NCAA CPL Flight Performance & Planning cheat sheet

Mass and balance is computed as: total mass = empty mass + crew + payload + usable fuel; each item's mass is multiplied by its arm (distance from the reference datum) to give a moment, and CG position = total moment / total mass.

The datum is an arbitrary vertical reference plane chosen by the manufacturer; arms forward of the datum are negative, aft are positive, so sign discipline is essential when summing moments.

Maximum take-off mass (MTOM), maximum landing mass (MLM), maximum zero-fuel mass (MZFM) and maximum ramp mass are separate limits; the MZFM limit applies with all usable fuel excluded and is normally the structural limit on payload.

Zero-fuel mass = take-off mass minus usable fuel; if ZFM exceeds MZFM, payload or fuel must be reduced before departure even if MTOM is satisfied.

The forward CG limit is normally set by elevator authority for rotation and landing flare; the aft CG limit is set by static and dynamic longitudinal stability, so an aft CG raises stall recovery risk and reduces stick-fixed stability.

Floor loading limits (kg per unit area) and running-load limits per metre of fuselage must be checked separately from total mass; a load within MTOM can still exceed a structural floor limit.

Load sheet terminology: DOW (dry operating mass) = empty mass + crew + crew baggage + catering + potable water; DOI is the corresponding index; traffic load = passengers + baggage + cargo; take-off mass = DOW + traffic load + take-off fuel.

Index method: index = (moment / constant) + K, where K is a negative or positive reference constant; the CG is read from a load sheet index table, and the index change per unit mass is constant only if the arm is constant.

For a mass moved within the aircraft, the CG shift = (mass moved x distance moved) / total mass, in the direction of the move; for a mass added or removed, CG shift = (mass x (arm of item - original CG)) / new total mass.

Density altitude = pressure altitude + 120 x (OAT - ISA temperature at that level), where ISA temperature = 15 C - 1.98 C per 1000 ft; density altitude governs take-off and climb performance.

Take-off distance required (TODR) must not exceed take-off distance available (TODA); take-off run required (TORR) must not exceed TORA; the screen height at the end of TODA is 35 ft for aeroplanes and 50 ft for jets under the applicable certification basis.

Balanced field length (BFL) is the field length at which the accelerate-stop distance equals the accelerate-go distance to 35 ft; V1 is the decision speed at which the critical engine failure is recognised and the stop or continue decision is made.

V speeds: V1 decision speed, VR rotation speed, V2 take-off safety speed (minimum at 35 ft), VMCA minimum control speed in the air, VMCG minimum control speed on the ground, VREF landing reference speed (normally 1.3 VS0 for the landing configuration).

Climb gradients for certification: for a twin-engine aeroplane, second-segment climb (gear up, one engine inoperative, V2, take-off flaps) requires a minimum gross gradient of 2.4%, reduced to 2.7% for three engines and 3.0% for four engines; the net gradient is the gross gradient minus 0.8% for twins and 0.9% for three engines.

Landing distance required (LDR) must not exceed landing distance available (LDA); the landing distance is measured from 50 ft above the threshold to a full stop, and is affected by runway slope, surface, wind, and runway condition (dry, wet, contaminated).

Headwind and tailwind components: use only 50% of a reported headwind and 150% of a reported tailwind when applying wind correction to take-off and landing distances, unless the operation specifies otherwise.

Runway slope: an uphill slope increases the take-off distance; a 1% uphill slope typically increases take-off distance by about 10% for a light twin, and the effect must be read from the aircraft flight manual, not estimated.

Obstacle clearance: the net take-off flight path must clear all obstacles by 35 ft vertically, and the net gradient is the gross gradient reduced by the specified margin; the second-segment climb is the limiting segment for obstacle clearance in most twins.

The operational flight plan (OFP) is the pilot's document that records the route, altitudes, fuel, masses, and performance; the ATS flight plan (ICAO FPL) is the message filed with air traffic services and is a different document.

True airspeed from indicated airspeed: TAS = IAS x (1 + 0.02 x altitude in thousands of feet) is a rough approximation; the precise relationship uses density ratio, TAS = IAS / sqrt(sigma), where sigma is the density ratio.

Mach number = TAS / local speed of sound; the speed of sound at sea level ISA is about 661 kt, decreasing with temperature to about 573 kt at the tropopause; above the tropopause, TAS for a given Mach increases with altitude.

Great-circle distance = 60 x angular distance in degrees; the rhumb line is a constant-track line that is longer than the great circle except on the equator or a meridian.

Wind triangle: heading = track - wind correction angle; the wind correction angle satisfies sin(WCA) = (wind speed x sin(wind angle - track)) / TAS, and groundspeed = TAS x cos(WCA) - wind speed x cos(wind angle - track).

Point of no return (PNR) for a given fuel: distance to PNR = (fuel available x groundspeed out x groundspeed back) / (fuel consumption x (groundspeed out + groundspeed back)); the equal-time point (ETP) uses the same formula with time instead of fuel.

Critical point (CP) is the point from which the fuel required to reach the destination equals the fuel required to return to base; it is computed with the same formula as the PNR but with the destination as the alternate.

