CAA NZ ATPL Theory - Advanced Aerodynamics, Performance and Systems Knowledge cheat sheet

Lift = ½ρV²S·CL; in steady level flight lift equals weight, so for a given weight CL must double if speed falls to 1/√2 of its original value.

Induced drag coefficient CDi = CL²/(π·A·e), where A is aspect ratio and e the Oswald efficiency factor; induced drag therefore falls with speed while parasite drag rises.

Total drag = parasite + induced; minimum drag occurs where CDi = CD0, and the speed for minimum drag is Vmd = √(2W/(ρS))·(1/√(πAeCD0))^0.5 form derived from that equality.

Best glide (still air) is flown at Vmd because it gives minimum drag and hence minimum glide angle; best endurance is also near Vmd, while best range is at a higher speed where CL ≈ √(CD0·πAe/3).

Load factor n = L/W = 1/cos φ in a level banked turn; stall speed increases by √n, so a 60° bank raises Vs by a factor of √2 (about 1.41).

Tightest level turn radius r = V²/(g·√(n²−1)) and rate of turn ω = g·√(n²−1)/V; both improve at low speed but are limited by the structural and stall boundaries of the V-n diagram.

Critical Mach number is the free-stream Mach at which airflow somewhere on the aircraft first reaches Mach 1; sweepback, thin sections and supercritical airfoils raise Mcrit and delay shock-induced drag rise.

The drag divergence Mach number lies above Mcrit where CD rises steeply; Mach buffet, trim change (tuck-under) and reduced elevator effectiveness accompany shock stall on the wing.

Boundary layer: laminar flow has lower skin friction but separates easily; transition and turbulent separation cause the stall, and vortex generators or turbulators re-energise flow to delay it.

Density altitude is pressure altitude corrected for temperature; high density altitude reduces thrust, lift and propeller efficiency, lengthening take-off and landing runs.

Take-off distance varies roughly with 1/σ² for normally aspirated engines (σ = density ratio) because both thrust and acceleration fall with density; a 10% density decrease can increase ground roll by over 20%.

Balanced field length (BFL) is the runway needed when the accelerate-stop distance equals the accelerate-go distance to 35 ft; V1 is chosen so that both distances equal the available runway.

Landing distance is measured from 50 ft over the threshold to full stop; it increases with weight (higher approach speed, squared effect on energy), tailwind, downslope and wet/contaminated runway.

Climb gradient % = (ROC/V) × 60 when ROC is in the same units per hour as V; for example 500 ft/min at 100 kt gives 500/(100×6076/60) ≈ 4.9%.

Specific range (air nautical miles per kg fuel) is maximised at the speed for best range, which for a piston aircraft is roughly 1.3 Vmd and for a jet is close to the speed for maximum L/D in still air.

Endurance is maximum time aloft, achieved near Vmd; range is maximum distance, achieved at a higher speed - do not confuse the two when planning fuel.

Headwind increases the still-air speed needed for best range; tailwind reduces it, because the wind alters the ground-speed-per-fuel relationship.

Runway slope: an upslope increases take-off distance and reduces landing distance; a 1% upslope typically adds about 10% to the take-off ground roll.

A constant-speed propeller in equilibrium has engine power absorbed by the propeller; if airspeed rises at fixed pitch, blade angle of attack falls and RPM tends to increase until the governor coarsens pitch.

Turbocharging maintains manifold pressure to a critical altitude; above it, power falls off, and overboost is prevented by the wastegate and manifold pressure limiter.

Detonation is uncontrolled explosive combustion causing high cylinder pressures and temperatures; pre-ignition is ignition before the spark. Rich mixture, low boost and cooled cylinders reduce detonation risk.

Carburettor icing is most likely at ambient temperatures between about −10 °C and +10 °C with high relative humidity; it occurs even at outside air temperatures well above freezing because of venturi cooling.

A failure of the vacuum pump leaves gyroscopic instruments (attitude indicator, heading indicator) unusable; the turn coordinator and altimeter/airspeed indicator remain electrically or pneumatically independent.

Hydraulic system pressure is regulated by a relief valve for safety and an unloading valve to offload the pump; accumulators damp pressure surges and supply emergency pressure.

Electrical: the battery provides starting power and emergency supply; the alternator/generator carries the normal load, and a failed alternator is indicated by zero charge with the battery draining.

Pitot-static blockage: a blocked pitot with open static gives an airspeed indicator that behaves like an altimeter (climbs as altitude rises); a blocked static makes ASI, altimeter and VSI all erroneous.

Fuel: unusable fuel is that which cannot be safely supplied in all flight attitudes; it is excluded from the usable fuel figure used for flight planning.

Weight and balance: total moment = Σ(weight × arm); CG position = total moment / total weight, expressed as a distance from the datum or as %MAC.

%MAC = (CG distance from leading edge − LEMAC) / MAC × 100; the CG must remain within the fore and aft limits for all loading and fuel states.

Maximum take-off mass (MTOM) and maximum landing mass (MLM) may differ; if an overweight landing must be made, a fuel-dump or performance penalty applies.

Zero fuel mass (ZFM) = operating empty mass + traffic load; it must not exceed MZFM, which protects the wing structure from excessive bending with fuel in the wings.

Moving a mass aft moves the CG aft by (mass × shift) / total mass; the same formula applies to ballast, cargo or a passenger relocation.

Forward CG increases stability but raises stall speed and elevator forces and lengthens take-off run; aft CG reduces stability and can cause pitch-up or tail stall.

Basic empty mass includes unusable fuel, full oil and standard equipment; operating mass adds crew and crew baggage, and these must not be double-counted.

Load sheet: dry operating mass + take-off fuel = take-off mass; subtract trip fuel for landing mass, and check all three against their respective limits.