ATPL Navigation (Sri Lanka CAA Pilot Licence Examinations) cheat sheet

Great circle distance (nm) = 60 × angular distance in degrees; use the angular arc between two points along the great circle for the shortest route.

Departure (nm) = change of longitude (min) × cos(latitude); apply only along a parallel of latitude, not for great circle legs.

Conversion angle = ½ × change of longitude between the two meridians, giving the angle between the great circle track and the rhumb line at each end.

Rhumb line maintains a constant track angle to all meridians; it appears as a straight line on a Mercator chart but is longer than the great circle.

Mercator scale factor = sec(latitude); the chart is conformal, so shapes are preserved but areas are exaggerated toward the poles.

Lambert conformal conic: great circles plot as approximately straight lines; scale is correct on the two standard parallels.

Polar stereographic chart: meridians are straight lines radiating from the pole; used for high-latitude navigation.

Solar time: LMT = UTC ± longitude/15 (east positive); 15° of longitude equals 1 hour of time change.

Track error from a single fix: TE = angular difference between planned track and the bearing to the fix; closing angle uses the remaining distance.

NDB/ADF: the ADF needle points to the station relative to aircraft heading; relative bearing + heading = magnetic bearing to the station (QDM).

VOR: the CDI indicates the selected radial; TO/FROM flag resolves the 180° ambiguity; a centered needle with a FROM flag means the aircraft is on the selected radial.

VOR line-of-sight range (nm) ≈ 1.23 × √(height in feet); use total height above ground for aircraft plus station.

DME measures slant range, so indicated distance always exceeds true ground distance; error is greatest directly overhead.

ILS localizer provides lateral guidance on a frequency band of 108.10–111.95 MHz (odd tenths); the glideslope is in the 328.6–335.4 MHz band.

ILS glideslope is normally 3°; at a 3° path the aircraft descends about 300 ft per nautical mile.

Marker beacons: outer marker at about 4 nm (blue, 400 Hz), middle marker at about 3500 ft (amber, 1300 Hz), inner marker at the threshold.

GPS needs at least 4 satellites for a 3D fix with receiver clock solved; RAIM detects (and with enough satellites excludes) faulty signals.

Secondary surveillance radar: Mode A gives identity, Mode C gives pressure altitude; a transponder reply is triggered by the interrogation.

Trip fuel covers takeoff to landing at the destination; contingency fuel is a percentage of trip fuel (commonly 5%) or a specified time.

Alternate fuel = fuel from destination to alternate plus approach and landing; final reserve is holding fuel for 30 minutes at 1500 ft above the alternate (turbine).

Fuel required = taxi + trip + contingency + alternate + final reserve + extra; compare with fuel on board for the go/no-go decision.

Specific range = nautical air miles per unit of fuel; maximum specific range occurs near the speed for maximum L/D (best glide).

Endurance (h) = fuel available ÷ fuel flow; range (nm) = endurance × TAS for still air, adjusted for wind.

Ground speed = TAS ± wind component; headwind reduces range and increases trip time; calculate the wind component along track.

PBN/equal-time point: the ETP is where time to the destination equals time back to the departure or alternate airfield.

Point of no return: fuel to continue equals fuel to return; it depends on wind, fuel remaining, and fuel flow.

In-flight monitoring: compare actual fuel flow and ground speed with the flight plan at each waypoint; a sustained negative trend requires recalculating fuel at destination.

Altimeter is a barometer calibrated to ISA; setting QNH makes it read elevation at the airfield, QFE reads zero on the ground, QNE (1013.25 hPa) gives flight level.

Altimeter error: 1 hPa ≈ 30 ft near the surface; flying from high to low pressure without resetting the subscale causes the aircraft to be lower than indicated.

Airspeed: IAS corrected for position and instrument error gives CAS; CAS corrected for compressibility gives EAS; EAS corrected for density gives TAS.

TAS ≈ IAS × (1 + 0.02 × altitude in thousands of feet) as a rough density correction; use the CRP/computer for accurate values.

Mach number = TAS ÷ local speed of sound; speed of sound depends only on temperature (about 661 kt at ISA sea level).