The navigation log records, for each leg: waypoint, track, TAS, wind, heading, groundspeed, distance, ETA, fuel flow, fuel remaining, and the fuel check against the flight plan; deviations beyond a defined tolerance require a re-plan.

Fuel is planned in the sequence: taxi fuel, trip fuel, contingency fuel, alternate fuel, final reserve fuel, and additional fuel; the sum is the minimum block fuel, and extra fuel is added at the commander's discretion.

Contingency fuel is normally 5% of the trip fuel, or 3% if the operator has an approved fuel scheme with a suitable en-route alternate; it is intended to cover unforeseen deviations from the planned route.

Final reserve fuel is the fuel required to fly for 30 minutes at holding speed at 1500 ft above the aerodrome in ISA conditions; for a turbine aeroplane it is normally 30 minutes, and the final reserve must not be planned to be used.

Alternate fuel is the fuel required to fly from the destination to the alternate, including a missed approach, a climb, and a descent; if two alternates are required, the fuel for the more distant one is used.

Taxi fuel is the fuel consumed before take-off, including APU and engine start; it is not part of trip fuel and must be added to the block fuel.

Fuel density: jet fuel density varies with temperature, so fuel mass must be computed from volume and density; a change of 1 C in fuel temperature changes the density of Jet A-1 by about 0.0008 kg/L, which matters for mass and balance.

In-flight fuel checks: the crew compares actual fuel remaining at each waypoint with the flight-plan fuel; if the actual fuel is below the planned fuel by more than the contingency fuel, a re-plan or diversion is required.

Minimum fuel and emergency fuel: 'minimum fuel' means the aircraft can only land with the final reserve intact; 'mayday fuel' is declared when the fuel remaining is below the final reserve, and the crew must declare an emergency.

The operational flight plan must contain: registration and type, date, crew, route and waypoints, cruise levels, masses, fuel figures, and the commander's signature; it is retained by the operator for the required period.

Fuel management in flight: the commander must ensure that the fuel remaining is sufficient for the planned flight plus the final reserve, and must monitor fuel against the flight plan at each waypoint.

In-flight replanning: if the destination becomes unavailable, the crew computes the fuel required to the new destination or alternate, and the commander decides whether to continue, divert, or hold.

The commander has final authority over fuel and may add extra fuel; the operator must provide a fuel policy that meets the applicable regulations, and the commander may deviate from it only in the interest of safety.

Fuel tankering is carried when fuel is cheaper at the departure aerodrome; the extra fuel increases the landing mass and the take-off mass, and the cost saving must be weighed against the performance penalty.

The flight plan fuel must be cross-checked against the aircraft's fuel gauges before departure, and the actual fuel on board must be recorded; a discrepancy between the planned and actual fuel must be resolved before take-off.

Fuel dumping is permitted only when the aircraft is above the maximum landing mass and the situation requires it; the dump must be conducted in accordance with the aircraft flight manual and ATC coordination.

The fuel log records the fuel on board at each waypoint, the fuel used, and the fuel remaining; it is the primary record for the post-flight fuel analysis and for the operator's fuel efficiency monitoring.

Mass and balance is computed as: total mass = empty mass + crew + payload + usable fuel; each item's mass is multiplied by its arm (distance from the reference datum) to give a moment, and CG position = total moment / total mass.

The datum is an arbitrary vertical reference plane chosen by the manufacturer; arms forward of the datum are negative, aft are positive, so sign discipline is essential when summing moments.

Maximum take-off mass (MTOM), maximum landing mass (MLM), maximum zero-fuel mass (MZFM) and maximum ramp mass are separate limits; the MZFM limit applies with all usable fuel excluded and is normally the structural limit on payload.

Zero-fuel mass = take-off mass minus usable fuel; if ZFM exceeds MZFM, payload or fuel must be reduced before departure even if MTOM is satisfied.

The forward CG limit is normally set by elevator authority for rotation and landing flare; the aft CG limit is set by static and dynamic longitudinal stability, so an aft CG raises stall recovery risk and reduces stick-fixed stability.

Floor loading limits (kg per unit area) and running-load limits per metre of fuselage must be checked separately from total mass; a load within MTOM can still exceed a structural floor limit.

Load sheet terminology: DOW (dry operating mass) = empty mass + crew + crew baggage + catering + potable water; DOI is the corresponding index; traffic load = passengers + baggage + cargo; take-off mass = DOW + traffic load + take-off fuel.

Index method: index = (moment / constant) + K, where K is a negative or positive reference constant; the CG is read from a load sheet index table, and the index change per unit mass is constant only if the arm is constant.

For a mass moved within the aircraft, the CG shift = (mass moved x distance moved) / total mass, in the direction of the move; for a mass added or removed, CG shift = (mass x (arm of item - original CG)) / new total mass.

Density altitude = pressure altitude + 120 x (OAT - ISA temperature at that level), where ISA temperature = 15 C - 1.98 C per 1000 ft; density altitude governs take-off and climb performance.

Take-off distance required (TODR) must not exceed take-off distance available (TODA); take-off run required (TORR) must not exceed TORA; the screen height at the end of TODA is 35 ft for aeroplanes and 50 ft for jets under the applicable certification basis.

