EASA ATPL 081 Principles of Flight cheat sheet

ISA sea level: 1013.25 hPa, 15 °C, density 1.225 kg/m³; troposphere lapse rate 1.98 °C per 1000 ft up to 36 090 ft (11 km), then isothermal to 20 km.

Density ratio σ = ρ/ρ0; for a given IAS, TAS = IAS/√σ, so TAS exceeds IAS at altitude for the same dynamic pressure.

Bernoulli along a streamline (incompressible): p + ½ρV² = constant; static pressure falls where velocity rises, and total pressure is unchanged in ideal flow.

Continuity: A1V1 = A2V2 for incompressible flow; mass flow ρAV is constant in a streamtube, so a narrowing streamtube accelerates the flow.

Dynamic pressure q = ½ρV²; it is the pressure available to generate lift and is the quantity IAS measures.

Venturi/streamtube: as area decreases, V increases, static pressure drops; a divergent duct slows flow and raises static pressure.

Two-dimensional flow assumes infinite span so spanwise flow is zero; real finite wings add tip effects and induced downwash.

Total pressure = static + dynamic; a pitot-static system measures the difference, and blockage or position error corrupts the reading.

Reynolds number Re = ρVc/μ; higher Re means relatively thinner boundary layer and later transition and separation.

Lift L = CL ½ρV²S; drag D = CD ½ρV²S; CL and CD are dimensionless and depend on angle of attack, camber, Re and Mach.

Aerofoil pressure distribution: upper surface suction dominates lift; the centre of pressure moves forward as angle of attack increases toward the stall.

Boundary layer: laminar flow has low skin friction but separates easily; turbulent flow has higher friction but resists adverse pressure gradients.

Transition is promoted by high Re, roughness and positive pressure gradient; separation occurs where the adverse gradient is too strong for the boundary layer to stay attached.

Stall occurs at the critical angle of attack (typically 15–18° for simple aerofoils) and is largely independent of weight, speed and density.

At the stall, CL peaks and then falls; the centre of pressure moves aft abruptly, producing a pitch-down (or, on some swept wings, pitch-up) tendency.

Drag components: profile (form + skin friction) and induced; total CD = CD0 + kCL², minimum drag occurs where parasite and induced drag are equal.

Lift curve slope: CL increases linearly with angle of attack up to the stall; camber shifts the zero-lift angle negative and raises CL at a given angle.

Leading-edge roughness or ice reduces maximum CL and lowers the stall angle; a wing stalls at a lower angle of attack when contaminated.

Induced drag coefficient CDi = CL²/(πAe) where A = b²/S is aspect ratio and e the Oswald efficiency; higher aspect ratio gives less induced drag.

Elliptical spanwise lift distribution gives minimum induced drag for a given span; taper approximates it but real wings carry more load near the root.

Sweep delays the onset of compressibility effects: effective Mach normal to the leading edge is M cos Λ, raising critical Mach number.

Sweep reduces lift-curve slope and increases stall speed; swept wings tend to pitch up at the stall and have strong tip stall and spanwise flow.

Dihedral produces a sideslip-induced rolling moment (dihedral effect) that contributes lateral static stability; anhedral is used on some high-wing or swept designs to reduce excessive stability.

Wingtip devices (winglets, fences) weaken tip vortices and reduce induced drag, effectively raising span efficiency without increasing span.

Flaps increase CLmax and camber, and add drag; Fowler flaps also increase wing area. Slats re-energise the upper-surface flow and raise the stall angle.

Leading-edge devices (slats, Krueger flaps) delay stall; trailing-edge flaps (plain, split, slotted, Fowler) raise CL and CD, with slotted flaps giving the largest CL gain.

Washout (reduced incidence at the tip) promotes root-first stall, preserving aileron effectiveness and improving stall warning.

Steady level flight: lift = weight, thrust = drag; in a climb, lift is slightly less than weight and thrust balances drag plus the weight component.

Load factor n = L/W; in a level turn n = 1/cos φ, so a 60° bank gives n = 2 and stall speed rises by √n.

