ATPL Performance (Australian CASA Pilot Theory Exams) cheat sheet

Take-off distance required (TODR) = take-off run required (TORR) + distance to 35 ft (or 50 ft for wet/contaminated) at V2, with all engines operating.

Balanced field length (BFL) is the runway length where accelerate-stop distance equals take-off distance to 35 ft, both equal to the available runway; V1 at BFL is V1(BFL).

V1 is chosen between V1(MCG) and V1(VR), and must not exceed V1(MAX) which is the brake-energy limit; if V1 is reduced, TODR increases.

Take-off mass limited by: field length, obstacle clearance, brake energy, tyre speed, and climb gradient requirements (2nd segment 2.4% for twin, 2.7% for tri, 3.0% for quad).

For a given mass, increasing pressure altitude or temperature increases TODR; decreasing pressure altitude or temperature decreases TODR.

Slope: 1% uphill increases TODR by approximately 5-10%, downhill decreases it; use airport analysis charts for exact values.

Wind: headwind decreases TODR, tailwind increases it; use only 50% of reported headwind and 150% of reported tailwind for conservative planning.

Contaminated runway: use contaminated runway charts; standing water or slush increases TODR and reduces braking action; V1 may be reduced.

Take-off climb segments: 1st segment (to 35 ft) V2, 2nd segment (35 ft to 400 ft) V2, 3rd segment (400 ft to 1500 ft) V2 to VFTO, final segment (1500 ft to 1500 ft) VFTO.

Climb gradient (%) = (ROC in ft/min × 60) / (TAS in knots × 101.27) × 100; or ROC (ft/min) = gradient (%) × TAS (kt) × 1.013.

For a given mass, climb gradient decreases with increasing altitude, temperature, and mass; best climb gradient speed (VX) is lower than best climb rate speed (VY).

Certification climb gradients: 2nd segment (take-off) 2.4% twin, 2.7% tri, 3.0% quad; 3rd segment (en-route) 1.2% twin, 1.5% tri, 1.7% quad; final segment 1.2%, 1.5%, 1.7% respectively.

Obstacle clearance: net take-off flight path = gross flight path minus 0.8% (twin) or 0.9% (tri/quad) gradient; net path must clear obstacles by 35 ft vertically.

Climb gradient required to clear obstacle = (obstacle height + 35 ft) / horizontal distance from 35 ft point to obstacle.

Rate of climb = (excess power / weight) × 1000; approximately ROC (ft/min) = (TAS × (T - D)) / W × 101.27.

Service ceiling is where ROC = 100 ft/min; absolute ceiling is where ROC = 0; climb performance decreases with altitude due to reduced engine power and increased TAS for same IAS.

En-route climb: use net gradient; if net gradient is less than required, reduce mass or wait for lower temperature.

Climb with one engine inoperative: reduce climb gradient; use drift-down procedure if cannot maintain altitude; MEA and MORA considerations.

Specific range (SR) = TAS / fuel flow (nm/kg or nm/lb); maximum SR occurs at a specific lift coefficient, typically at a speed slightly above minimum drag speed.

Long range cruise (LRC) speed is approximately 1.02 × maximum range cruise (MRC) speed and gives 99% of maximum specific range while improving stability and reducing time.

Maximum endurance speed (minimum fuel flow) is lower than maximum range speed; endurance (hours) = fuel available / fuel flow.

Cruise altitude selection: higher altitude reduces fuel flow but requires longer climb; optimum altitude increases with decreasing mass and is where specific range is maximum for given conditions.

Cost index (CI) = fuel cost per hour / time cost per hour; CI = 0 gives maximum range (minimum fuel), CI = max gives maximum speed (minimum time).

Cruise performance charts: for given mass, altitude, temperature, and wind, provide TAS, fuel flow, and specific range; use interpolation for intermediate values.

Wind effect: headwind reduces ground speed and specific range in ground terms; tailwind increases them; for maximum range in wind, increase speed in headwind, decrease in tailwind.

Fuel flow increases with altitude for a given TAS? Actually, for a given Mach number, fuel flow decreases with altitude until tropopause; above tropopause, TAS decreases for same Mach, so fuel flow may increase.

Cruise climb: as fuel is burned, mass decreases, optimum altitude increases; step climb to higher altitude when specific range improvement exceeds climb fuel penalty.

Landing distance required (LDR) = landing distance from 50 ft (or 35 ft for some) to stop, including air distance and ground roll; must not exceed landing distance available (LDA).

Landing mass limited by: LDA, obstacle clearance, brake energy, and go-around climb gradient (2.1% twin, 2.4% tri, 2.7% quad).

VREF = 1.3 × VS0 (stall speed in landing configuration) or 1.23 × VS1G; VAPP = VREF + wind correction (half headwind plus full gust, not less than 5 kt).

Landing distance increases with: higher mass, higher altitude, higher temperature, tailwind, downhill slope, contaminated runway, and lower braking action.

For contaminated runway, use contaminated landing distance charts; increase LDR by factors for snow, slush, ice, and standing water.

Brake energy limit: maximum kinetic energy that brakes can absorb; if exceeded, reduce landing mass or use more runway.

Landing climb: go-around climb gradient must be at least 2.1% (twin) in landing configuration at VREF, with one engine inoperative.

Quick turnaround: consider brake cooling; if brakes are hot, next take-off may be brake-energy limited.

Reverse thrust: not included in landing distance calculations for certification, but may be used operationally; wet runway may allow credit for reverse thrust in some cases.

Fuel required = taxi fuel + trip fuel + contingency fuel (5% of trip fuel or 5 min hold, whichever greater) + alternate fuel + final reserve fuel (30 min hold at 1500 ft) + additional fuel if needed.

Trip fuel = fuel from take-off to landing at destination, including climb, cruise, and descent; use flight planning charts or computer flight plan.

Alternate fuel = fuel from destination to alternate, including approach and landing; required when destination weather is below certain criteria.

Final reserve fuel = 30 minutes holding at 1500 ft above aerodrome in clean configuration at holding speed; for turbine aircraft, 30 min; for piston, 45 min.

Contingency fuel = 5% of trip fuel or 5 minutes holding, whichever is greater; may be reduced with en-route alternate or fuel monitoring.

Additional fuel: for cases where alternate not available, or for isolated aerodromes, or for specific operations (e.g., ETOPS).

Fuel density: Jet A-1 density typically 0.78-0.80 kg/L; use actual density for conversion between mass and volume; temperature affects density.

Specific fuel consumption (SFC) = fuel flow / thrust (or power); for cruise, use SFC to estimate fuel flow from thrust or power.

Fuel planning: use integrated range method; for long flights, step climb to maintain optimum altitude as mass decreases; account for wind and temperature deviations.