Turn indicator: a standard rate turn is 3°/s, requiring about (TAS/10) + 7 degrees of bank for a rate-one turn.

Attitude indicator uses a gyroscope with two degrees of freedom and is erectible; it indicates pitch and roll independent of the magnetic field.

Heading indicator (directional gyro) drifts due to real and apparent precession; realign with the magnetic compass periodically in straight, level flight.

Magnetic compass: acceleration and turning errors are largest on easterly and westerly headings; it is unreliable in turns and during acceleration.

Mass and balance: total mass = empty mass + payload + fuel; the centre of gravity must lie within the certified forward and aft limits for all phases.

Moment = mass × arm; CG position = total moment ÷ total mass, measured from the datum.

Moving a mass: shift of CG = (mass moved × distance moved) ÷ total mass.

Adding or removing mass: new CG = (original total moment ± added moment) ÷ (original total mass ± added mass).

Forward CG limit is restricted by elevator authority and landing flare; aft CG limit is restricted by longitudinal stability and stall recovery.

Maximum zero-fuel mass excludes usable fuel; maximum takeoff mass includes fuel and is limited by runway, climb, and obstacle performance.

Load sheet: check dry operating mass, takeoff mass, landing mass, and zero-fuel mass against limits; the CG envelope is plotted as mass versus CG position.

Fuel burn shifts CG because fuel has an arm; fuel in wing tanks near the CG has little effect, while fuselage or tail fuel has a large effect.

Underload = allowed mass − actual mass; use it to determine how much payload can still be added within limits.

Great circle distance (nm) = 60 × angular distance in degrees; use the angular arc between two points along the great circle for the shortest route.

Departure (nm) = change of longitude (min) × cos(latitude); apply only along a parallel of latitude, not for great circle legs.

Conversion angle = ½ × change of longitude between the two meridians, giving the angle between the great circle track and the rhumb line at each end.

Rhumb line maintains a constant track angle to all meridians; it appears as a straight line on a Mercator chart but is longer than the great circle.

Mercator scale factor = sec(latitude); the chart is conformal, so shapes are preserved but areas are exaggerated toward the poles.

Lambert conformal conic: great circles plot as approximately straight lines; scale is correct on the two standard parallels.

Polar stereographic chart: meridians are straight lines radiating from the pole; used for high-latitude navigation.

Solar time: LMT = UTC ± longitude/15 (east positive); 15° of longitude equals 1 hour of time change.

Track error from a single fix: TE = angular difference between planned track and the bearing to the fix; closing angle uses the remaining distance.

NDB/ADF: the ADF needle points to the station relative to aircraft heading; relative bearing + heading = magnetic bearing to the station (QDM).

VOR: the CDI indicates the selected radial; TO/FROM flag resolves the 180° ambiguity; a centered needle with a FROM flag means the aircraft is on the selected radial.

VOR line-of-sight range (nm) ≈ 1.23 × √(height in feet); use total height above ground for aircraft plus station.

DME measures slant range, so indicated distance always exceeds true ground distance; error is greatest directly overhead.

ILS localizer provides lateral guidance on a frequency band of 108.10–111.95 MHz (odd tenths); the glideslope is in the 328.6–335.4 MHz band.

ILS glideslope is normally 3°; at a 3° path the aircraft descends about 300 ft per nautical mile.

Marker beacons: outer marker at about 4 nm (blue, 400 Hz), middle marker at about 3500 ft (amber, 1300 Hz), inner marker at the threshold.

GPS needs at least 4 satellites for a 3D fix with receiver clock solved; RAIM detects (and with enough satellites excludes) faulty signals.

Secondary surveillance radar: Mode A gives identity, Mode C gives pressure altitude; a transponder reply is triggered by the interrogation.

Trip fuel covers takeoff to landing at the destination; contingency fuel is a percentage of trip fuel (commonly 5%) or a specified time.

Alternate fuel = fuel from destination to alternate plus approach and landing; final reserve is holding fuel for 30 minutes at 1500 ft above the alternate (turbine).

Fuel required = taxi + trip + contingency + alternate + final reserve + extra; compare with fuel on board for the go/no-go decision.

Specific range = nautical air miles per unit of fuel; maximum specific range occurs near the speed for maximum L/D (best glide).

