DGCA ATPL Air Navigation cheat sheet

1 minute of arc of latitude = 1 NM = 1.852 km; 1 minute of arc of longitude = 1 NM × cos(latitude).

Great-circle distance between two points: use haversine or spherical law of cosines with angular distance σ where cos σ = sin φ1 sin φ2 + cos φ1 cos φ2 cos Δλ.

Departure (NM east-west) = change of longitude in minutes × cos(mean latitude).

Initial great-circle track from A to B: tan θ = sin Δλ / (cos φ1 tan φ2 − sin φ1 cos Δλ); final track differs by the convergence angle.

Conversion angle (rhumb vs great circle) ≈ ½ × change of longitude × sin(mean latitude).

Variation east, magnetic least: True → Magnetic subtract easterly variation; Variation west, magnetic best: add westerly variation.

Deviation is aircraft-specific and read from the compass correction card; Magnetic + Deviation = Compass (east deviation subtract).

Time: UTC = LMT − longitude/15 (east positive); zone time differs from UTC by whole hours of the zone meridian.

VOR gives magnetic bearing from the station (radial); CDI centred with TO/FROM flag gives the selected course.

VOR accuracy ±1° to ±2° at the station, degrading with distance; line-of-sight, so range ≈ 1.23 × √(height in feet) NM.

DME measures slant range; ground distance = √(slant² − altitude²); error is largest directly overhead.

NDB/ADF: relative bearing + magnetic heading = magnetic bearing to station; ADF needle points to the station, subject to quadrantal error.

ILS: localizer 90 Hz left / 150 Hz right, glide path 90 Hz above / 150 Hz below; fly toward the stronger-signal side.

ILS glide path is normally 3°; nominal threshold crossing height about 50 ft; localizer width ≈ 2.5°–3° full scale each side.

GNSS position from trilateration of pseudoranges; RAIM detects faults, requires adequate satellite geometry (low HDOP/VDOP).

Primary radar gives range and azimuth; secondary surveillance radar uses transponder codes and Mode S for selective interrogation.

Trip fuel = fuel from brake release to touchdown at destination; contingency fuel is typically 5% of trip fuel.

Total fuel = taxi + trip + contingency + alternate + final reserve + additional/extra fuel.

Point of No Return (equal-time point): distance from departure = D × GS_out / (GS_out + GS_return).

Critical Point (equal-fuel point): distance from departure = D × GS_out × (fuel available) / (GS_out + GS_return) scaled by consumption.

Equal-time point differs from equal-fuel point when fuel flow differs between outbound and return.

Specific range = air distance per unit fuel; maximum specific range occurs near the tangent from origin to the fuel-flow vs TAS curve.

Pilot navigation: fix, compare with DR, compute track error and closing angle, then apply correction = track error + closing angle.

Fuel monitoring: compare fuel used against flight-plan figures at each waypoint; a persistent shortfall requires re-planning or diversion.

Upper winds are forecast in degrees true, speed in knots; apply variation to convert to magnetic for flight planning.

Temperature at altitude: ISA = 15 °C − 1.98 °C per 1000 ft up to 36,090 ft (tropopause, −56.5 °C).

True altitude = indicated altitude + (ISA deviation × 4 ft per °C per 1000 ft) for the layer considered.

Cold-air correction: when temperature is below ISA, true altitude is lower than indicated; add 4 ft per °C per 1000 ft to minimum safe altitudes.

QNH set on the subscale gives elevation above mean sea level at the aerodrome; QFE gives height above the aerodrome reference point.

Pressure altitude = indicated altitude with 1013.2 hPa set; use for flight levels above the transition altitude.

Jet streams: core wind ≥ 60 kt, typically near tropopause; CAT is most likely on the cold (polar) side of the core.

Wind at altitude from forecast charts: interpolate between standard levels; wind direction is where wind blows from, true north referenced.

Moment = mass × arm; centre of gravity = total moment / total mass.

Maximum take-off mass = dry operating mass + traffic load + take-off fuel; landing mass excludes trip fuel.

Dry operating mass = basic empty mass + crew + crew baggage + pantry/operating items.

CG shift after moving a mass: ΔCG = (mass moved × distance moved) / total mass.

CG limits are expressed as %MAC; %MAC = (CG − LEMAC) / (MAC length) × 100.

Zero fuel mass = take-off mass − take-off fuel; must not exceed MZFM.