Turn radius r = V²/(g tan φ); rate of turn ω = g tan φ / V, so higher speed increases radius and reduces rate for a given bank.

Stall speed in a turn Vs(n) = Vs √n; the aeroplane stalls at the same angle of attack regardless of bank, but at a higher speed.

Gust load increment Δn = ρ V a U /(2 W/S) approximately; a sharp-edged gust produces a load rise proportional to speed and gust velocity and inversely to wing loading.

Climb gradient = (T − D)/W; best angle of climb (Vx) maximises height gained per distance, best rate (Vy) maximises height per time.

In a steady glide, tan γ = D/L, so the flattest glide occurs at maximum L/D; headwind reduces range and increases the required glide angle.

Manoeuvring speed VA is the speed at which full deflection of one primary control reaches the limit load factor without structural damage; it decreases with weight.

Load factor limits: typically +2.5/−1.0 g for utility and +3.8/−1.5 g for aerobatic categories; the V-n diagram bounds speed and load combinations.

Static stability: the initial tendency to return to equilibrium; positive static stability requires a restoring moment, and dynamic stability adds damping of the resulting oscillation.

Longitudinal static stability requires the centre of gravity forward of the neutral point; the static margin is the distance between them as a fraction of mean aerodynamic chord.

The tailplane provides a negative (downward) lift contribution in most conventional layouts, so aft CG reduces stability and increases trim drag.

Dihedral effect gives lateral static stability: sideslip produces a rolling moment that tends to level the wings; too much dihedral causes Dutch roll and spiral instability.

Directional static stability is provided by the fin and rear fuselage; sideslip produces a yawing moment that weathercocks the aircraft into the relative wind.

Dutch roll is a coupled yaw-roll oscillation; it is dynamically stable if damped, and yaw dampers are fitted to meet handling requirements.

Spiral divergence is a slow, weakly damped roll-yaw mode; it is normally countered by pilot or autopilot input rather than by design damping.

Phugoid is a long-period, low-damping oscillation of speed and altitude at nearly constant angle of attack; it is usually lightly damped and easily controlled.

Short-period pitch oscillation is heavily damped and high frequency; inadequate short-period damping is a certification concern.

Primary controls: ailerons (roll), elevator (pitch), rudder (yaw); secondary controls: flaps, slats, spoilers/speedbrakes, trim tabs.

Adverse yaw: the descending aileron produces more induced drag, yawing the nose away from the turn; differential ailerons and rudder input counter it.

Spoilers spoil lift and increase drag; they are used for roll control (spoilerons), speedbrake function and lift dumping on landing.

Trim tabs move in the opposite direction to the control surface, reducing the hinge moment needed to hold a deflection; they do not change the aircraft's stability.

Flap extension lowers the stall speed and increases CLmax, but adds drag and produces a nose-down pitching moment; retraction reduces drag and increases stall speed.

Slats increase CLmax and stall angle by re-energising the upper-surface boundary layer; automatic slats extend at high angle of attack and low speed.

Fly-by-wire replaces mechanical linkages with electrical signalling and computers; it enables envelope protection, normal/alternate/direct law reversion and C* or g-command laws.

Control surface effectiveness falls with increasing dynamic pressure; at high speed, reduced deflection is needed to avoid overstressing the structure.

Elevator authority is limited at aft CG and at high altitude; pitch trim and Mach trim compensate for speed and Mach-related pitching moments.

A stall is an angle-of-attack exceedance, not a speed; any speed, attitude or power setting can produce a stall if the critical angle is exceeded.

Recognition cues: stall warning horn or stick shaker, buffet, reduced control effectiveness, nose drop or wing drop, and loss of altitude.

Recovery: reduce angle of attack by moving the control column forward, level the wings with coordinated rudder, then apply power and recover smoothly from the descent.

A spin requires both stall and yaw: one wing stalls more deeply than the other, producing autorotation about a vertical axis with a steep, low-speed descent.

Spin phases: incipient, fully developed and recovery; the autorotation is sustained by the differential lift and drag of the two wings.