Endurance (h) = fuel available ÷ fuel flow; range (nm) = endurance × TAS for still air, adjusted for wind.

Ground speed = TAS ± wind component; headwind reduces range and increases trip time; calculate the wind component along track.

PBN/equal-time point: the ETP is where time to the destination equals time back to the departure or alternate airfield.

Point of no return: fuel to continue equals fuel to return; it depends on wind, fuel remaining, and fuel flow.

In-flight monitoring: compare actual fuel flow and ground speed with the flight plan at each waypoint; a sustained negative trend requires recalculating fuel at destination.

Altimeter is a barometer calibrated to ISA; setting QNH makes it read elevation at the airfield, QFE reads zero on the ground, QNE (1013.25 hPa) gives flight level.

Altimeter error: 1 hPa ≈ 30 ft near the surface; flying from high to low pressure without resetting the subscale causes the aircraft to be lower than indicated.

Airspeed: IAS corrected for position and instrument error gives CAS; CAS corrected for compressibility gives EAS; EAS corrected for density gives TAS.

TAS ≈ IAS × (1 + 0.02 × altitude in thousands of feet) as a rough density correction; use the CRP/computer for accurate values.

Mach number = TAS ÷ local speed of sound; speed of sound depends only on temperature (about 661 kt at ISA sea level).

Turn indicator: a standard rate turn is 3°/s, requiring about (TAS/10) + 7 degrees of bank for a rate-one turn.

Attitude indicator uses a gyroscope with two degrees of freedom and is erectible; it indicates pitch and roll independent of the magnetic field.

Heading indicator (directional gyro) drifts due to real and apparent precession; realign with the magnetic compass periodically in straight, level flight.

Magnetic compass: acceleration and turning errors are largest on easterly and westerly headings; it is unreliable in turns and during acceleration.

Mass and balance: total mass = empty mass + payload + fuel; the centre of gravity must lie within the certified forward and aft limits for all phases.

Moment = mass × arm; CG position = total moment ÷ total mass, measured from the datum.

Moving a mass: shift of CG = (mass moved × distance moved) ÷ total mass.

Adding or removing mass: new CG = (original total moment ± added moment) ÷ (original total mass ± added mass).

Forward CG limit is restricted by elevator authority and landing flare; aft CG limit is restricted by longitudinal stability and stall recovery.

Maximum zero-fuel mass excludes usable fuel; maximum takeoff mass includes fuel and is limited by runway, climb, and obstacle performance.

Load sheet: check dry operating mass, takeoff mass, landing mass, and zero-fuel mass against limits; the CG envelope is plotted as mass versus CG position.

Fuel burn shifts CG because fuel has an arm; fuel in wing tanks near the CG has little effect, while fuselage or tail fuel has a large effect.

Underload = allowed mass − actual mass; use it to determine how much payload can still be added within limits.

Great circle distance (nm) = 60 × angular distance in degrees; use the angular arc between two points along the great circle for the shortest route.

Departure (nm) = change of longitude (min) × cos(latitude); apply only along a parallel of latitude, not for great circle legs.

Conversion angle = ½ × change of longitude between the two meridians, giving the angle between the great circle track and the rhumb line at each end.

Rhumb line maintains a constant track angle to all meridians; it appears as a straight line on a Mercator chart but is longer than the great circle.

Mercator scale factor = sec(latitude); the chart is conformal, so shapes are preserved but areas are exaggerated toward the poles.

Lambert conformal conic: great circles plot as approximately straight lines; scale is correct on the two standard parallels.

Polar stereographic chart: meridians are straight lines radiating from the pole; used for high-latitude navigation.

Solar time: LMT = UTC ± longitude/15 (east positive); 15° of longitude equals 1 hour of time change.

Track error from a single fix: TE = angular difference between planned track and the bearing to the fix; closing angle uses the remaining distance.

NDB/ADF: the ADF needle points to the station relative to aircraft heading; relative bearing + heading = magnetic bearing to the station (QDM).

VOR: the CDI indicates the selected radial; TO/FROM flag resolves the 180° ambiguity; a centered needle with a FROM flag means the aircraft is on the selected radial.

