Brunei DCA CPL(A) General Navigation cheat sheet

The Earth is modelled as an oblate spheroid: equatorial radius 6378.1 km, polar radius 6356.8 km, flattening about 1/298.3.

A sphere of radius 6371 km is used for most navigation calculation; errors from the spherical assumption stay small over short legs.

Great-circle distance on a sphere: d = 60 × angular distance in arcminutes of arc, so 1 minute of arc equals 1 nautical mile.

Position is expressed as latitude (0° to 90° N/S from the equator) and longitude (0° to 180° E/W from Greenwich).

1 minute of latitude is close to 1 NM everywhere; 1 minute of longitude equals 1 NM × cos(latitude).

Parallels of latitude are small circles except the equator; meridians are semi-great circles converging at the poles.

The shortest path between two points on the surface is the great-circle arc; its track angle changes continuously along the route.

Latitude sign conventions: north positive, south negative; longitude east positive, west negative for computation.

Latitude/longitude (geodetic) is referenced to the ellipsoid; charted positions use the WGS-84 datum unless the chart states otherwise.

Conversion of degrees-minutes-seconds to decimal degrees: decimal = degrees + minutes/60 + seconds/3600.

Change of latitude in minutes of arc equals change of latitude in nautical miles directly.

Departure (distance along a parallel) in NM = change of longitude in minutes × cos(mean latitude).

Difference of longitude between two meridians is the smaller angular difference; the other route is 360° minus that value.

Magnetic/true references and datum shifts must be reconciled before plotting a GNSS position on a non-WGS-84 chart.

A position given as a bearing and distance from a known point (radial/DME fix) is converted to lat/long by resolving the components.

Grid coordinates (e.g. UTM or Lambert grid) require a grid convergence correction to convert grid direction to true direction.

A rhumb line (loxodrome) crosses every meridian at the same true track; it plots as a straight line on a Mercator chart.

A great circle is the shortest distance but plots as a curved line on a Mercator chart, concave toward the nearer pole.

On a Mercator chart, the rhumb-line distance exceeds the great-circle distance except along the equator or a meridian.

Great-circle initial track: tan(initial course) = sin(dLon) / (cos(Lat1)·tan(Lat2) − sin(Lat1)·cos(dLon)).

Great-circle distance: cos(d) = sin(Lat1)·sin(Lat2) + cos(Lat1)·cos(Lat2)·cos(dLon), with d in degrees.

Vertex of a great circle is its highest latitude point; tracks change by 180° of direction at the vertex.

Rhumb-line course from A to B: use the mean latitude method for short legs, Mercator sailing for long legs.

Composite great circles combine a great-circle leg with a limiting parallel when the direct great circle exceeds safe latitude.

Mercator: conformal, rhumb lines straight, scale increases with latitude; used for plotting and short/medium legs.

Lambert conformal conic: conformal, great circles approximately straight; used for high-latitude and mid-latitude area charts.

Polar stereographic: conformal, used for polar navigation where meridians radiate from the pole.

Transverse Mercator and oblique Mercator: used for specific grid systems and special-route charts.

Scale is the ratio of chart distance to Earth distance; a chart is only strictly correct at its standard parallel(s).

Chart projection limitations: shape, area, distance and direction cannot all be preserved simultaneously.

Large-scale charts (e.g. 1:250,000) give more detail; small-scale charts (e.g. 1:5,000,000) give wide-area coverage.

Chart datum, magnetic variation, and edition date must be checked before use; outdated charts may show withdrawn navaids.

True track (TRK) is the path over the ground; true heading (HDG) is the direction the aircraft nose points.

Drift angle = track − heading; positive drift means the aircraft is being pushed right of heading.

Wind triangle: groundspeed vector = true airspeed vector + wind vector.

Wind correction angle: sin(WCA) = (wind speed / TAS) × sin(wind direction − desired track).

Headwind component = wind speed × cos(angle between wind and track); crosswind component = wind speed × sin(angle).

Groundspeed = TAS × cos(WCA) + headwind component (approximately TAS + tailwind component for small WCA).

Dead reckoning position is computed from last known position using heading, TAS, elapsed time and wind estimate.

Track made good (TMG) is derived from two fixes; the difference between TMG and planned track gives the actual drift.

Variation is the angle between true north and magnetic north at a location; it is east or west of true north.

