CPL Aerodynamics cheat sheet

Lift equation: L = ½ρV²SC_L; lift rises with the square of true airspeed, so doubling TAS quadruples dynamic pressure.

Induced drag: D_i = L²/(½ρV²πeAR); it varies inversely with span efficiency e and aspect ratio AR, and inversely with V².

Total drag = parasite drag (∝V²) + induced drag (∝1/V²); L/D is maximum where parasite drag equals induced drag, at C_L = √(C_D0·πeAR).

Bernoulli and Newton both describe lift: pressure difference across the wing plus downward momentum change of air; neither alone explains all cases.

Angle of attack is the angle between the chord line and the relative airflow; it is independent of pitch attitude and airspeed.

Critical angle of attack is fixed for a given wing and configuration; stall always occurs at that angle regardless of weight, speed, or bank.

Load factor n = L/W = 1/cos φ in a level banked turn; a 60° bank doubles load factor and raises stall speed by √2.

In steady level flight, thrust = drag and lift = weight; excess thrust governs climb gradient, excess power governs rate of climb.

Dihedral produces a lateral component of lift in sideslip, giving positive roll stability; sweepback contributes similarly at higher speeds.

Rate of climb ROC = excess power/W = (P_avail − P_required)/W; best ROC occurs at the speed for maximum excess power.

Climb gradient = excess thrust/W = (T − D)/W; best angle of climb uses the speed for maximum excess thrust.

V_Y is normally greater than V_X; into wind, V_X increases and V_Y decreases in practical terms, and the reverse downwind.

Piston-engine power falls with altitude while TAS for a given IAS rises about 2% per 1000 ft; TAS ≈ IAS × (1 + 0.02 × altitude in thousands of feet).

Takeoff and landing distances vary approximately with the square of weight in the same conditions; a 10% weight increase raises ground roll about 20%.

Density altitude increases with elevation, temperature, and humidity; higher density altitude lengthens takeoff roll, reduces climb, and raises TAS for a given IAS.

Endurance is maximum at minimum power required speed (roughly 1.3 V_stall); range is maximum at the best L/D or best specific-range speed.

Glide range is greatest at best L/D speed; headwind raises the speed for best glide range, tailwind lowers it, and weight raises the speed but not the ratio.

Landing distance increases with the square of approach speed; a 10% excess approach speed adds about 21% to the landing roll.

Static stability requires a restoring moment after disturbance; positive static and positive dynamic stability together give a stable aircraft.

Longitudinal static stability requires the centre of gravity ahead of the neutral point; static margin = (neutral point − CG) expressed as a percentage of mean chord.

Dihedral effect (roll due to sideslip) must be balanced against weathercock (directional) stability; too much dihedral gives Dutch roll or spiral instability.

Adverse yaw is yaw opposite to the intended turn, caused by aileron drag; rudder into the turn coordinates the manoeuvre.

Ailerons control roll about the longitudinal axis, elevators pitch about the lateral axis, and rudder yaws about the normal axis.

Elevator effectiveness falls with altitude because true airspeed for a given IAS rises, reducing the angle of attack change per unit deflection.

Control forces are reduced by aerodynamic balance (horn, inset hinge, tabs); a trim tab holds a control position without continuous pilot force.

Static margin shrinks as CG moves aft; at the neutral point stability is zero, and behind it the aircraft is longitudinally unstable.

Directional stability is provided mainly by the vertical fin; the fin's moment arm and area determine weathercock stability.

Stall occurs at the critical angle of attack, typically 15–18° for light aircraft; it is independent of airspeed, weight, and attitude.

Stall speed in a turn: V_S(n) = V_S1 × √n; at 60° bank load factor is 2 and stall speed rises 41%.

A spin needs both stall and yaw: one wing stalls more deeply than the other, giving autorotation; recovery is power idle, ailerons neutral, full opposite rudder, then elevator forward.

Spin recovery order: reduce power, neutralise ailerons, apply full opposite rudder, ease elevator forward to break the stall, then centralise rudder and recover.

Critical Mach number is the free-stream Mach at which airflow somewhere on the aircraft first reaches Mach 1; it falls as the wing's thickness-to-chord ratio rises.

At the critical Mach number, shock waves form, causing Mach buffet, tuck-under, and loss of elevator effectiveness; sweepback raises critical Mach.

Speed of sound in air depends only on temperature: a ≈ 39 × √(T in kelvin) knots, or about 661 kt at sea level ISA.

Mach number M = TAS/a; for the same IAS, Mach number rises with altitude because temperature and local speed of sound fall.

Shock stall occurs when shock-induced separation causes loss of lift and buffet before the aircraft itself reaches Mach 1.