Adding mass aft of the CG moves the CG aft; adding mass forward of the CG moves it forward.

Floor-loading limits and running-load limits constrain where mass may be placed in the cabin or hold.

Take-off distance available (TODA) = TORA + clearway; take-off run available (TORA) is the runway length usable for ground run.

Balanced field length: V1 chosen so that accelerate-stop distance equals accelerate-go distance to 35 ft.

V speeds: V1 decision, VR rotation, V2 take-off safety (≥ 1.13 VS1 at 35 ft), VREF landing reference (≈ 1.3 VS1).

Climb gradient (%) = (height gained / horizontal distance) × 100; required net gradient for second segment is 2.4% for twins.

Landing distance required must not exceed landing distance available; multiply by 1.67 (dry) or 1.92 (wet) for dispatch planning.

Density altitude increases with temperature and pressure altitude; higher density altitude increases take-off and landing distances.

Headwind decreases ground roll and improves climb gradient; tailwind degrades both and is limited by AFM.

Cruise: long-range cruise speed maximises specific range; maximum endurance occurs at minimum fuel flow, not maximum speed.

Pitot-static: airspeed from dynamic pressure, altimeter from static pressure, VSI from rate of static-pressure change.

Blockage of the pitot (static clear) causes airspeed to read as an altimeter; blockage of the static causes airspeed over-read in climb.

Gyroscopic instruments rely on rigidity (attitude/heading) and precession (turn coordinator/rate gyro).

IRS/INS position drifts with time (≈ 1–2 NM/h); update with radio or GNSS fixes.

FMS navigation: RNAV path built from waypoints; LNAV lateral, VNAV vertical; ANP must be less than RNP for the procedure.

ADC (air data computer) supplies pressure altitude and computed airspeed to the FMS; TAS is derived from CAS and temperature.

Radio altimeter measures height above terrain (0–2500 ft), used for low-level approach and GPWS.

EFIS/EICAS integrate attitude, navigation display and engine data; failure modes require reversion to standby instruments.

Semi-circular rule: magnetic tracks 000–179° use odd flight levels; 180–359° use even flight levels (above transition altitude).

Transition altitude is where the altimeter is set to 1013.2 hPa; transition level is the lowest usable flight level above it.

RVSM airspace (FL290–FL410) requires 1000 ft separation and approved altimetry/autopilot equipment.

MNPS/NAT: track and flight-level adherence, position reporting at designated points, contingency procedures for drift.

Reduced vertical separation and oceanic procedures require accurate navigation (RNP 4/RNP 10) and regular position checks.

Aircraft must carry navigation equipment appropriate to the route: VOR/DME, ADF, GNSS, or IRS as required by the flight plan.

Position reporting format: aircraft identification, position, time, flight level, next position and ETA.

Altimeter setting regions: use QNH below transition altitude, standard 1013.2 hPa above; cross-check on descent.

Mercator: rhumb lines are straight, scale varies with secant of latitude, great circles are curved except at the equator.

Lambert conformal conic: great circles are nearly straight, scale is constant on standard parallels.

Polar stereographic: used for high latitudes; scale increases away from the pole of projection.

Chart scale 1:500,000 means 1 cm on chart = 5 km on the ground; 1 NM = 1.852 km.

Grid north vs true north vs magnetic north: grid convergence is the angle between grid north and true north.

Isogonic lines join points of equal magnetic variation; agonic lines join points of zero variation.

Topographic chart symbols: spot heights, contours, and elevation tints give terrain elevation for MSA and obstacle clearance.

Plotting: measure track with a protractor from true north, then apply variation and deviation to obtain compass heading.

VOR radial is the magnetic bearing from the station; the OBS selects the desired course and the CDI shows deviation.

DME paired with VOR gives slant range; at 30,000 ft and 60 NM ground distance the slant error is small but grows close-in.

NDB bearing is relative; ADF card with heading gives magnetic bearing; coastal refraction bends LF waves toward the coast.

ILS localizer and glide path are protected by critical areas; holding short of the CAT I/II/III holding point protects signals.

Marker beacons: outer ≈ 4 NM, middle ≈ 3500 ft, inner ≈ 1000 ft from threshold (varies by airport).

GNSS RAIM availability must be checked for the approach; SBAS/GBAS improve integrity and accuracy.