VOR line-of-sight range (nm) ≈ 1.23 × √(height in feet); use total height above ground for aircraft plus station.

DME measures slant range, so indicated distance always exceeds true ground distance; error is greatest directly overhead.

ILS localizer provides lateral guidance on a frequency band of 108.10–111.95 MHz (odd tenths); the glideslope is in the 328.6–335.4 MHz band.

ILS glideslope is normally 3°; at a 3° path the aircraft descends about 300 ft per nautical mile.

Marker beacons: outer marker at about 4 nm (blue, 400 Hz), middle marker at about 3500 ft (amber, 1300 Hz), inner marker at the threshold.

GPS needs at least 4 satellites for a 3D fix with receiver clock solved; RAIM detects (and with enough satellites excludes) faulty signals.

Secondary surveillance radar: Mode A gives identity, Mode C gives pressure altitude; a transponder reply is triggered by the interrogation.

Trip fuel covers takeoff to landing at the destination; contingency fuel is a percentage of trip fuel (commonly 5%) or a specified time.

Alternate fuel = fuel from destination to alternate plus approach and landing; final reserve is holding fuel for 30 minutes at 1500 ft above the alternate (turbine).

Fuel required = taxi + trip + contingency + alternate + final reserve + extra; compare with fuel on board for the go/no-go decision.

Specific range = nautical air miles per unit of fuel; maximum specific range occurs near the speed for maximum L/D (best glide).

Endurance (h) = fuel available ÷ fuel flow; range (nm) = endurance × TAS for still air, adjusted for wind.

Ground speed = TAS ± wind component; headwind reduces range and increases trip time; calculate the wind component along track.

PBN/equal-time point: the ETP is where time to the destination equals time back to the departure or alternate airfield.

Point of no return: fuel to continue equals fuel to return; it depends on wind, fuel remaining, and fuel flow.

In-flight monitoring: compare actual fuel flow and ground speed with the flight plan at each waypoint; a sustained negative trend requires recalculating fuel at destination.

Altimeter is a barometer calibrated to ISA; setting QNH makes it read elevation at the airfield, QFE reads zero on the ground, QNE (1013.25 hPa) gives flight level.

Altimeter error: 1 hPa ≈ 30 ft near the surface; flying from high to low pressure without resetting the subscale causes the aircraft to be lower than indicated.

Airspeed: IAS corrected for position and instrument error gives CAS; CAS corrected for compressibility gives EAS; EAS corrected for density gives TAS.

TAS ≈ IAS × (1 + 0.02 × altitude in thousands of feet) as a rough density correction; use the CRP/computer for accurate values.

Mach number = TAS ÷ local speed of sound; speed of sound depends only on temperature (about 661 kt at ISA sea level).

Turn indicator: a standard rate turn is 3°/s, requiring about (TAS/10) + 7 degrees of bank for a rate-one turn.

Attitude indicator uses a gyroscope with two degrees of freedom and is erectible; it indicates pitch and roll independent of the magnetic field.

Heading indicator (directional gyro) drifts due to real and apparent precession; realign with the magnetic compass periodically in straight, level flight.

Magnetic compass: acceleration and turning errors are largest on easterly and westerly headings; it is unreliable in turns and during acceleration.

Mass and balance: total mass = empty mass + payload + fuel; the centre of gravity must lie within the certified forward and aft limits for all phases.

Moment = mass × arm; CG position = total moment ÷ total mass, measured from the datum.

Moving a mass: shift of CG = (mass moved × distance moved) ÷ total mass.

Adding or removing mass: new CG = (original total moment ± added moment) ÷ (original total mass ± added mass).

Forward CG limit is restricted by elevator authority and landing flare; aft CG limit is restricted by longitudinal stability and stall recovery.

Maximum zero-fuel mass excludes usable fuel; maximum takeoff mass includes fuel and is limited by runway, climb, and obstacle performance.

Load sheet: check dry operating mass, takeoff mass, landing mass, and zero-fuel mass against limits; the CG envelope is plotted as mass versus CG position.

Fuel burn shifts CG because fuel has an arm; fuel in wing tanks near the CG has little effect, while fuselage or tail fuel has a large effect.

