# GATE Aerospace Engineering Syllabus

## Subject Code: AE

### Course Structure

Sections/Units Topics
Section A Engineering Mathematics
Topics (Core)
1 Linear Algebra
2 Calculus
3 Differential Equations
Topics (Special)
1 Fourier Series
2 Laplace Transforms
3 Numerical Methods for Linear and Nonlinear Algebraic Equations
4 Numerical Integration
5 Differentiation
Section B Flight Mechanics
Topics (Core)
1 Basics
2 Airplane performance
3 Static stability
Topics (Special)
1 Dynamic stability
2 Euler Angles
3 Equations of Motion
4 Aerodynamic Forces and Moments
5 Stability & Control Derivatives
6 Decoupling of Longitudinal and Lateral-Directional Dynamics
7 Longitudinal Modes
8 Lateral-Directional Modes
Section C Space Dynamics
Topics (Core)
1 Central Force Motion
2 Determination of Trajectory
3 Orbital Period in Simple Cases
Topics (Special)
1 Orbit Transfer
2 In-plane and Out-of-Plane
Section D Aerodynamics
Topics (Core)
1 Basic Fluid Mechanics
2 Airfoils and wings
3 Compressible Flows
Topics (Special)
1 Elementary Ideas of Viscous Flows Including Boundary Layers
2 Wind Tunnel Testing
3 Measurement and Visualization Techniques
Section E Structures
Topics (Core)
1 Strength of Materials
2 Flight Vehicle Structure
3 Structural Dynamics
Topics (Special)
1 Vibration of Beams
2 Theory of Elasticity
3 Equilibrium and compatibility equations, Airy’s stress function
Section F Propulsion
Topics (Core)
1 Basics
2 Thermodynamics of Aircraft Engines
3 Axial Compressors
4 Axial Turbines
5 Centrifugal Compressor
6 Rocket Propulsion
No Special Topic
NoteIn each of the following subjects the topics have been divided into two categories – Core Topics and Special Topics. The corresponding sections of the question paper will contain 90% of their questions on Core Topics and the remaining 10% on Special Topics.

### Course Syllabus

Section A: Engineering Mathematics

Core Topics

Unit 1: Linear Algebra

• Vector algebra
• Matrix algebra
• Systems of linear equations
• Rank of a matrix
• Eigenvalues and eigenvectors

Unit 2: Calculus

• Functions of single variable
• Limits
• Continuity and differentiability
• Mean value theorem
• Chain rule
• Partial derivatives
• Maxima and minima
• Divergence and curl
• Directional derivatives
• Integration −
• Line
• surface and volume integrals
• Theorems of Stokes
• Gauss and Green

Unit 3: Differential Equations

• First order linear and nonlinear differential equations
• Higher order linear ODEs with constant coefficients
• Partial differential equations and separation of variables methods

Section B: Flight Mechanics

Core Topics

Unit 1: Basics

• Atmosphere −
• Properties
• Standard atmosphere
• Classification of aircraft
• Airplane (fixed wing aircraft) configuration and various parts

Unit 2: Airplane performance

• Pressure altitude −
• Equivalent
• Calibrated
• Indicated Air Speeds
• Primary flight instruments −
• Altimeter
• ASI
• VSI
• Turn-bank indicator
• Drag polar
• Takeoff and landing
• Absolute and service ceiling
• Cruise
• cruise climb
• Endurance or loiter
• Turning flight
• V-n diagram
• Winds −
• Tail
• Cross winds

Unit 3: Static stability

• Angle of attack, sideslip
• Roll, pitch & yaw controls
• Longitudinal stick fixed & free stability
• Horizontal tail position and size
• Directional stability
• Vertical tail position and size
• Dihedral stability
• Wing dihedral
• Sweep & position
• Hinge moments, stick forces

Section C: Space Dynamics

Core Topics

• Central force motion
• Determination of trajectory
• Orbital period in simple cases

Section D: Aerodynamics

Core Topics

Unit 1: Basic Fluid Mechanics

• Conservation laws −
• Mass
• Momentum (Integral and differential form)
• Potential flow theory −
• Sources
• Sinks
• Doublets
• Line vortex and their superposition
• Viscosity −
• Reynold's number

Unit 2: Airfoils and wings

• Airfoil nomenclature
• Aerodynamic coefficients −
• Lift
• Drag
• Moment
• Kutta-Joukoswki theorem −
• Thin airfoil theory
• Kutta condition
• Starting vortex
• Finite wing theory
• Induced drag
• Prandtl lifting line theory
• Critical and drag divergence Mach number

Unit 3: Compressible Flows

• Basic concepts of compressibility
• Conservation equations
• One dimensional compressible flows
• Fanno flow
• Rayleigh flow
• Isentropic flows
• Normal and oblique shocks
• Prandtl-Meyer flow
• Flow through nozzles and diffusers

Section E: Structures

Core Topics

• Strength of Materials −

• States of stress and strain

• Stress and strain transformation

• Mohr's Circle. Principal stresses

• Three-dimensional Hooke's law

• Plane stress and Strain

• Failure theories −

• Maximum stress

• Tresca

• Von Mises

• Strain energy −

• Castigliano's principles

• Analysis of statically determinate and indeterminate trusses and beams

• Elastic flexural buckling of columns

Unit 2: Flight vehicle structures

• Characteristics of aircraft structures and materials
• Torsion, bending and flexural shear of thin-walled sections

Unit 3: Structural Dynamics

• Free and forced vibrations of undamped and damped SDOF systems
• Free vibrations of undamped 2-DOF systems

Section F: Propulsion

Core Topics

Unit 1: Basics

• Thermodynamics
• Boundary layers and heat transfer and combustion thermochemistry

Unit 2: Thermodynamics of aircraft engines

• Thrust
• Efficiency and engine performance of turbojet
• Turboprop
• Turbo shaft
• Turbofan and ramjet engines
• Thrust augmentation of turbojets and turbofan engines
• Aerothermodynamics of non-rotating propulsion components such as −
• Intakes
• Combustor
• Nozzle

Unit 3: Axial compressors

• Angular momentum
• Work and compression
• Characteristic performance of a single axial compressor stage
• Efficiency of the compressor
• Degree of reaction

Unit 4: Axial turbines

• Axial turbine stage efficiency

Unit 5: Centrifugal compressor

• Centrifugal compressor stage dynamics
• Inducer
• Impeller
• Diffuser

Unit 6: Rocket propulsion

• Thrust equation and specific impulse
• Vehicle acceleration
• Drag
• Gravity losses
• Multi-staging of rockets
• Classification of chemical rockets
• Performance of solid and liquid propellant rockets