Radar: primary returns from precipitation and terrain; secondary returns from transponder; range resolution depends on pulse length.

Radio failure: follow the published lost-communication procedure; squawk 7600 and maintain last assigned level or route.

Fuel flow (kg/h) = specific fuel consumption × thrust or power; trip fuel = flow × time.

Endurance = fuel available / fuel flow; range = endurance × ground speed.

Wind triangle: GS = TAS ± wind component along track; drift = arcsin((wind speed × sin wind angle)/TAS).

Heading = track − drift (wind from left gives positive drift); apply variation and deviation to get compass heading.

PET (point of no return) with unequal fuel flows: use the equal-fuel formula, not the equal-time formula.

Alternate fuel is from destination to alternate at the planned mass and forecast wind.

Contingency fuel is typically 5% of trip fuel or a fixed time, depending on operator/regulatory requirement.

Fuel monitoring: compare actual fuel used with planned at each waypoint; adjust speed or route if trend is adverse.

Wind at altitude is referenced to true north in forecasts; convert to magnetic for navigation.

ISA temperature lapse: 2 °C per 1000 ft up to tropopause; above, temperature is constant.

True altitude error = 4 ft per °C ISA deviation per 1000 ft; cold temperatures give lower true altitude.

QNH is the pressure reduced to mean sea level; QFE is the pressure at the aerodrome.

Pressure altitude is used above the transition altitude; altimeter set to 1013.2 hPa.

Jet stream core winds ≥ 60 kt; CAT risk is greatest on the cold side and near the tropopause.

Wind shear on approach: headwind decreasing causes airspeed loss and undershoot tendency.

Forecast winds aloft: interpolate between standard levels; use the nearest forecast for the flight level and route.

Moment = mass × arm; CG = total moment / total mass.

%MAC = (CG − LEMAC) / MAC × 100; MAC length is the mean aerodynamic chord.

Moving mass: ΔCG = (mass × distance) / total mass.

MTOM = DOM + traffic load + take-off fuel; MLM excludes trip fuel.

MZFM = MTOM − take-off fuel; must not exceed MZFM.

Aft CG reduces static stability and increases cruise speed but reduces pitch authority.

Forward CG increases stall speed and reduces range; check CG limits at take-off and landing.

Floor loading and running load limits restrict mass placement in the cabin and holds.

TODA = TORA + clearway; ASDA = TORA + stopway.

Balanced field length: V1 where accelerate-stop = accelerate-go to 35 ft.

V2 ≥ 1.13 VS1 at 35 ft; VREF ≈ 1.3 VS1.

Second-segment climb gradient: 2.4% twins, 2.7% trijets, 3.0% quads (net).

Landing distance required × 1.67 (dry) or 1.92 (wet) must not exceed LDA.

Density altitude increases with temperature and pressure altitude, increasing take-off and landing distances.

Headwind reduces ground roll and improves climb; tailwind degrades both.

Long-range cruise speed maximises specific range; maximum endurance at minimum fuel flow.

Pitot-static: airspeed from dynamic pressure; altimeter from static pressure; VSI from rate of static change.

Pitot blockage with static clear: airspeed behaves like an altimeter.

Static blockage: airspeed over-reads in climb, under-reads in descent.

Gyro rigidity gives attitude/heading; precession gives turn rate.

IRS drift ≈ 1–2 NM/h; update with radio or GNSS fixes.

FMS: LNAV lateral, VNAV vertical; ANP must be less than RNP for the procedure.

Radio altimeter measures height above terrain (0–2500 ft) for approach and GPWS.

ADC supplies pressure altitude and computed airspeed to the FMS; TAS derived from CAS and temperature.

Semi-circular rule: 000–179° magnetic use odd flight levels; 180–359° use even flight levels.

Transition altitude: altimeter set to 1013.2 hPa above it; transition level is the lowest usable FL.

RVSM (FL290–FL410): 1000 ft separation, approved altimetry and autopilot.

MNPS/NAT: track and level adherence, position reporting, contingency for drift.

RNP 4/RNP 10 oceanic navigation requires regular position checks and accurate equipment.

Carry navigation equipment appropriate to route: VOR/DME, ADF, GNSS, IRS as required.

Position report: identification, position, time, flight level, next position and ETA.

Altimeter setting: QNH below transition altitude, 1013.2 hPa above; cross-check on descent.