GATE AE key terms

A form of deductive reasoning in which a conclusion is drawn from two premises that share a common term. Candidates must judge whether the conclusion necessarily follows from the stated premises.

The skill of reading tables, charts, and graphs to extract numerical facts and compute ratios, percentages, or trends. It tests quick arithmetic and accurate comparison of quantities.

A scalar λ for which a square matrix A and a nonzero vector x satisfy Ax = λx. Eigenvalues reveal natural frequencies, stability, and principal directions of linear systems.

An integral transform that converts a function of time into a function of a complex variable s. It turns linear differential equations into algebraic equations that are easier to solve.

A family of numerical step-by-step schemes for solving ordinary differential equations. The fourth-order version evaluates the slope at four points per step to obtain good accuracy.

A vector calculus result stating that the flux of a vector field through a closed surface equals the volume integral of its divergence. It converts surface integrals into volume integrals.

The angle between the chord line of a wing and the undisturbed relative airflow. Increasing it raises lift until the wing stalls at the critical angle.

The ratio of lift to weight, or of total aerodynamic force to weight, usually expressed in g. It defines the structural loading in manoeuvres and gusts.

The distance between the aircraft centre of gravity and the neutral point, expressed as a fraction of mean aerodynamic chord. A positive margin means the aircraft is statically stable in pitch.

The centre of gravity position at which the aircraft is neutrally stable in pitch, so the slope of pitching moment coefficient with lift coefficient is zero.

A long-period longitudinal oscillation in which the aircraft slowly exchanges kinetic and potential energy while angle of attack stays nearly constant. It is usually lightly damped and easily controlled.

A coupled lateral-directional oscillation combining yaw and roll, typically with a short period. It arises from the interplay of directional and dihedral stability.

A plot of load factor against equivalent airspeed showing the flight envelope and structural limits. It defines the manoeuvring and gust boundaries within which the aircraft must operate safely.

An elliptical transfer orbit tangent to two circular orbits, using two impulsive burns. It is the minimum-energy two-impulse transfer between coplanar circular orbits.

The change in velocity required to perform a manoeuvre, computed from the rocket equation or vis-viva relation. It is the standard currency for comparing mission propulsion costs.

The angle measured at the focus of an orbit from periapsis to the satellite position vector, in the direction of motion. It locates the body along its Keplerian ellipse.

The minimum speed at a given radius that allows a body to coast to infinity without further thrust. For Earth at the surface it is about 11.2 km/s.

The ratio of the Laplace transform of the output to that of the input, with zero initial conditions. It describes the input-output dynamics of a linear time-invariant system.

A pair of graphs showing the magnitude and phase of a system frequency response against logarithmic frequency. Gain and phase margins are read directly from it.

The amount by which the loop gain can be increased before a closed-loop system becomes unstable, measured at the phase crossover frequency. It is expressed in decibels or as a ratio.

The additional phase lag that can be tolerated at the gain crossover frequency before the closed-loop system becomes unstable. It is a direct indicator of damping.

A property of a state-space system meaning that any initial state can be driven to any final state in finite time by some input. It is tested using the rank of the controllability matrix.

A model of a dynamic system using first-order vector differential equations for the state and algebraic equations for the output. It handles multiple inputs and outputs naturally.

A dimensionless ratio of inertial to viscous forces in a flow. It determines whether the boundary layer is laminar or turbulent and controls transition and separation.

The ratio of flow speed to the local speed of sound. It classifies flow as subsonic, transonic, supersonic, or hypersonic and governs compressibility effects.

The thin region next to a solid surface where viscous forces are significant and velocity rises from zero at the wall to the free-stream value. Its state controls skin friction and separation.

A thin, nearly discontinuous region across which supersonic flow decelerates, with abrupt rises in pressure, temperature, and entropy. It may be normal, oblique, or detached.

Drag produced as a by-product of lift, caused by downwash and trailing vortices. It decreases with increasing aspect ratio and grows with the square of the lift coefficient.

An isentropic turning of a supersonic flow through a convex corner, producing a fan of expansion waves. It accelerates the flow and lowers pressure and temperature.

The slope of the linear portion of a stress-strain curve, measuring a material stiffness in tension or compression. Higher values mean less deformation for a given stress.

The point in a beam cross-section through which a transverse shear force must act to produce no twisting. For symmetric sections it lies on an axis of symmetry.

A sudden loss of stiffness and lateral deflection of a slender member under compressive load, occurring below the material yield stress. It depends strongly on length, end conditions, and bending stiffness.

Progressive damage and cracking of a material under repeated or fluctuating stress below the ultimate strength. It is characterised by an S-N curve and a fatigue limit.

A local increase in stress near holes, notches, or abrupt changes in section. It is quantified by a factor Kt and matters most for fatigue and brittle materials.

The thrust produced per unit weight flow rate of propellant, expressed in seconds. It measures propellant efficiency; higher values give more total impulse for the same mass.

The forward force produced by accelerating a fluid rearward. For a jet engine it equals mass flow times velocity increment plus the pressure-area term at the nozzle.

The ratio of mass flow through the fan bypass duct to that through the core engine. High bypass ratios improve propulsive efficiency and reduce fuel burn and noise.

The ratio of compressor exit stagnation pressure to inlet stagnation pressure. It sets the overall pressure ratio and strongly influences thermal efficiency and turbine inlet temperature requirements.

Tsiolkovsky relation giving velocity change as specific impulse times gravitational acceleration times the natural logarithm of initial-to-final mass ratio. It shows why propellant mass fraction dominates rocket performance.