Balanced field length (BFL) is the field length at which the accelerate-stop distance equals the accelerate-go distance to 35 ft; V1 is the decision speed at which the critical engine failure is recognised and the stop or continue decision is made.

V speeds: V1 decision speed, VR rotation speed, V2 take-off safety speed (minimum at 35 ft), VMCA minimum control speed in the air, VMCG minimum control speed on the ground, VREF landing reference speed (normally 1.3 VS0 for the landing configuration).

Climb gradients for certification: for a twin-engine aeroplane, second-segment climb (gear up, one engine inoperative, V2, take-off flaps) requires a minimum gross gradient of 2.4%, reduced to 2.7% for three engines and 3.0% for four engines; the net gradient is the gross gradient minus 0.8% for twins and 0.9% for three engines.

Landing distance required (LDR) must not exceed landing distance available (LDA); the landing distance is measured from 50 ft above the threshold to a full stop, and is affected by runway slope, surface, wind, and runway condition (dry, wet, contaminated).

Headwind and tailwind components: use only 50% of a reported headwind and 150% of a reported tailwind when applying wind correction to take-off and landing distances, unless the operation specifies otherwise.

Runway slope: an uphill slope increases the take-off distance; a 1% uphill slope typically increases take-off distance by about 10% for a light twin, and the effect must be read from the aircraft flight manual, not estimated.

Obstacle clearance: the net take-off flight path must clear all obstacles by 35 ft vertically, and the net gradient is the gross gradient reduced by the specified margin; the second-segment climb is the limiting segment for obstacle clearance in most twins.

The operational flight plan (OFP) is the pilot's document that records the route, altitudes, fuel, masses, and performance; the ATS flight plan (ICAO FPL) is the message filed with air traffic services and is a different document.

True airspeed from indicated airspeed: TAS = IAS x (1 + 0.02 x altitude in thousands of feet) is a rough approximation; the precise relationship uses density ratio, TAS = IAS / sqrt(sigma), where sigma is the density ratio.

Mach number = TAS / local speed of sound; the speed of sound at sea level ISA is about 661 kt, decreasing with temperature to about 573 kt at the tropopause; above the tropopause, TAS for a given Mach increases with altitude.

Great-circle distance = 60 x angular distance in degrees; the rhumb line is a constant-track line that is longer than the great circle except on the equator or a meridian.

Wind triangle: heading = track - wind correction angle; the wind correction angle satisfies sin(WCA) = (wind speed x sin(wind angle - track)) / TAS, and groundspeed = TAS x cos(WCA) - wind speed x cos(wind angle - track).

Point of no return (PNR) for a given fuel: distance to PNR = (fuel available x groundspeed out x groundspeed back) / (fuel consumption x (groundspeed out + groundspeed back)); the equal-time point (ETP) uses the same formula with time instead of fuel.

Critical point (CP) is the point from which the fuel required to reach the destination equals the fuel required to return to base; it is computed with the same formula as the PNR but with the destination as the alternate.

The navigation log records, for each leg: waypoint, track, TAS, wind, heading, groundspeed, distance, ETA, fuel flow, fuel remaining, and the fuel check against the flight plan; deviations beyond a defined tolerance require a re-plan.

Fuel is planned in the sequence: taxi fuel, trip fuel, contingency fuel, alternate fuel, final reserve fuel, and additional fuel; the sum is the minimum block fuel, and extra fuel is added at the commander's discretion.

Contingency fuel is normally 5% of the trip fuel, or 3% if the operator has an approved fuel scheme with a suitable en-route alternate; it is intended to cover unforeseen deviations from the planned route.

Final reserve fuel is the fuel required to fly for 30 minutes at holding speed at 1500 ft above the aerodrome in ISA conditions; for a turbine aeroplane it is normally 30 minutes, and the final reserve must not be planned to be used.

Alternate fuel is the fuel required to fly from the destination to the alternate, including a missed approach, a climb, and a descent; if two alternates are required, the fuel for the more distant one is used.

Taxi fuel is the fuel consumed before take-off, including APU and engine start; it is not part of trip fuel and must be added to the block fuel.

Fuel density: jet fuel density varies with temperature, so fuel mass must be computed from volume and density; a change of 1 C in fuel temperature changes the density of Jet A-1 by about 0.0008 kg/L, which matters for mass and balance.

In-flight fuel checks: the crew compares actual fuel remaining at each waypoint with the flight-plan fuel; if the actual fuel is below the planned fuel by more than the contingency fuel, a re-plan or diversion is required.

Minimum fuel and emergency fuel: 'minimum fuel' means the aircraft can only land with the final reserve intact; 'mayday fuel' is declared when the fuel remaining is below the final reserve, and the crew must declare an emergency.

The operational flight plan must contain: registration and type, date, crew, route and waypoints, cruise levels, masses, fuel figures, and the commander's signature; it is retained by the operator for the required period.

Fuel management in flight: the commander must ensure that the fuel remaining is sufficient for the planned flight plus the final reserve, and must monitor fuel against the flight plan at each waypoint.