Lift equation: L = ½ρV²SC_L; lift rises with the square of true airspeed, so doubling TAS quadruples dynamic pressure.

Induced drag: D_i = L²/(½ρV²πeAR); it varies inversely with span efficiency e and aspect ratio AR, and inversely with V².

Total drag = parasite drag (∝V²) + induced drag (∝1/V²); L/D is maximum where parasite drag equals induced drag, at C_L = √(C_D0·πeAR).

Bernoulli and Newton both describe lift: pressure difference across the wing plus downward momentum change of air; neither alone explains all cases.

Angle of attack is the angle between the chord line and the relative airflow; it is independent of pitch attitude and airspeed.

Critical angle of attack is fixed for a given wing and configuration; stall always occurs at that angle regardless of weight, speed, or bank.

Load factor n = L/W = 1/cos φ in a level banked turn; a 60° bank doubles load factor and raises stall speed by √2.

In steady level flight, thrust = drag and lift = weight; excess thrust governs climb gradient, excess power governs rate of climb.

Dihedral produces a lateral component of lift in sideslip, giving positive roll stability; sweepback contributes similarly at higher speeds.

Rate of climb ROC = excess power/W = (P_avail − P_required)/W; best ROC occurs at the speed for maximum excess power.

Climb gradient = excess thrust/W = (T − D)/W; best angle of climb uses the speed for maximum excess thrust.

V_Y is normally greater than V_X; into wind, V_X increases and V_Y decreases in practical terms, and the reverse downwind.

Piston-engine power falls with altitude while TAS for a given IAS rises about 2% per 1000 ft; TAS ≈ IAS × (1 + 0.02 × altitude in thousands of feet).

Takeoff and landing distances vary approximately with the square of weight in the same conditions; a 10% weight increase raises ground roll about 20%.

Density altitude increases with elevation, temperature, and humidity; higher density altitude lengthens takeoff roll, reduces climb, and raises TAS for a given IAS.

Endurance is maximum at minimum power required speed (roughly 1.3 V_stall); range is maximum at the best L/D or best specific-range speed.

Glide range is greatest at best L/D speed; headwind raises the speed for best glide range, tailwind lowers it, and weight raises the speed but not the ratio.

Landing distance increases with the square of approach speed; a 10% excess approach speed adds about 21% to the landing roll.

Static stability requires a restoring moment after disturbance; positive static and positive dynamic stability together give a stable aircraft.

Longitudinal static stability requires the centre of gravity ahead of the neutral point; static margin = (neutral point − CG) expressed as a percentage of mean chord.

Dihedral effect (roll due to sideslip) must be balanced against weathercock (directional) stability; too much dihedral gives Dutch roll or spiral instability.

Adverse yaw is yaw opposite to the intended turn, caused by aileron drag; rudder into the turn coordinates the manoeuvre.

Ailerons control roll about the longitudinal axis, elevators pitch about the lateral axis, and rudder yaws about the normal axis.

Elevator effectiveness falls with altitude because true airspeed for a given IAS rises, reducing the angle of attack change per unit deflection.

Control forces are reduced by aerodynamic balance (horn, inset hinge, tabs); a trim tab holds a control position without continuous pilot force.

Static margin shrinks as CG moves aft; at the neutral point stability is zero, and behind it the aircraft is longitudinally unstable.

Directional stability is provided mainly by the vertical fin; the fin's moment arm and area determine weathercock stability.

Stall occurs at the critical angle of attack, typically 15–18° for light aircraft; it is independent of airspeed, weight, and attitude.

Stall speed in a turn: V_S(n) = V_S1 × √n; at 60° bank load factor is 2 and stall speed rises 41%.

A spin needs both stall and yaw: one wing stalls more deeply than the other, giving autorotation; recovery is power idle, ailerons neutral, full opposite rudder, then elevator forward.

Spin recovery order: reduce power, neutralise ailerons, apply full opposite rudder, ease elevator forward to break the stall, then centralise rudder and recover.

Critical Mach number is the free-stream Mach at which airflow somewhere on the aircraft first reaches Mach 1; it falls as the wing's thickness-to-chord ratio rises.

At the critical Mach number, shock waves form, causing Mach buffet, tuck-under, and loss of elevator effectiveness; sweepback raises critical Mach.

Speed of sound in air depends only on temperature: a ≈ 39 × √(T in kelvin) knots, or about 661 kt at sea level ISA.

Mach number M = TAS/a; for the same IAS, Mach number rises with altitude because temperature and local speed of sound fall.

Shock stall occurs when shock-induced separation causes loss of lift and buffet before the aircraft itself reaches Mach 1.