Underload = allowed mass − actual mass; use it to determine how much payload can still be added within limits.

Great circle distance (nm) = 60 × angular distance in degrees; use the angular arc between two points along the great circle for the shortest route.

Departure (nm) = change of longitude (min) × cos(latitude); apply only along a parallel of latitude, not for great circle legs.

Conversion angle = ½ × change of longitude between the two meridians, giving the angle between the great circle track and the rhumb line at each end.

Rhumb line maintains a constant track angle to all meridians; it appears as a straight line on a Mercator chart but is longer than the great circle.

Mercator scale factor = sec(latitude); the chart is conformal, so shapes are preserved but areas are exaggerated toward the poles.

Lambert conformal conic: great circles plot as approximately straight lines; scale is correct on the two standard parallels.

Polar stereographic chart: meridians are straight lines radiating from the pole; used for high-latitude navigation.

Solar time: LMT = UTC ± longitude/15 (east positive); 15° of longitude equals 1 hour of time change.

Track error from a single fix: TE = angular difference between planned track and the bearing to the fix; closing angle uses the remaining distance.

NDB/ADF: the ADF needle points to the station relative to aircraft heading; relative bearing + heading = magnetic bearing to the station (QDM).

VOR: the CDI indicates the selected radial; TO/FROM flag resolves the 180° ambiguity; a centered needle with a FROM flag means the aircraft is on the selected radial.

VOR line-of-sight range (nm) ≈ 1.23 × √(height in feet); use total height above ground for aircraft plus station.

DME measures slant range, so indicated distance always exceeds true ground distance; error is greatest directly overhead.

ILS localizer provides lateral guidance on a frequency band of 108.10–111.95 MHz (odd tenths); the glideslope is in the 328.6–335.4 MHz band.

ILS glideslope is normally 3°; at a 3° path the aircraft descends about 300 ft per nautical mile.

Marker beacons: outer marker at about 4 nm (blue, 400 Hz), middle marker at about 3500 ft (amber, 1300 Hz), inner marker at the threshold.

GPS needs at least 4 satellites for a 3D fix with receiver clock solved; RAIM detects (and with enough satellites excludes) faulty signals.

Secondary surveillance radar: Mode A gives identity, Mode C gives pressure altitude; a transponder reply is triggered by the interrogation.

Trip fuel covers takeoff to landing at the destination; contingency fuel is a percentage of trip fuel (commonly 5%) or a specified time.

Alternate fuel = fuel from destination to alternate plus approach and landing; final reserve is holding fuel for 30 minutes at 1500 ft above the alternate (turbine).

Fuel required = taxi + trip + contingency + alternate + final reserve + extra; compare with fuel on board for the go/no-go decision.

Specific range = nautical air miles per unit of fuel; maximum specific range occurs near the speed for maximum L/D (best glide).

Endurance (h) = fuel available ÷ fuel flow; range (nm) = endurance × TAS for still air, adjusted for wind.

Ground speed = TAS ± wind component; headwind reduces range and increases trip time; calculate the wind component along track.

PBN/equal-time point: the ETP is where time to the destination equals time back to the departure or alternate airfield.

Point of no return: fuel to continue equals fuel to return; it depends on wind, fuel remaining, and fuel flow.

In-flight monitoring: compare actual fuel flow and ground speed with the flight plan at each waypoint; a sustained negative trend requires recalculating fuel at destination.

Altimeter is a barometer calibrated to ISA; setting QNH makes it read elevation at the airfield, QFE reads zero on the ground, QNE (1013.25 hPa) gives flight level.

Altimeter error: 1 hPa ≈ 30 ft near the surface; flying from high to low pressure without resetting the subscale causes the aircraft to be lower than indicated.

Airspeed: IAS corrected for position and instrument error gives CAS; CAS corrected for compressibility gives EAS; EAS corrected for density gives TAS.

TAS ≈ IAS × (1 + 0.02 × altitude in thousands of feet) as a rough density correction; use the CRP/computer for accurate values.

Mach number = TAS ÷ local speed of sound; speed of sound depends only on temperature (about 661 kt at ISA sea level).

Turn indicator: a standard rate turn is 3°/s, requiring about (TAS/10) + 7 degrees of bank for a rate-one turn.