In-flight replanning: if the destination becomes unavailable, the crew computes the fuel required to the new destination or alternate, and the commander decides whether to continue, divert, or hold.

The commander has final authority over fuel and may add extra fuel; the operator must provide a fuel policy that meets the applicable regulations, and the commander may deviate from it only in the interest of safety.

Fuel tankering is carried when fuel is cheaper at the departure aerodrome; the extra fuel increases the landing mass and the take-off mass, and the cost saving must be weighed against the performance penalty.

The flight plan fuel must be cross-checked against the aircraft's fuel gauges before departure, and the actual fuel on board must be recorded; a discrepancy between the planned and actual fuel must be resolved before take-off.

Fuel dumping is permitted only when the aircraft is above the maximum landing mass and the situation requires it; the dump must be conducted in accordance with the aircraft flight manual and ATC coordination.

The fuel log records the fuel on board at each waypoint, the fuel used, and the fuel remaining; it is the primary record for the post-flight fuel analysis and for the operator's fuel efficiency monitoring.

Mass and balance is computed as: total mass = empty mass + crew + payload + usable fuel; each item's mass is multiplied by its arm (distance from the reference datum) to give a moment, and CG position = total moment / total mass.

The datum is an arbitrary vertical reference plane chosen by the manufacturer; arms forward of the datum are negative, aft are positive, so sign discipline is essential when summing moments.

Maximum take-off mass (MTOM), maximum landing mass (MLM), maximum zero-fuel mass (MZFM) and maximum ramp mass are separate limits; the MZFM limit applies with all usable fuel excluded and is normally the structural limit on payload.

Zero-fuel mass = take-off mass minus usable fuel; if ZFM exceeds MZFM, payload or fuel must be reduced before departure even if MTOM is satisfied.

The forward CG limit is normally set by elevator authority for rotation and landing flare; the aft CG limit is set by static and dynamic longitudinal stability, so an aft CG raises stall recovery risk and reduces stick-fixed stability.

Floor loading limits (kg per unit area) and running-load limits per metre of fuselage must be checked separately from total mass; a load within MTOM can still exceed a structural floor limit.

Load sheet terminology: DOW (dry operating mass) = empty mass + crew + crew baggage + catering + potable water; DOI is the corresponding index; traffic load = passengers + baggage + cargo; take-off mass = DOW + traffic load + take-off fuel.

Index method: index = (moment / constant) + K, where K is a negative or positive reference constant; the CG is read from a load sheet index table, and the index change per unit mass is constant only if the arm is constant.

For a mass moved within the aircraft, the CG shift = (mass moved x distance moved) / total mass, in the direction of the move; for a mass added or removed, CG shift = (mass x (arm of item - original CG)) / new total mass.

Density altitude = pressure altitude + 120 x (OAT - ISA temperature at that level), where ISA temperature = 15 C - 1.98 C per 1000 ft; density altitude governs take-off and climb performance.

Take-off distance required (TODR) must not exceed take-off distance available (TODA); take-off run required (TORR) must not exceed TORA; the screen height at the end of TODA is 35 ft for aeroplanes and 50 ft for jets under the applicable certification basis.

Balanced field length (BFL) is the field length at which the accelerate-stop distance equals the accelerate-go distance to 35 ft; V1 is the decision speed at which the critical engine failure is recognised and the stop or continue decision is made.

V speeds: V1 decision speed, VR rotation speed, V2 take-off safety speed (minimum at 35 ft), VMCA minimum control speed in the air, VMCG minimum control speed on the ground, VREF landing reference speed (normally 1.3 VS0 for the landing configuration).

Climb gradients for certification: for a twin-engine aeroplane, second-segment climb (gear up, one engine inoperative, V2, take-off flaps) requires a minimum gross gradient of 2.4%, reduced to 2.7% for three engines and 3.0% for four engines; the net gradient is the gross gradient minus 0.8% for twins and 0.9% for three engines.

Landing distance required (LDR) must not exceed landing distance available (LDA); the landing distance is measured from 50 ft above the threshold to a full stop, and is affected by runway slope, surface, wind, and runway condition (dry, wet, contaminated).

Headwind and tailwind components: use only 50% of a reported headwind and 150% of a reported tailwind when applying wind correction to take-off and landing distances, unless the operation specifies otherwise.

Runway slope: an uphill slope increases the take-off distance; a 1% uphill slope typically increases take-off distance by about 10% for a light twin, and the effect must be read from the aircraft flight manual, not estimated.

Obstacle clearance: the net take-off flight path must clear all obstacles by 35 ft vertically, and the net gradient is the gross gradient reduced by the specified margin; the second-segment climb is the limiting segment for obstacle clearance in most twins.

The operational flight plan (OFP) is the pilot's document that records the route, altitudes, fuel, masses, and performance; the ATS flight plan (ICAO FPL) is the message filed with air traffic services and is a different document.

True airspeed from indicated airspeed: TAS = IAS x (1 + 0.02 x altitude in thousands of feet) is a rough approximation; the precise relationship uses density ratio, TAS = IAS / sqrt(sigma), where sigma is the density ratio.

