NCAA CPL Principles of Flight cheat sheet

Bernoulli's equation for steady, incompressible, frictionless flow along a streamline: p + ½ρV² + ρgh = constant; accelerating air therefore drops in static pressure.

Continuity equation: A₁V₁ = A₂V₂ for incompressible flow; a streamtube narrowing forces velocity up and static pressure down.

Boundary layer transitions from laminar to turbulent; turbulent layers resist separation better but produce higher skin friction.

Adverse pressure gradient (pressure rising in the direction of flow) thickens and eventually separates the boundary layer; separation causes loss of lift and rise in pressure drag.

Downwash behind a wing tilts the relative wind downward, rotating the lift vector rearward; the rearward component is induced drag.

Reynolds number Re = ρVL/μ compares inertial to viscous forces and determines laminar versus turbulent behaviour at model or full scale.

Aspect ratio AR = b²/S; higher AR reduces induced drag coefficient because C_Di = C_L²/(π·e·AR).

For a cambered aerofoil the zero-lift angle is negative; the lift-curve slope stays near 0.1 per degree until stall.

Equivalent airspeed EAS = TAS·√(ρ/ρ₀); it equals TAS at sea level in ISA conditions and tracks dynamic pressure.

Calibrated airspeed corrects indicated airspeed for position error and instrument error; TAS additionally corrects for density altitude.

True airspeed rises roughly 2% per 1,000 ft for a fixed IAS at constant Mach below the tropopause.

Speed of sound a = √(γRT); in dry air at sea level it is about 661 kt (340 m/s) and falls with temperature, roughly 1 kt per °C.

Mach number M = TAS/a; at a fixed TAS, Mach rises as temperature (and hence a) falls with altitude.

Dynamic pressure q = ½ρV² governs indicated airspeed and structural loads; Mach governs compressibility effects.

Overspeed in the low-altitude regime is limited by VMO (IAS); at high altitude the limit is MMO, and the crossover point defines the corner speed.

Total temperature exceeds static temperature by T₀/T = 1 + 0.2M²; ram rise matters for turbine-engine and airframe temperature limits.

Two-dimensional flow describes an infinite-span aerofoil: section lift coefficient depends only on angle of attack and camber.

Three-dimensional flow adds spanwise pressure gradients; air escapes around the tips, creating tip vortices and downwash.

Elliptical spanwise lift distribution minimises induced drag for a given span and total lift.

Washout (reduced incidence at the tip) delays tip stall and preserves aileron effectiveness at high angle of attack.

Wingtip vortices are strongest when heavy, slow and clean; wake turbulence separation distances scale with weight and inversely with speed.

Ground effect reduces induced drag and downwash when height is below about one wingspan; lift increases for a given angle of attack.

Interference between fuselage, nacelles and wing alters local flow; nacelle/wing junctions can generate separation and buffet.

Leading-edge vortices on swept or slender wings generate additional lift at high angle of attack but can burst abruptly, causing pitch-up.

Lift L = C_L·½ρV²·S; for steady level flight lift equals weight, so required C_L rises as speed falls.

Parasite drag D_p = C_Dp·½ρV²·S varies with V²; induced drag varies with 1/V², so total drag is minimum where they are equal.

Minimum drag speed occurs at C_L = √(C_D0/(π·e·AR)); flying slower than this puts the aircraft on the back side of the drag curve.

Lift-to-drag ratio L/D = C_L/C_D is the glide ratio in still air and the measure of aerodynamic efficiency.

Drag rise occurs as Mach increases toward the critical Mach number; wave drag appears once local flow exceeds M = 1.

Flaps increase C_Lmax and C_D; a given flap setting trades stall speed for drag and pitch change.

Induced drag coefficient C_Di = C_L²/(π·e·AR); it dominates at high angle of attack and low speed.

Skin friction depends on wetted area and surface condition; form drag depends on shape and separation.

Trailing-edge flaps raise section camber: Fowler flaps also increase wing area, giving the largest C_Lmax gain.

Leading-edge devices (slats, Krueger flaps) re-energise the upper surface flow and delay stall to higher angle of attack.

Slats and flaps used together produce a higher C_Lmax than either alone but add significant drag and pitching-moment change.

Vortex generators mix high-energy free stream into the boundary layer, delaying separation and improving control effectiveness at high angle of attack.

Winglets reduce tip vortex strength and hence induced drag; they also add wetted area and structural bending loads.

Boundary-layer control by suction or blowing delays separation but costs power and complexity, so it is rare in service aircraft.

Spoilers and speed brakes increase drag and spoil lift; they are used for descent control and roll control.

Drag reduction measures include laminar-flow surfaces, gap seals, fairings and reduced wetted area; each must be traded against weight and cost.

Static stability requires a restoring moment after a disturbance; dynamic stability requires the resulting oscillation to decay.

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 chord.

Dihedral produces lateral stability through sideslip: a sideslip toward one wing raises that wing's angle of attack and rolls the aircraft away from the slip.

Directional stability is provided mainly by the vertical fin; fin stall or loss of fin authority can cause Dutch roll or spiral divergence.

Control effectiveness depends on dynamic pressure and surface area; authority falls with speed squared, so control forces are light at low speed and heavy at high speed.

Elevator trim balances the pitching moment; a mistrim or runaway trim produces large stick forces and is a common cause of loss of control.

Phugoid is a long-period, low-damping speed/altitude oscillation; short-period pitch oscillation is usually heavily damped.

Positive manoeuvring stability means stick force per g increases with load factor; a minimum gradient is required for certification.

