ATPL Navigation cheat sheet

Earth model: oblate spheroid with equatorial radius 6378.1 km and polar radius 6356.8 km; flattening 1/298.3. A sphere of radius 6371 km is used for most navigation calculations.

1 minute of latitude equals 1 nautical mile (1852 m) on the sphere; 1 minute of longitude equals 1 NM times the cosine of the latitude.

Great circle: shortest path between two points, plane passes through Earth's centre; its track direction changes continuously except along the equator or a meridian.

Rhumb line: constant track, cuts every meridian at the same angle; longer than the great circle except on the equator or a meridian.

Conversion: departure (NM) = change of longitude in minutes x cos(latitude); use mean latitude for short legs.

Initial great-circle bearing from A to B: use the spherical sine/cosine rules or the Napier analogy; verify with the approximate formula tan(initial course) = sin(dLon) / (cos(latA) x tan(latB) - sin(latA) x cos(dLon)).

Vertex of a great circle is the highest latitude reached; at the vertex the track is 090 or 270 degrees true.

Position formats: degrees-minutes-seconds, degrees-decimal minutes, and MGRS/UTM grid; WGS 84 is the standard geodetic datum for GNSS.

Variation: angle between true north and magnetic north at a place; east variation means magnetic north lies east of true north, so magnetic bearing = true bearing - east variation.

Deviation: angle between magnetic north and the compass north of a particular installation; caused by aircraft magnetic fields and electrical circuits.

Memory rule: True Virgins Make Dull Company = True + Variation = Magnetic + Deviation = Compass; add easterly, subtract westerly.

Isogonals join points of equal variation; the agonic line joins points of zero variation. Variation changes with time (annual change) and with position.

Earth's magnetic field: dip (inclination) is 0 at the magnetic equator and 90 degrees at the magnetic poles; the horizontal component drives the compass.

Direct-reading (wet) compass: magnetic needles in fluid; errors include turning and acceleration errors, northerly turning error largest at high latitude.

Remote-reading compass (flux valve / gyro): flux valve senses horizontal component; slaving unit corrects the directional gyro; fast erection and no turning error.

Compass swing determines residual deviation; deviation card is valid for the aircraft's electrical and magnetic configuration at the time of the swing.

Mercator projection: cylindrical, conformal (angles and shapes preserved), scale increases with latitude; rhumb lines are straight lines, great circles are curved.

Lambert conformal conic: cone intersects or is tangent to the sphere; conformal; great circles approximate straight lines; standard parallels define the scale.

Polar stereographic: used for polar charts; conformal; meridians are straight lines radiating from the pole.

Transverse Mercator: cylinder wrapped around a meridian; used for UTM grid; scale is true on the central meridian.

Scale: representative fraction 1:500,000 means 1 unit on the chart equals 500,000 units on the ground; 1 NM = 1 minute of latitude.

Aeronautical chart symbols: aerodrome, controlled airspace, danger/restricted areas, radio navigation aids, obstacles, and elevation tints.

Chart date and edition must be checked; airspace and frequencies change frequently, so use current charts and NOTAMs.

Plotting: measure tracks with a protractor from a true meridian; on Lambert charts use the nearest meridian because meridians converge.

Triangle of velocities: heading and true airspeed form one side, wind velocity the second, resulting track and ground speed the third.

Wind correction angle: sin(WCA) = (wind speed x sin(wind angle to track)) / TAS; track = heading + WCA.

Ground speed: GS = TAS x cos(WCA) + wind component along track; headwind reduces GS, tailwind increases it.

Drift = track - heading; positive drift to the right; heading = required track - drift (correct for wind).

Time = distance / ground speed; fuel = fuel flow x time; always use GS, not TAS, for time and fuel planning.

Wind vector from forecast: direction is the direction the wind comes from; convert to a vector pointing toward the direction the air moves.

Multi-leg DR: compute each leg separately, then accumulate time, fuel, and position; update with fixes to correct accumulated error.