Mach number = TAS / local speed of sound; the speed of sound at sea level ISA is about 661 kt, decreasing with temperature to about 573 kt at the tropopause; above the tropopause, TAS for a given Mach increases with altitude.

Great-circle distance = 60 x angular distance in degrees; the rhumb line is a constant-track line that is longer than the great circle except on the equator or a meridian.

Wind triangle: heading = track - wind correction angle; the wind correction angle satisfies sin(WCA) = (wind speed x sin(wind angle - track)) / TAS, and groundspeed = TAS x cos(WCA) - wind speed x cos(wind angle - track).

Point of no return (PNR) for a given fuel: distance to PNR = (fuel available x groundspeed out x groundspeed back) / (fuel consumption x (groundspeed out + groundspeed back)); the equal-time point (ETP) uses the same formula with time instead of fuel.

Critical point (CP) is the point from which the fuel required to reach the destination equals the fuel required to return to base; it is computed with the same formula as the PNR but with the destination as the alternate.

The navigation log records, for each leg: waypoint, track, TAS, wind, heading, groundspeed, distance, ETA, fuel flow, fuel remaining, and the fuel check against the flight plan; deviations beyond a defined tolerance require a re-plan.

Fuel is planned in the sequence: taxi fuel, trip fuel, contingency fuel, alternate fuel, final reserve fuel, and additional fuel; the sum is the minimum block fuel, and extra fuel is added at the commander's discretion.

Contingency fuel is normally 5% of the trip fuel, or 3% if the operator has an approved fuel scheme with a suitable en-route alternate; it is intended to cover unforeseen deviations from the planned route.

Final reserve fuel is the fuel required to fly for 30 minutes at holding speed at 1500 ft above the aerodrome in ISA conditions; for a turbine aeroplane it is normally 30 minutes, and the final reserve must not be planned to be used.

Alternate fuel is the fuel required to fly from the destination to the alternate, including a missed approach, a climb, and a descent; if two alternates are required, the fuel for the more distant one is used.

Taxi fuel is the fuel consumed before take-off, including APU and engine start; it is not part of trip fuel and must be added to the block fuel.

Fuel density: jet fuel density varies with temperature, so fuel mass must be computed from volume and density; a change of 1 C in fuel temperature changes the density of Jet A-1 by about 0.0008 kg/L, which matters for mass and balance.

In-flight fuel checks: the crew compares actual fuel remaining at each waypoint with the flight-plan fuel; if the actual fuel is below the planned fuel by more than the contingency fuel, a re-plan or diversion is required.

Minimum fuel and emergency fuel: 'minimum fuel' means the aircraft can only land with the final reserve intact; 'mayday fuel' is declared when the fuel remaining is below the final reserve, and the crew must declare an emergency.

The operational flight plan must contain: registration and type, date, crew, route and waypoints, cruise levels, masses, fuel figures, and the commander's signature; it is retained by the operator for the required period.

Fuel management in flight: the commander must ensure that the fuel remaining is sufficient for the planned flight plus the final reserve, and must monitor fuel against the flight plan at each waypoint.

In-flight replanning: if the destination becomes unavailable, the crew computes the fuel required to the new destination or alternate, and the commander decides whether to continue, divert, or hold.

The commander has final authority over fuel and may add extra fuel; the operator must provide a fuel policy that meets the applicable regulations, and the commander may deviate from it only in the interest of safety.

Fuel tankering is carried when fuel is cheaper at the departure aerodrome; the extra fuel increases the landing mass and the take-off mass, and the cost saving must be weighed against the performance penalty.

The flight plan fuel must be cross-checked against the aircraft's fuel gauges before departure, and the actual fuel on board must be recorded; a discrepancy between the planned and actual fuel must be resolved before take-off.

Fuel dumping is permitted only when the aircraft is above the maximum landing mass and the situation requires it; the dump must be conducted in accordance with the aircraft flight manual and ATC coordination.

The fuel log records the fuel on board at each waypoint, the fuel used, and the fuel remaining; it is the primary record for the post-flight fuel analysis and for the operator's fuel efficiency monitoring.

Mass and balance is computed as: total mass = empty mass + crew + payload + usable fuel; each item's mass is multiplied by its arm (distance from the reference datum) to give a moment, and CG position = total moment / total mass.

The datum is an arbitrary vertical reference plane chosen by the manufacturer; arms forward of the datum are negative, aft are positive, so sign discipline is essential when summing moments.

Maximum take-off mass (MTOM), maximum landing mass (MLM), maximum zero-fuel mass (MZFM) and maximum ramp mass are separate limits; the MZFM limit applies with all usable fuel excluded and is normally the structural limit on payload.

Zero-fuel mass = take-off mass minus usable fuel; if ZFM exceeds MZFM, payload or fuel must be reduced before departure even if MTOM is satisfied.

The forward CG limit is normally set by elevator authority for rotation and landing flare; the aft CG limit is set by static and dynamic longitudinal stability, so an aft CG raises stall recovery risk and reduces stick-fixed stability.

