GATE Aerospace Engineering Flight Mechanics Syllabus

What does the Vertical Speed Indicator (VSI) measure and how?

It measures rate of climb or descent by sensing the rate of change of static pressure, using a calibrated leak (capillary/metering orifice) so the diaphragm responds to how fast static pressure changes; reading is in feet per minute (or m/s).

Why does a VSI exhibit lag, and what is instantaneous VSI (IVSI)?

The calibrated leak takes time to equalize pressures, causing a few seconds' lag after a pitch change. An IVSI adds accelerometer-driven (dashpot) pumps that immediately respond to vertical acceleration, reducing lag.

What two pieces of information does the turn-and-bank (turn coordinator) indicator provide?

The turn needle/aircraft symbol shows rate (and direction) of turn (driven by a gyroscope via precession), and the inclinometer ball shows whether the turn is coordinated (slip or skid).

In the turn-and-bank indicator, what do ball-to-the-inside and ball-to-the-outside indicate?

Ball to the inside indicates a slip (too little rate of turn / too much bank, insufficient rudder); ball to the outside indicates a skid (too much rate of turn / too little bank, excess rudder). A centred ball means coordinated flight.

Define a standard-rate turn and the turn rate it corresponds to.

A standard-rate (rate-one) turn is $3^\circ$ per second, completing a $360^\circ$ turn in 2 minutes; the turn coordinator's index marks are calibrated to it.

Define the angle of attack $\alpha$.

It is the angle between the chord line of the wing/airfoil and the direction of the relative wind (freestream velocity vector); it largely governs the lift coefficient.

Define the sideslip angle $\beta$.

It is the angle between the aircraft's velocity vector and its plane of symmetry (the $x$-$z$ plane): $\beta = \sin^{-1}\!\left(\dfrac{v}{V}\right)$, where $v$ is the lateral velocity component and $V$ the total speed. Nonzero $\beta$ means the relative wind has a sideways component.

How does lift coefficient vary with angle of attack below stall, and what defines the stall?

Below stall, $C_L$ increases approximately linearly with $\alpha$: $C_L = C_{L\alpha}(\alpha - \alpha_{L=0})$. Stall occurs at the critical angle of attack where $C_L$ reaches $C_{L,max}$, beyond which the flow separates and lift drops sharply.

State the definitions of the lift, drag, and pitching-moment coefficients.

$$C_L = \frac{L}{\tfrac{1}{2}\rho V^2 S}, \quad C_D = \frac{D}{\tfrac{1}{2}\rho V^2 S}, \quad C_M = \frac{M}{\tfrac{1}{2}\rho V^2 S\,c}$$ where $S$ is reference (wing) area and $c$ the mean chord.

Resolve the resultant aerodynamic force into its components relative to the relative wind.

The component perpendicular to the relative wind is lift $L$; the component parallel to (and opposing) the relative wind is drag $D$. The resultant $R = \sqrt{L^2 + D^2}$.

List the four forces acting on an airplane in steady level flight and the equilibrium conditions.

Lift $L$, weight $W$, thrust $T$, and drag $D$. In steady level flight: $L = W$ and $T = D$ (all forces balanced, zero net moment).

Which control surface produces roll, and how does it generate a rolling moment?

Ailerons. They deflect asymmetrically (one up, one down) on opposite wings, changing each wing's lift differentially, creating a net rolling moment about the longitudinal axis.

What is adverse yaw and how does it arise during a roll?

When ailerons deflect, the down-going (more-lift) wing also has more induced drag, yawing the nose away from the intended turn direction; it is countered with coordinated rudder, differential ailerons, or Frise ailerons.

Which control surface produces pitch, and how?

The elevator (on the horizontal stabilizer). Deflecting it changes the tail's lift, producing a pitching moment about the aircraft's centre of gravity (lateral axis), raising or lowering the nose.

Which control surface produces yaw, and how?

The rudder (on the vertical stabilizer). Deflecting it generates a side force on the tail, creating a yawing moment about the vertical axis, swinging the nose left or right.

Define static longitudinal stability and the sign condition for it.

It is the tendency to return toward trim after a pitch disturbance. The condition is $\dfrac{dC_M}{d\alpha} < 0$ (with $C_{M0} > 0$ for trim at positive lift): a nose-up disturbance must produce a restoring nose-down moment.