Stall occurs when the critical angle of attack is exceeded, regardless of speed, attitude or weight; the stall warning must precede it.

Stall speed in level flight V_s = √(2W/(ρ·S·C_Lmax)); it rises with the square root of load factor.

Accelerated stall speed V_s(n) = V_s1·√n; at 60° bank in level flight the load factor is 2 and stall speed is 1.41 times the 1g value.

A wing stalls progressively from the root if washout is present; tip stall causes wing drop and loss of aileron control.

A spin requires both stall and yaw: one wing exceeds the critical angle before the other, producing autorotation.

Recovery from a spin: reduce power, apply full opposite rudder, ease the elevator forward to break the stall, then centralise controls and recover from the dive.

Stall strips and leading-edge cuffs change the local stall sequence and can make stall characteristics more benign.

Angle-of-attack indicators and stall warning vanes measure local flow angle and are independent of weight and density altitude.

With one engine inoperative, the operating engine's thrust offset creates a yawing moment toward the failed engine; rudder must oppose it.

V_MC is the minimum control speed in the air: below it, full rudder cannot hold heading after an engine failure with the other at takeoff power.

V_MCA is the air minimum control speed demonstrated for certification; it is determined with the aircraft in a specified configuration and weight.

Critical engine is the engine whose failure produces the greatest yawing moment; on a conventional twin it is usually the one whose propeller slipstream aids the fin.

Single-engine service ceiling is the altitude at which the aircraft can climb at a defined rate (often 50 ft/min) on one engine.

Drift-down after engine failure requires flying at the speed for minimum sink or best single-engine climb, not the all-engines best-glide speed.

Asymmetric thrust also produces a rolling moment; aileron and rudder must be coordinated, and the aircraft may need to be flown with a bank toward the live engine.

V_MC decreases with altitude because rudder authority depends on dynamic pressure, while yaw from thrust offset does not fall as fast.

Load factor n = L/W; in a level turn n = 1/cos(bank angle), so 60° bank gives n = 2.

Turn radius r = V²/(g·tan φ) and rate of turn ω = g·tan φ/V; both improve with bank but load factor and stall speed rise.

Rate of climb ROC = (T − D)·V/W, or excess power divided by weight; best rate of climb speed maximises excess power.

Best angle of climb (V_X) maximises height gained per unit ground distance and is used for obstacle clearance; V_X is lower than V_Y.

Glide range is maximised at the speed for best L/D; headwind increases the speed to fly, tailwind decreases it.

Takeoff and landing distances scale with weight, density altitude and wind; a 10% weight increase raises takeoff distance by roughly 20%.

Specific range for a jet is maximised near the speed for minimum drag-to-Mach ratio; for a propeller aircraft at best L/D.

Manoeuvre load limits: normal category 3.8g positive, 1.52g negative; utility 4.4g; aerobatic 6.0g, with a 1.5 safety factor in design.

Propeller thrust T = (mass flow)·(velocity increase); thrust falls as forward speed rises at fixed rpm.

Blade element theory combines section lift and drag along the blade with induced velocity to predict thrust and torque.

Advance ratio J = V/(n·D) describes the operating point; propeller efficiency η = (thrust·V)/shaft power.

Fixed-pitch propellers reach peak efficiency at one design advance ratio; constant-speed units vary blade angle to hold rpm and efficiency across the envelope.

Blade angle is set by the pitch-change mechanism; coarse pitch suits high speed, fine pitch suits takeoff and climb.

Propeller slipstream increases local velocity over the wing and tail, raising lift and elevator effectiveness at low speed.

Windmilling propeller drag can exceed the drag of a feathered propeller; feathering reduces drag and yaw after engine failure.

Propeller tip speed must stay below the speed of sound; excessive tip Mach causes noise, vibration and efficiency loss.

Critical Mach number is the free-stream Mach at which local flow first reaches M = 1, usually on the upper wing surface.

Above the critical Mach, shock waves form; the associated pressure rise separates the boundary layer and causes drag rise and buffet.

Mach tuck is a nose-down pitching moment caused by aft movement of the centre of pressure as shock-induced separation develops.

The area rule reduces wave drag by smoothing the cross-sectional area distribution along the fuselage.

Swept and thin wings raise the critical Mach number by reducing the local velocity normal to the leading edge.

Supersonic flow expands and compresses through oblique shocks; total pressure is lost across shocks, so ram recovery is never perfect.

Control reversal and aileron buzz can occur when shock-induced separation changes the effective stiffness or flow over control surfaces.

Coffin corner is the altitude band where VMO and MMO converge, leaving a narrow usable speed range.

The V-n diagram plots load factor against equivalent airspeed; its boundaries are the stall lines, the manoeuvre limits and the dive speed V_D.

V_A is the design manoeuvring speed: at or below it, full control deflection cannot exceed the limit load factor before stall.

V_NE is the never-exceed speed; V_NO is the maximum structural cruising speed, above which flight is permitted only in smooth air.

V_FE and V_LE are flap and landing-gear extension speeds; exceeding them can cause structural damage.

V_B is the design speed for maximum gust intensity; it sits between V_NO and V_C.

Gust load factor Δn = (ρ·V·a·K_g·U)/W depends on gust velocity, true airspeed and wing loading.

Operating limitations include maximum operating altitude, maximum differential pressure and maximum takeoff/landing weights.

Exceeding the flight envelope may produce flutter, structural failure or loss of control; flutter is a dynamic aeroelastic instability that can destroy the structure rapidly.