Floor loading limits (kg per unit area) and running-load limits per metre of fuselage must be checked separately from total mass; a load within MTOM can still exceed a structural floor limit.

Load sheet terminology: DOW (dry operating mass) = empty mass + crew + crew baggage + catering + potable water; DOI is the corresponding index; traffic load = passengers + baggage + cargo; take-off mass = DOW + traffic load + take-off fuel.

Index method: index = (moment / constant) + K, where K is a negative or positive reference constant; the CG is read from a load sheet index table, and the index change per unit mass is constant only if the arm is constant.

For a mass moved within the aircraft, the CG shift = (mass moved x distance moved) / total mass, in the direction of the move; for a mass added or removed, CG shift = (mass x (arm of item - original CG)) / new total mass.

Density altitude = pressure altitude + 120 x (OAT - ISA temperature at that level), where ISA temperature = 15 C - 1.98 C per 1000 ft; density altitude governs take-off and climb performance.

Take-off distance required (TODR) must not exceed take-off distance available (TODA); take-off run required (TORR) must not exceed TORA; the screen height at the end of TODA is 35 ft for aeroplanes and 50 ft for jets under the applicable certification basis.

Balanced field length (BFL) is the field length at which the accelerate-stop distance equals the accelerate-go distance to 35 ft; V1 is the decision speed at which the critical engine failure is recognised and the stop or continue decision is made.

V speeds: V1 decision speed, VR rotation speed, V2 take-off safety speed (minimum at 35 ft), VMCA minimum control speed in the air, VMCG minimum control speed on the ground, VREF landing reference speed (normally 1.3 VS0 for the landing configuration).

Climb gradients for certification: for a twin-engine aeroplane, second-segment climb (gear up, one engine inoperative, V2, take-off flaps) requires a minimum gross gradient of 2.4%, reduced to 2.7% for three engines and 3.0% for four engines; the net gradient is the gross gradient minus 0.8% for twins and 0.9% for three engines.

Landing distance required (LDR) must not exceed landing distance available (LDA); the landing distance is measured from 50 ft above the threshold to a full stop, and is affected by runway slope, surface, wind, and runway condition (dry, wet, contaminated).

Headwind and tailwind components: use only 50% of a reported headwind and 150% of a reported tailwind when applying wind correction to take-off and landing distances, unless the operation specifies otherwise.

Runway slope: an uphill slope increases the take-off distance; a 1% uphill slope typically increases take-off distance by about 10% for a light twin, and the effect must be read from the aircraft flight manual, not estimated.

Obstacle clearance: the net take-off flight path must clear all obstacles by 35 ft vertically, and the net gradient is the gross gradient reduced by the specified margin; the second-segment climb is the limiting segment for obstacle clearance in most twins.

The operational flight plan (OFP) is the pilot's document that records the route, altitudes, fuel, masses, and performance; the ATS flight plan (ICAO FPL) is the message filed with air traffic services and is a different document.

True airspeed from indicated airspeed: TAS = IAS x (1 + 0.02 x altitude in thousands of feet) is a rough approximation; the precise relationship uses density ratio, TAS = IAS / sqrt(sigma), where sigma is the density ratio.

Mach number = TAS / local speed of sound; the speed of sound at sea level ISA is about 661 kt, decreasing with temperature to about 573 kt at the tropopause; above the tropopause, TAS for a given Mach increases with altitude.

Great-circle distance = 60 x angular distance in degrees; the rhumb line is a constant-track line that is longer than the great circle except on the equator or a meridian.

Wind triangle: heading = track - wind correction angle; the wind correction angle satisfies sin(WCA) = (wind speed x sin(wind angle - track)) / TAS, and groundspeed = TAS x cos(WCA) - wind speed x cos(wind angle - track).

Point of no return (PNR) for a given fuel: distance to PNR = (fuel available x groundspeed out x groundspeed back) / (fuel consumption x (groundspeed out + groundspeed back)); the equal-time point (ETP) uses the same formula with time instead of fuel.

Critical point (CP) is the point from which the fuel required to reach the destination equals the fuel required to return to base; it is computed with the same formula as the PNR but with the destination as the alternate.

The navigation log records, for each leg: waypoint, track, TAS, wind, heading, groundspeed, distance, ETA, fuel flow, fuel remaining, and the fuel check against the flight plan; deviations beyond a defined tolerance require a re-plan.

Fuel is planned in the sequence: taxi fuel, trip fuel, contingency fuel, alternate fuel, final reserve fuel, and additional fuel; the sum is the minimum block fuel, and extra fuel is added at the commander's discretion.

Contingency fuel is normally 5% of the trip fuel, or 3% if the operator has an approved fuel scheme with a suitable en-route alternate; it is intended to cover unforeseen deviations from the planned route.

Final reserve fuel is the fuel required to fly for 30 minutes at holding speed at 1500 ft above the aerodrome in ISA conditions; for a turbine aeroplane it is normally 30 minutes, and the final reserve must not be planned to be used.

Alternate fuel is the fuel required to fly from the destination to the alternate, including a missed approach, a climb, and a descent; if two alternates are required, the fuel for the more distant one is used.