What is the neutral point and how does it relate to the static margin?

The neutral point is the CG location where $\dfrac{dC_M}{d\alpha} = 0$ (neutral longitudinal stability). Static margin $= \dfrac{x_{NP} - x_{CG}}{c}$; a positive static margin (CG ahead of neutral point) means the aircraft is statically stable.

What is the aerodynamic centre of an airfoil and its significance?

The point about which the pitching moment coefficient is independent of angle of attack ($\frac{dC_M}{d\alpha}=0$ there). For thin subsonic airfoils it is near the quarter-chord ($0.25c$); it is the natural reference for moment data.

What is the centre of pressure, and how does it differ from the aerodynamic centre?

The centre of pressure is the point where the resultant aerodynamic force effectively acts (zero moment there); it moves with angle of attack. The aerodynamic centre is fixed (about $0.25c$) and has a constant (generally nonzero) moment.

Distinguish parasite drag and induced drag.

Parasite drag (skin friction + pressure/form + interference) rises with speed: $\propto V^2$. Induced drag (due to lift/wingtip vortices) falls with speed: $\propto 1/V^2$. Total drag is minimized where the two are equal.

Give the expression for the induced drag coefficient of a finite wing.

$$C_{D,i} = \frac{C_L^2}{\pi e\, AR}$$ where $AR$ is aspect ratio and $e$ is the Oswald span efficiency factor; higher aspect ratio reduces induced drag.

Define aspect ratio of a wing.

$$AR = \frac{b^2}{S} = \frac{b}{\bar{c}}$$ where $b$ is span, $S$ the planform area, and $\bar c$ the mean chord. High AR wings have lower induced drag.

What is the stall speed formula in level flight?

$$V_{stall} = \sqrt{\frac{2W}{\rho S\, C_{L,max}}}$$ the minimum speed at which lift equals weight at maximum lift coefficient.

Define the Mach number and the speed regimes it delineates.

$$M = \frac{V}{a}, \quad a = \sqrt{\gamma R T}$$ Regimes: subsonic ($M<0.8$), transonic ($0.8<M<1.2$), supersonic ($1.2<M<5$), hypersonic ($M>5$); $a$ is the local speed of sound.

How are lift and bank angle related in a steady, coordinated level turn?

The load factor $n = \dfrac{L}{W} = \dfrac{1}{\cos\phi}$, where $\phi$ is the bank angle; lift must exceed weight to provide centripetal force, so steeper banks demand more lift and increase stall speed by $\sqrt{n}$.

What is the Reynolds number and its physical significance in aerodynamics?

$$Re = \frac{\rho V L}{\mu} = \frac{V L}{\nu}$$ the ratio of inertial to viscous forces; it governs boundary-layer behaviour (laminar vs turbulent) and flow similarity.

State Bernoulli's equation for steady, incompressible, inviscid flow.

$$p + \tfrac{1}{2}\rho V^2 + \rho g z = \text{constant}$$ along a streamline; for horizontal flow, total (stagnation) pressure $p_0 = p + \tfrac{1}{2}\rho V^2$.

What is a trim tab and its purpose?

A small auxiliary surface on a primary control surface that, when set, holds the control surface at a position to maintain a desired attitude with zero pilot stick force, relieving control loads (e.g. elevator trim for level flight).

What is dihedral and which stability does it primarily provide?

Dihedral is the upward angle of the wings from the horizontal when viewed from the front. It provides lateral (roll) stability: a sideslip produces a restoring rolling moment that levels the aircraft.

Compare conventional, canard, and tailless (flying-wing) airplane configurations.

Conventional has the horizontal stabilizer aft of the wing (downward trimming load); canard places a foreplane ahead of the wing (lifting, can avoid main-wing stall); tailless/flying-wing has no separate horizontal tail, using wing reflex/sweep and elevons for pitch trim and control.

What is the static source error (position error) affecting the pitot-static instruments, and which instruments are influenced?

It is the error from imperfect sensing of true static pressure due to local airflow at the static port (varies with airspeed/AoA). It affects all pitot-static instruments: the altimeter, ASI, and VSI, and is corrected when converting IAS to CAS.