Attitude indicator uses a gyroscope with two degrees of freedom and is erectible; it indicates pitch and roll independent of the magnetic field.

Heading indicator (directional gyro) drifts due to real and apparent precession; realign with the magnetic compass periodically in straight, level flight.

Magnetic compass: acceleration and turning errors are largest on easterly and westerly headings; it is unreliable in turns and during acceleration.

Mass and balance: total mass = empty mass + payload + fuel; the centre of gravity must lie within the certified forward and aft limits for all phases.

Moment = mass × arm; CG position = total moment ÷ total mass, measured from the datum.

Moving a mass: shift of CG = (mass moved × distance moved) ÷ total mass.

Adding or removing mass: new CG = (original total moment ± added moment) ÷ (original total mass ± added mass).

Forward CG limit is restricted by elevator authority and landing flare; aft CG limit is restricted by longitudinal stability and stall recovery.

Maximum zero-fuel mass excludes usable fuel; maximum takeoff mass includes fuel and is limited by runway, climb, and obstacle performance.

Load sheet: check dry operating mass, takeoff mass, landing mass, and zero-fuel mass against limits; the CG envelope is plotted as mass versus CG position.

Fuel burn shifts CG because fuel has an arm; fuel in wing tanks near the CG has little effect, while fuselage or tail fuel has a large effect.

Underload = allowed mass − actual mass; use it to determine how much payload can still be added within limits.

Great circle distance (nm) = 60 × angular distance in degrees; use the angular arc between two points along the great circle for the shortest route.

Departure (nm) = change of longitude (min) × cos(latitude); apply only along a parallel of latitude, not for great circle legs.

Conversion angle = ½ × change of longitude between the two meridians, giving the angle between the great circle track and the rhumb line at each end.

Rhumb line maintains a constant track angle to all meridians; it appears as a straight line on a Mercator chart but is longer than the great circle.

Mercator scale factor = sec(latitude); the chart is conformal, so shapes are preserved but areas are exaggerated toward the poles.

Lambert conformal conic: great circles plot as approximately straight lines; scale is correct on the two standard parallels.

Polar stereographic chart: meridians are straight lines radiating from the pole; used for high-latitude navigation.

Solar time: LMT = UTC ± longitude/15 (east positive); 15° of longitude equals 1 hour of time change.

Track error from a single fix: TE = angular difference between planned track and the bearing to the fix; closing angle uses the remaining distance.

NDB/ADF: the ADF needle points to the station relative to aircraft heading; relative bearing + heading = magnetic bearing to the station (QDM).

VOR: the CDI indicates the selected radial; TO/FROM flag resolves the 180° ambiguity; a centered needle with a FROM flag means the aircraft is on the selected radial.

VOR line-of-sight range (nm) ≈ 1.23 × √(height in feet); use total height above ground for aircraft plus station.

DME measures slant range, so indicated distance always exceeds true ground distance; error is greatest directly overhead.

ILS localizer provides lateral guidance on a frequency band of 108.10–111.95 MHz (odd tenths); the glideslope is in the 328.6–335.4 MHz band.

ILS glideslope is normally 3°; at a 3° path the aircraft descends about 300 ft per nautical mile.

Marker beacons: outer marker at about 4 nm (blue, 400 Hz), middle marker at about 3500 ft (amber, 1300 Hz), inner marker at the threshold.

GPS needs at least 4 satellites for a 3D fix with receiver clock solved; RAIM detects (and with enough satellites excludes) faulty signals.

Secondary surveillance radar: Mode A gives identity, Mode C gives pressure altitude; a transponder reply is triggered by the interrogation.

Trip fuel covers takeoff to landing at the destination; contingency fuel is a percentage of trip fuel (commonly 5%) or a specified time.

Alternate fuel = fuel from destination to alternate plus approach and landing; final reserve is holding fuel for 30 minutes at 1500 ft above the alternate (turbine).

Fuel required = taxi + trip + contingency + alternate + final reserve + extra; compare with fuel on board for the go/no-go decision.

Specific range = nautical air miles per unit of fuel; maximum specific range occurs near the speed for maximum L/D (best glide).