Taxi fuel is the fuel consumed before take-off, including APU and engine start; it is not part of trip fuel and must be added to the block fuel.

Fuel density: jet fuel density varies with temperature, so fuel mass must be computed from volume and density; a change of 1 C in fuel temperature changes the density of Jet A-1 by about 0.0008 kg/L, which matters for mass and balance.

In-flight fuel checks: the crew compares actual fuel remaining at each waypoint with the flight-plan fuel; if the actual fuel is below the planned fuel by more than the contingency fuel, a re-plan or diversion is required.

Minimum fuel and emergency fuel: 'minimum fuel' means the aircraft can only land with the final reserve intact; 'mayday fuel' is declared when the fuel remaining is below the final reserve, and the crew must declare an emergency.

The operational flight plan must contain: registration and type, date, crew, route and waypoints, cruise levels, masses, fuel figures, and the commander's signature; it is retained by the operator for the required period.

Fuel management in flight: the commander must ensure that the fuel remaining is sufficient for the planned flight plus the final reserve, and must monitor fuel against the flight plan at each waypoint.

In-flight replanning: if the destination becomes unavailable, the crew computes the fuel required to the new destination or alternate, and the commander decides whether to continue, divert, or hold.

The commander has final authority over fuel and may add extra fuel; the operator must provide a fuel policy that meets the applicable regulations, and the commander may deviate from it only in the interest of safety.

Fuel tankering is carried when fuel is cheaper at the departure aerodrome; the extra fuel increases the landing mass and the take-off mass, and the cost saving must be weighed against the performance penalty.

The flight plan fuel must be cross-checked against the aircraft's fuel gauges before departure, and the actual fuel on board must be recorded; a discrepancy between the planned and actual fuel must be resolved before take-off.

Fuel dumping is permitted only when the aircraft is above the maximum landing mass and the situation requires it; the dump must be conducted in accordance with the aircraft flight manual and ATC coordination.

The fuel log records the fuel on board at each waypoint, the fuel used, and the fuel remaining; it is the primary record for the post-flight fuel analysis and for the operator's fuel efficiency monitoring.

Mass and balance is computed as: total mass = empty mass + crew + payload + usable fuel; each item's mass is multiplied by its arm (distance from the reference datum) to give a moment, and CG position = total moment / total mass.

The datum is an arbitrary vertical reference plane chosen by the manufacturer; arms forward of the datum are negative, aft are positive, so sign discipline is essential when summing moments.

Maximum take-off mass (MTOM), maximum landing mass (MLM), maximum zero-fuel mass (MZFM) and maximum ramp mass are separate limits; the MZFM limit applies with all usable fuel excluded and is normally the structural limit on payload.

Zero-fuel mass = take-off mass minus usable fuel; if ZFM exceeds MZFM, payload or fuel must be reduced before departure even if MTOM is satisfied.

The forward CG limit is normally set by elevator authority for rotation and landing flare; the aft CG limit is set by static and dynamic longitudinal stability, so an aft CG raises stall recovery risk and reduces stick-fixed stability.

Floor loading limits (kg per unit area) and running-load limits per metre of fuselage must be checked separately from total mass; a load within MTOM can still exceed a structural floor limit.

Load sheet terminology: DOW (dry operating mass) = empty mass + crew + crew baggage + catering + potable water; DOI is the corresponding index; traffic load = passengers + baggage + cargo; take-off mass = DOW + traffic load + take-off fuel.

Index method: index = (moment / constant) + K, where K is a negative or positive reference constant; the CG is read from a load sheet index table, and the index change per unit mass is constant only if the arm is constant.

For a mass moved within the aircraft, the CG shift = (mass moved x distance moved) / total mass, in the direction of the move; for a mass added or removed, CG shift = (mass x (arm of item - original CG)) / new total mass.

Density altitude = pressure altitude + 120 x (OAT - ISA temperature at that level), where ISA temperature = 15 C - 1.98 C per 1000 ft; density altitude governs take-off and climb performance.

Take-off distance required (TODR) must not exceed take-off distance available (TODA); take-off run required (TORR) must not exceed TORA; the screen height at the end of TODA is 35 ft for aeroplanes and 50 ft for jets under the applicable certification basis.

Balanced field length (BFL) is the field length at which the accelerate-stop distance equals the accelerate-go distance to 35 ft; V1 is the decision speed at which the critical engine failure is recognised and the stop or continue decision is made.

V speeds: V1 decision speed, VR rotation speed, V2 take-off safety speed (minimum at 35 ft), VMCA minimum control speed in the air, VMCG minimum control speed on the ground, VREF landing reference speed (normally 1.3 VS0 for the landing configuration).

Climb gradients for certification: for a twin-engine aeroplane, second-segment climb (gear up, one engine inoperative, V2, take-off flaps) requires a minimum gross gradient of 2.4%, reduced to 2.7% for three engines and 3.0% for four engines; the net gradient is the gross gradient minus 0.8% for twins and 0.9% for three engines.

Landing distance required (LDR) must not exceed landing distance available (LDA); the landing distance is measured from 50 ft above the threshold to a full stop, and is affected by runway slope, surface, wind, and runway condition (dry, wet, contaminated).