Rule of thumb: 60-to-1, 1 degree of drift per 60 NM equals 1 NM offset; useful for quick wind correction estimates.

Visual navigation: compare chart features (rivers, roads, towns, coastlines) with the ground; use line features and prominent landmarks as checkpoints.

Map reading: orient the chart with north up; use the thumb line and clock code to keep position awareness.

Position fixing: visual fix, VOR/DME radial-distance fix, NDB bearing, GNSS, and radar; a fix from two or more lines of position is best.

Lost procedure: maintain heading and altitude, note time, use radio navigation aids and ATC; climb if terrain and airspace permit to improve radio and visual range.

Track error and closing angle: use the 1-in-60 rule to compute heading corrections from a fix.

ETA revision: new ETA = time at fix + remaining distance / revised GS; keep ATC informed of significant changes.

Diversion: choose a suitable aerodrome, compute new heading, GS, time and fuel; confirm with a positive fix before committing.

Use of GNSS in visual flight does not replace map reading; cross-check the moving map against ground features.

Radio waves travel at the speed of light (3 x 10^8 m/s); VHF is line-of-sight, range approximately 1.23 x sqrt(height in feet) NM.

ADF/NDB: relative bearing from the aircraft to the station; magnetic bearing = magnetic heading + relative bearing; QDM is magnetic bearing to the station.

VOR: radial is the magnetic bearing from the station; CDI shows deviation from the selected radial; TO/FROM flag indicates direction relative to the station.

DME: slant range in NM; ground distance = sqrt(DME^2 - altitude^2); accuracy improves with distance from the station.

ILS: localizer gives lateral guidance (108-112 MHz), glide path gives vertical guidance (329.15-335 MHz); decision height and missed approach apply.

Radar: primary radar uses echoes; secondary surveillance radar uses transponder replies (Mode A identity, Mode C altitude).

GNSS: position from pseudoranges to satellites; RAIM monitors integrity; augmentation (SBAS/GBAS) improves accuracy and integrity.

RNAV/PBN: navigation performance is defined by RNP (onboard performance monitoring and alerting) and RNAV (no onboard monitoring requirement).

RNAV permits flight on any desired path within the coverage of navigation aids or GNSS, rather than direct to/from stations.

FMS: flight management computer, navigation database, and control display unit; computes LNAV and VNAV guidance and performance predictions.

Navigation database: ARINC 424 format; contains waypoints, airways, procedures, and navaids; must be current and the correct cycle for the flight.

Waypoint types: fly-by (turns after the waypoint) and fly-over (turns over the waypoint); procedure turns and holds are coded in the database.

LNAV follows the active route; VNAV follows altitude and speed constraints; autopilot modes must be monitored against the flight plan.

PBN: RNP AR requires special authorization; RNP values are in NM (e.g., RNP 0.3); RNAV 1 and RNAV 2 apply to terminal and en-route phases.

Database and route validation: check the route against the cleared route, confirm waypoint sequence, and verify legs and constraints before departure.

FMS failure or database mismatch: revert to conventional navigation, notify ATC, and follow the operator's procedures.

Polar navigation: use grid navigation or true tracks referenced to the Greenwich meridian; magnetic compass unreliable near the magnetic poles.

Grid track uses grid north (usually the Greenwich meridian direction on polar charts); grid track = true track - convergence (sign per convention).

Oceanic navigation: use GNSS with RAIM, and cross-check with IRS; required navigation performance and contingency procedures apply.

Great-circle planning: use spherical trigonometry or the great-circle formula; the route is shortest but track changes continuously.

Rhumb-line planning: constant track, longer than the great circle; use Mercator charts and the Mercator sailing formulas.

ETOPS/oceanic: track offsets, contingency fuel, and position reporting (ADS-C/CPDLC) are part of the navigation plan.

Convergence: at high latitude, meridians converge rapidly; chart scale and grid references must be handled carefully.

Adverse weather: wind and temperature forecasts affect GS and fuel; use the latest forecasts and update the plan in flight.