Endurance (h) = fuel available ÷ fuel flow; range (nm) = endurance × TAS for still air, adjusted for wind.

Ground speed = TAS ± wind component; headwind reduces range and increases trip time; calculate the wind component along track.

PBN/equal-time point: the ETP is where time to the destination equals time back to the departure or alternate airfield.

Point of no return: fuel to continue equals fuel to return; it depends on wind, fuel remaining, and fuel flow.

In-flight monitoring: compare actual fuel flow and ground speed with the flight plan at each waypoint; a sustained negative trend requires recalculating fuel at destination.

Altimeter is a barometer calibrated to ISA; setting QNH makes it read elevation at the airfield, QFE reads zero on the ground, QNE (1013.25 hPa) gives flight level.

Altimeter error: 1 hPa ≈ 30 ft near the surface; flying from high to low pressure without resetting the subscale causes the aircraft to be lower than indicated.

Airspeed: IAS corrected for position and instrument error gives CAS; CAS corrected for compressibility gives EAS; EAS corrected for density gives TAS.

TAS ≈ IAS × (1 + 0.02 × altitude in thousands of feet) as a rough density correction; use the CRP/computer for accurate values.

Mach number = TAS ÷ local speed of sound; speed of sound depends only on temperature (about 661 kt at ISA sea level).

Turn indicator: a standard rate turn is 3°/s, requiring about (TAS/10) + 7 degrees of bank for a rate-one turn.

Attitude indicator uses a gyroscope with two degrees of freedom and is erectible; it indicates pitch and roll independent of the magnetic field.

Heading indicator (directional gyro) drifts due to real and apparent precession; realign with the magnetic compass periodically in straight, level flight.

Magnetic compass: acceleration and turning errors are largest on easterly and westerly headings; it is unreliable in turns and during acceleration.

Mass and balance: total mass = empty mass + payload + fuel; the centre of gravity must lie within the certified forward and aft limits for all phases.

Moment = mass × arm; CG position = total moment ÷ total mass, measured from the datum.

Moving a mass: shift of CG = (mass moved × distance moved) ÷ total mass.

Adding or removing mass: new CG = (original total moment ± added moment) ÷ (original total mass ± added mass).

Forward CG limit is restricted by elevator authority and landing flare; aft CG limit is restricted by longitudinal stability and stall recovery.

Maximum zero-fuel mass excludes usable fuel; maximum takeoff mass includes fuel and is limited by runway, climb, and obstacle performance.

Load sheet: check dry operating mass, takeoff mass, landing mass, and zero-fuel mass against limits; the CG envelope is plotted as mass versus CG position.

Fuel burn shifts CG because fuel has an arm; fuel in wing tanks near the CG has little effect, while fuselage or tail fuel has a large effect.

Underload = allowed mass − actual mass; use it to determine how much payload can still be added within limits.

Great circle distance (nm) = 60 × angular distance in degrees; use the angular arc between two points along the great circle for the shortest route.

Departure (nm) = change of longitude (min) × cos(latitude); apply only along a parallel of latitude, not for great circle legs.

Conversion angle = ½ × change of longitude between the two meridians, giving the angle between the great circle track and the rhumb line at each end.

Rhumb line maintains a constant track angle to all meridians; it appears as a straight line on a Mercator chart but is longer than the great circle.

Mercator scale factor = sec(latitude); the chart is conformal, so shapes are preserved but areas are exaggerated toward the poles.

Lambert conformal conic: great circles plot as approximately straight lines; scale is correct on the two standard parallels.

Polar stereographic chart: meridians are straight lines radiating from the pole; used for high-latitude navigation.

Solar time: LMT = UTC ± longitude/15 (east positive); 15° of longitude equals 1 hour of time change.

Track error from a single fix: TE = angular difference between planned track and the bearing to the fix; closing angle uses the remaining distance.

NDB/ADF: the ADF needle points to the station relative to aircraft heading; relative bearing + heading = magnetic bearing to the station (QDM).

VOR: the CDI indicates the selected radial; TO/FROM flag resolves the 180° ambiguity; a centered needle with a FROM flag means the aircraft is on the selected radial.

VOR line-of-sight range (nm) ≈ 1.23 × √(height in feet); use total height above ground for aircraft plus station.

