Appl. Mech. 514). Foundations of Structural Mechanics I. Prerequisite: Aero. Eng. 414.

(3).Elements of the analysis of structures. Includes plates of various shapes, loading and boundary conditions, effects of in-plane loading; shells of revolution, cylindrical shells, bending

and membrane theories; plastic analysis of structures, beams, frames, plates; plastic collapsemechanism. Applications of aerospace interest.

515(Appl. Mech. 515). Foundations of Structural Mechanics II. Prerequisite: Aero. Eng. 514.

(3).Behavior of structures in a thermal environment, heat conduction, aerodynamic heating ofhigh speed vehicles, thermal stresses and deflections, thermal instabilities, discussion of ma

terial properties at elevated temperature. Elements of the theory of linear viscoelasticity.

520. Gasdynamics I. Prerequisite: Aero. Eng. 420 or 425. (3).Gasdynamics at an intermediate level: Thermodynamics; the conservation equations; vortic-ity theorems; unsteady one-dimensional flow; the method of characteristics; stationary and

moving shock waves; two-dimensional steady flow including method of small perturbations.

521. Experimental Gasdynamics. Prerequisite: Aero. Eng. 330 and 420. (3).Experimental methods in modem gasdynamics; physical principles and interpretation. Shoppractice and theory of instrument design: mechanics, electronics, and optics. Measurement ofvelocity, pressure, density, temperature, composition, energy and mass transfer in fluids and


522. Gasdynamics II. Prerequisite: Aero. Eng. 520. (3).The Navier-Stokes equations, including elementary discussion of tensors; exact solutions.Laminar boundary-layer theory; asymptotic concepts; solutions for incompressible boundarylayers. Compressible boundary layers; special solutions; transformation of equations; heat


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126 I AEROSPACE ENGINEERING

529. Introduction to Energy Transfer. Prerequisite: Aero. Eng. 330. (3).A survey of energy transfer processes including unsteady heat conduction, convection innon-reactive and reactive flows, and radiation. Aerospace applications, including re-entryheating, ablation, rocket nozzle cooling, radiative transfer, satellite heating, convection indissociated flows.


532. Introduction to Gaskinetics and Real Gas Effects. Prerequisite .Aero. Eng. 420. (3).A study of some modern topics of flow problems not covered in the traditional gasdynamics ofideal gases: concepts of gaskinetics. aerodynamics of free molecules, shock transition layer,real gas effects, high temperature effects, multicomponent flows, etc.

535. Rocket Propulsion. Prerequisite: Aero. Eng. 430 or 435. (3).Analysis and performance of liquid and solid propellant rocket powerplants; propellant ther

mochemistry, heat transfer, system considerations, advanced rocket propulsion techniques.

540(Appi, Mech. 540). Intermediate Dynamics. Prerequisite: Appl. Mech. 240. I. (4).Kinematics of motion, particle dynamics, Lagrange's equations. Rigid body dynamics including Euler's equations, the Poinsot construction, spin stabilization, the rotation matrix.Vibrations of coupled systems, orthogonality relationships, generalized co-ordinates and

generalized system parameters.

542. Astrodynamics I. Prerequisite: Aero. Eng. 340. I. (3).The study of motion of spacecraft in a vacuum and in the atmosphere with emphasis on pre

liminary mission planning. Analysis of trajectories in suborbital, orbital, lunar, and inter

planetary operations. Aerodynamic forces and heating characteristics and their effect on the



Structural and viscous damping. Influence coefficient methods for typical flight structures.

Response of structures to random and shock loads. Lab demonstration.

544. Aeroelasticity. Prerequisite: Aero. Eng. 414 or 540. (3).An introduction to aeroelasticity. Vibration and flutter of elastic bodies exposed to fluid flow.Static divergence and flutter of airplane wings. Flutter of flat plates and thin walled cylindersat supersonic speeds. Oscillations of structures due to vortex shedding.


548. Astrodynamics II. Prerequisite: Aero. Eng. 542. (3).Orbit determination. Systems of canonical equations. Perturbation theory with applicationsto the motion of an artificial satellite. Lunar and planetary theories.

549( Appl. Mech. 549) (Mech. Eng. 549). Random Vibrations of Mechanical Systems. Prerequisite: Appl. Mech. 240. (3).

Random mechanical inputs; wind buffeting; earthquakes; surface irregularities. Engineeringapplications include response of linear spring-mass system and an elastic beam to single and






dimensions. Explicit, linear perturbation, and velocity-to-be gained guidance modes.