Headwind and tailwind components: use only 50% of a reported headwind and 150% of a reported tailwind when applying wind correction to take-off and landing distances, unless the operation specifies otherwise.

Runway slope: an uphill slope increases the take-off distance; a 1% uphill slope typically increases take-off distance by about 10% for a light twin, and the effect must be read from the aircraft flight manual, not estimated.

Obstacle clearance: the net take-off flight path must clear all obstacles by 35 ft vertically, and the net gradient is the gross gradient reduced by the specified margin; the second-segment climb is the limiting segment for obstacle clearance in most twins.

The operational flight plan (OFP) is the pilot's document that records the route, altitudes, fuel, masses, and performance; the ATS flight plan (ICAO FPL) is the message filed with air traffic services and is a different document.

True airspeed from indicated airspeed: TAS = IAS x (1 + 0.02 x altitude in thousands of feet) is a rough approximation; the precise relationship uses density ratio, TAS = IAS / sqrt(sigma), where sigma is the density ratio.

Mach number = TAS / local speed of sound; the speed of sound at sea level ISA is about 661 kt, decreasing with temperature to about 573 kt at the tropopause; above the tropopause, TAS for a given Mach increases with altitude.

Great-circle distance = 60 x angular distance in degrees; the rhumb line is a constant-track line that is longer than the great circle except on the equator or a meridian.

Wind triangle: heading = track - wind correction angle; the wind correction angle satisfies sin(WCA) = (wind speed x sin(wind angle - track)) / TAS, and groundspeed = TAS x cos(WCA) - wind speed x cos(wind angle - track).

Point of no return (PNR) for a given fuel: distance to PNR = (fuel available x groundspeed out x groundspeed back) / (fuel consumption x (groundspeed out + groundspeed back)); the equal-time point (ETP) uses the same formula with time instead of fuel.

Critical point (CP) is the point from which the fuel required to reach the destination equals the fuel required to return to base; it is computed with the same formula as the PNR but with the destination as the alternate.

The navigation log records, for each leg: waypoint, track, TAS, wind, heading, groundspeed, distance, ETA, fuel flow, fuel remaining, and the fuel check against the flight plan; deviations beyond a defined tolerance require a re-plan.

Fuel is planned in the sequence: taxi fuel, trip fuel, contingency fuel, alternate fuel, final reserve fuel, and additional fuel; the sum is the minimum block fuel, and extra fuel is added at the commander's discretion.

Contingency fuel is normally 5% of the trip fuel, or 3% if the operator has an approved fuel scheme with a suitable en-route alternate; it is intended to cover unforeseen deviations from the planned route.

Final reserve fuel is the fuel required to fly for 30 minutes at holding speed at 1500 ft above the aerodrome in ISA conditions; for a turbine aeroplane it is normally 30 minutes, and the final reserve must not be planned to be used.

Alternate fuel is the fuel required to fly from the destination to the alternate, including a missed approach, a climb, and a descent; if two alternates are required, the fuel for the more distant one is used.

Taxi fuel is the fuel consumed before take-off, including APU and engine start; it is not part of trip fuel and must be added to the block fuel.

Fuel density: jet fuel density varies with temperature, so fuel mass must be computed from volume and density; a change of 1 C in fuel temperature changes the density of Jet A-1 by about 0.0008 kg/L, which matters for mass and balance.

In-flight fuel checks: the crew compares actual fuel remaining at each waypoint with the flight-plan fuel; if the actual fuel is below the planned fuel by more than the contingency fuel, a re-plan or diversion is required.

Minimum fuel and emergency fuel: 'minimum fuel' means the aircraft can only land with the final reserve intact; 'mayday fuel' is declared when the fuel remaining is below the final reserve, and the crew must declare an emergency.

The operational flight plan must contain: registration and type, date, crew, route and waypoints, cruise levels, masses, fuel figures, and the commander's signature; it is retained by the operator for the required period.

Fuel management in flight: the commander must ensure that the fuel remaining is sufficient for the planned flight plus the final reserve, and must monitor fuel against the flight plan at each waypoint.

In-flight replanning: if the destination becomes unavailable, the crew computes the fuel required to the new destination or alternate, and the commander decides whether to continue, divert, or hold.

The commander has final authority over fuel and may add extra fuel; the operator must provide a fuel policy that meets the applicable regulations, and the commander may deviate from it only in the interest of safety.

Fuel tankering is carried when fuel is cheaper at the departure aerodrome; the extra fuel increases the landing mass and the take-off mass, and the cost saving must be weighed against the performance penalty.

The flight plan fuel must be cross-checked against the aircraft's fuel gauges before departure, and the actual fuel on board must be recorded; a discrepancy between the planned and actual fuel must be resolved before take-off.

Fuel dumping is permitted only when the aircraft is above the maximum landing mass and the situation requires it; the dump must be conducted in accordance with the aircraft flight manual and ATC coordination.

The fuel log records the fuel on board at each waypoint, the fuel used, and the fuel remaining; it is the primary record for the post-flight fuel analysis and for the operator's fuel efficiency monitoring.