DME measures slant range, so indicated distance always exceeds true ground distance; error is greatest directly overhead.

ILS localizer provides lateral guidance on a frequency band of 108.10–111.95 MHz (odd tenths); the glideslope is in the 328.6–335.4 MHz band.

ILS glideslope is normally 3°; at a 3° path the aircraft descends about 300 ft per nautical mile.

Marker beacons: outer marker at about 4 nm (blue, 400 Hz), middle marker at about 3500 ft (amber, 1300 Hz), inner marker at the threshold.

GPS needs at least 4 satellites for a 3D fix with receiver clock solved; RAIM detects (and with enough satellites excludes) faulty signals.

Secondary surveillance radar: Mode A gives identity, Mode C gives pressure altitude; a transponder reply is triggered by the interrogation.

Trip fuel covers takeoff to landing at the destination; contingency fuel is a percentage of trip fuel (commonly 5%) or a specified time.

Alternate fuel = fuel from destination to alternate plus approach and landing; final reserve is holding fuel for 30 minutes at 1500 ft above the alternate (turbine).

Fuel required = taxi + trip + contingency + alternate + final reserve + extra; compare with fuel on board for the go/no-go decision.

Specific range = nautical air miles per unit of fuel; maximum specific range occurs near the speed for maximum L/D (best glide).

Endurance (h) = fuel available ÷ fuel flow; range (nm) = endurance × TAS for still air, adjusted for wind.

Ground speed = TAS ± wind component; headwind reduces range and increases trip time; calculate the wind component along track.

PBN/equal-time point: the ETP is where time to the destination equals time back to the departure or alternate airfield.

Point of no return: fuel to continue equals fuel to return; it depends on wind, fuel remaining, and fuel flow.

In-flight monitoring: compare actual fuel flow and ground speed with the flight plan at each waypoint; a sustained negative trend requires recalculating fuel at destination.

Altimeter is a barometer calibrated to ISA; setting QNH makes it read elevation at the airfield, QFE reads zero on the ground, QNE (1013.25 hPa) gives flight level.

Altimeter error: 1 hPa ≈ 30 ft near the surface; flying from high to low pressure without resetting the subscale causes the aircraft to be lower than indicated.

Airspeed: IAS corrected for position and instrument error gives CAS; CAS corrected for compressibility gives EAS; EAS corrected for density gives TAS.

TAS ≈ IAS × (1 + 0.02 × altitude in thousands of feet) as a rough density correction; use the CRP/computer for accurate values.

Mach number = TAS ÷ local speed of sound; speed of sound depends only on temperature (about 661 kt at ISA sea level).

Turn indicator: a standard rate turn is 3°/s, requiring about (TAS/10) + 7 degrees of bank for a rate-one turn.

Attitude indicator uses a gyroscope with two degrees of freedom and is erectible; it indicates pitch and roll independent of the magnetic field.

Heading indicator (directional gyro) drifts due to real and apparent precession; realign with the magnetic compass periodically in straight, level flight.

Magnetic compass: acceleration and turning errors are largest on easterly and westerly headings; it is unreliable in turns and during acceleration.

Mass and balance: total mass = empty mass + payload + fuel; the centre of gravity must lie within the certified forward and aft limits for all phases.

Moment = mass × arm; CG position = total moment ÷ total mass, measured from the datum.

Moving a mass: shift of CG = (mass moved × distance moved) ÷ total mass.

Adding or removing mass: new CG = (original total moment ± added moment) ÷ (original total mass ± added mass).

Forward CG limit is restricted by elevator authority and landing flare; aft CG limit is restricted by longitudinal stability and stall recovery.

Maximum zero-fuel mass excludes usable fuel; maximum takeoff mass includes fuel and is limited by runway, climb, and obstacle performance.

Load sheet: check dry operating mass, takeoff mass, landing mass, and zero-fuel mass against limits; the CG envelope is plotted as mass versus CG position.

Fuel burn shifts CG because fuel has an arm; fuel in wing tanks near the CG has little effect, while fuselage or tail fuel has a large effect.

Underload = allowed mass − actual mass; use it to determine how much payload can still be added within limits.