Mechanization by inertial and other means, including strapped-down and stable-platform in-

ertial systems. Celestial navigation procedures with deterministic and redundant meas

urements. Application of Kalman filtering to recursive navigation theory.

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574. Control of Aircraft, Missiles, and Space Vehicles. Prerequisite: preceded or accompanied by C.I.C.E. 550. 11. (2).

Analysis and synthesis of autopilots for aircraft and cruise-type missiles. Design of thrust-

vector control systems including effects of elastic structures and fuel sloshing. Attitude con

trol systems for space vehicles; mechanization using jet thrusters and inertia wheels; gravitygradient moments.

575. Optimization of Space Trajectories. Prerequisite: permission of instructor. 11.fi).Necessary and sufficient conditions for ordinary extremum and variational problems, withemphasis on the problem of Bolza. Applications of the calculus of variations to optimal space

trajectories. Problems with control and state variable inequality constraints. Iterative compu

tational methods for two-point boundary-value problems, including the gradient method.



596. Aurora and Airglow. Prerequisite: permission of instructor. 11.fi).Morphology and physics of the aurora and airglow. Emission spectra in the aurora and their

atomic and molecular origin; proton aurora; metastable excitation; calculation of emissionprofiles. Night- and day-glow; pre-dawn and post-twilight enhancements; mid-latitude redarc; excitation mechanisms.

61(XAppl. Mech. 610). Finite Element Methods in Mechanics II. Prerequisite: Aero. Eng.510(Appl. Mech. 510) (Mech. Eng. 557). II. (3).



621. Dynamics of Compressible Fluids. Prerequisite: Aero. Eng. 520. (3).Theory of characteristics; shock-wave phenomena; interaction problems; hodograph transformation; transonic flow.

627. Continuum Theory of Fluids. Prerequisite: Aero. Eng. 520. (3).Physical concepts underlying the flow of fluids acted upon by stresses arising from viscosityand from electromagnetic and gravity fields. Invariant analysis of stress-strain relations.Maxwell's equations, analysis of electromagnetic stresses and energy dissipation in movingmedia, the equations of motion and energy in a moving fluid, and some solutions of the com

plete equations.

628. Statistical Theory of Fluids. Prerequisite: Aero. Eng. 532. (3).A study of the flows of neutral and charged particles from the viewpoint of kinetic theory;Chapman-Enskog theory of transport phenomena, dynamics of rarefied gases, plasma kine

tics without external magnetic field, plasma oscillations and Landau damping, microinsta-bilities, plasma interactions.

632. Gas Flows with Chemical Reactions. Prerequisite: Aero. Eng. 532. 620. (3).Thermodynamics of gas mixtures, chemical kinetics, conservation equations for multicom-ponent reacting gas mixtures. Deflagration and detonation waves. Nozzle flows and boun

dary layers with reaction and diffusion.

673(Elec.-Comp. Eng. 673) (Nuc. Eng. 673). Topics in Theoretical Plasma Physics. Prerequisite: Nuc. Eng. 571 or Elec.-Comp. Eng. 580orAero. Eng. 726. I and 11.fi). This course

may be taken for credit more than once.An advanced course in theoretical plasma physics covering topics of current research interest. Specific content will vary from year to year. Representative topics include: studies ofweakly ionized plasmas with applications to gas lasers; space plasmas; laser fusion plasmas;and nonlinear plasma dynamics and plasma turbulence.

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l2SI AEROSPACE ENGINEERING

721. Turbulence. Prerequisite: Aero. Eng. 620. (3).Physical and mathematical description of turbulence in boundary layers, wakes, jets, and be

hind grids, turbulent fields; theories for turbulent mass, momentum, heat, and particle diffusion.

726. Introduction to Plasma Dynamics. Prerequisite: permission of instructor. (3).Physical properties of a plasma; particle orbit theory ; collective phenomena in a plasma; kine

tic equations for a plasma; instabilities; transport phenomena and derivation of the mag-

netohydrodynamic equations.

729. Special Topics in Gasdynamics. Prerequisite: permission of instructor. ( To be arranged).Advanced topics of current interest.







990. Dissertation Pre-Candidate. I and II (2-8); IIia and lUb (1-4).Election for dissertation work by doctoral student not yet admitted to status as a Candidate.


a doctoral candidate. 1 and II (8); IIia and Ulb (4).Election for dissertation work by doctoral student who has been admitted to status as a Candidate.

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College of Engineering : [catalog]. - Aerospace … open to studentsenrolled in the College of...

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