Standard spin recovery: close the throttles, neutralise ailerons, apply full opposite rudder, push the column forward to break the stall, then centralise controls and recover.

Aileron use during a spin can aggravate autorotation; the recovery relies on anti-spin rudder and unstalling the wing.

Prevention: maintain speed above the stall margin, limit bank and load factor, avoid crossed controls and uncoordinated flight, and respect the CG limit.

Wing drop at the stall is countered by rudder, not aileron; aileron deflection increases the angle of attack on the descending wing and may deepen the stall.

Speed of sound a = √(γRT); in the ISA troposphere it falls with temperature, from about 340 m/s at sea level to about 295 m/s at the tropopause.

Mach number M = TAS/a; local Mach on the wing exceeds freestream Mach where the flow accelerates over the upper surface.

Critical Mach number Mcrit is the freestream Mach at which local flow first reaches Mach 1; it is lowered by thickness, camber and lift.

At M > Mcrit, shock waves form; the shock causes a pressure rise, boundary-layer separation and a large drag rise (wave drag) near M = 1.

Mach buffet is caused by shock-induced separation; it occurs at high altitude and high Mach, and the buffet boundary limits the flight envelope.

Tuck-under (Mach tuck) is a nose-down pitching moment as the centre of pressure moves aft behind the shock; Mach trim or a Mach trim system counters it.

Sweep, thin aerofoils, area ruling and supercritical sections raise Mcrit and reduce wave drag.

Above M = 1, control effectiveness and stability change; shock-induced separation can cause control reversal or loss of elevator effectiveness.

Coffin corner: at high altitude the low-speed buffet (stall) and high-speed buffet boundaries converge, narrowing the usable speed range.

Thrust T = ṁ(Vj − V0); propeller efficiency η = (thrust × TAS)/shaft power, and it peaks at a design advance ratio.

Advance ratio J = V/(nD); blade angle and advance ratio together determine angle of attack of the blade element and hence thrust and efficiency.

Slip is the difference between geometric pitch speed and actual speed; effective pitch is less than geometric pitch because air is accelerated rearward.

Blade angle increases from root to tip so that the helical path gives a near-constant angle of attack along the blade; twist is built into the blade.

Constant-speed propeller: a governor varies blade angle to hold selected rpm; as speed rises, blade angle increases to absorb the power.

Fixed-pitch propeller: rpm rises with speed, so at high TAS the blade angle of attack falls and efficiency drops; a climb propeller favours low speed.

Asymmetric blade effect (P-factor): at high angle of attack the descending blade takes a larger bite, producing a yawing moment toward the descending-blade side.

Propeller slipstream corkscrews around the fuselage and adds a yawing and pitching effect, most noticeable at high power and low speed.

Windmilling drag and reverse thrust: coarse or reversed blade angles convert the propeller into a large drag source, used for descent and landing roll.

V speeds: VNE never exceed, VNO max structural cruising, VA manoeuvring, VFE flap extend, VLE/VLO gear, VS stall, VMC minimum control speed.

VA decreases with weight; it is the speed above which a full control deflection can overstress the structure, so it is not a fixed value.

VNE is a structural and flutter limit; it is marked by the red radial on the ASI, and VNO is the top of the green arc.

The V-n diagram: limit load factor and speed define the manoeuvring envelope; gust lines cut across it and define the gust envelope.

Wake turbulence: generated by wingtip vortices, strongest when heavy, clean and slow; it sinks and drifts with wind, so stay above and upwind of the preceding aircraft.

Vortex behaviour: vortices sink about 100–150 ft per minute and level off a few hundred feet below the flight path; they persist longest in stable, light-wind conditions.

Windshear: a sudden change of wind speed or direction; a decreasing headwind or increasing tailwind causes a loss of airspeed and lift, so apply full power and pitch to the flight director or attitude.

Microburst and downburst produce severe low-level windshear; escape by maximum thrust, wings level, and not chasing the airspeed indicator.

VMC is the minimum control speed in the air with the critical engine failed; below it, full rudder cannot maintain heading.