Deviation is the angle between magnetic north and compass north caused by aircraft magnetic fields; it is aircraft- and heading-specific.

Conversion rule: True Virgins Make Dull Company - True + Variation = Magnetic; Magnetic + Deviation = Compass.

East variation/deviation is added when converting true to compass; west is subtracted. Reverse the signs when converting compass to true.

Isogonals are lines of equal variation on a chart; agonic lines join points of zero variation.

Magnetic dip (inclination) is the vertical component of the Earth's field; it is zero at the magnetic equator and 90° at the magnetic poles.

Compass swinging determines residual deviation; a deviation card is valid for the aircraft's installed equipment and heading.

Magnetic heading is used for ATC and flight-plan reporting; true heading is used for chart plotting and wind calculations.

UTC is the reference time standard; local mean time (LMT) = UTC + longitude/15° (east positive, west negative).

Zone time (ZT) = UTC + zone offset; standard zones are 15° wide, offset by whole hours, with some political exceptions.

Time conversion: add east longitude, subtract west longitude when converting UTC to LMT.

Sunrise/sunset times are tabulated for latitude and date in UTC; apply longitude correction to obtain LMT.

The equation of time (up to about ±16 minutes) corrects apparent solar time to mean solar time.

Day of the year and latitude determine the duration of daylight; polar regions experience midnight sun or polar night.

Crossing the International Date Line (about 180° longitude) changes the calendar date by one day.

Elapsed time between two UTC timestamps is independent of zone changes; use UTC for all navigation calculations.

Leg time = leg distance / groundspeed; ETA = departure time + cumulative leg time.

Fuel required = (fuel flow × leg time) + reserve; fuel flow is usually given in kg/h or lb/h.

Specific range = distance flown / fuel used; it peaks near the optimum cruise altitude and speed.

Endurance = usable fuel / fuel flow; range = endurance × groundspeed.

Wind effect on range: headwind reduces specific range, tailwind increases it; the effect grows with wind speed.

Point of no return (PNR) and equal-time point (ETP) are found by balancing fuel or time to/from the destination and base.

Fuel for a diversion = fuel flow × (distance to alternate / groundspeed to alternate).

Cumulative navigation log: track, TAS, wind, WCA, groundspeed, leg time, fuel and ETA are computed leg by leg.

VOR provides magnetic bearing from the station; the CDI shows the selected radial and TO/FROM sense.

DME measures slant range; at high altitude the slant-range error over the station is significant, but it is small at long range.

NDB/ADF gives relative bearing; magnetic bearing = relative bearing + magnetic heading.

ILS localizer gives lateral guidance; glideslope gives vertical guidance; both are referenced to the runway.

Radar and secondary surveillance radar provide range and bearing from the ground station for position fixing.

A position fix requires at least two lines of position; three or more allow a check for gross error.

Cockpit warnings: a VOR/NDB with a large crossing angle gives the best fix geometry; shallow angles magnify error.

Radio altitude measures height above terrain, not altitude above mean sea level.

RNAV allows flight on any desired path within the coverage of the navigation aids or sensors available.

GNSS position is derived from pseudo-range measurements to at least four satellites; a fifth improves integrity checking.

RAIM detects and isolates faulty satellite signals; it requires sufficient satellites in view.

PBN specifies required navigation performance (RNP) or RNAV values; RNP includes on-board performance monitoring and alerting.

RNP AR (authorization required) permits curved approaches and lower minima with special crew and aircraft approval.

SBAS (e.g. EGNOS, WAAS) augments GNSS for accuracy and integrity; GBAS provides local augmentation at an airport.

GNSS accuracy is degraded by ionospheric/tropospheric delay, multipath, satellite geometry (DOP) and receiver noise.

Navigation specification values (e.g. RNAV 1, RNP 0.3) state the total system error in nautical miles, 95% of the time.

Basic empty mass + payload + fuel = take-off mass; landing mass = take-off mass − trip fuel.

Maximum take-off mass, maximum landing mass and maximum zero-fuel mass are structural limits that must not be exceeded.

Centre of gravity (CG) position affects stability, stall speed and fuel consumption; forward CG increases drag and fuel burn.

Aft CG reduces longitudinal stability and may reduce fuel burn but can make the aircraft difficult to recover from a stall.

Mass and balance calculations: moment = mass × arm; CG = total moment / total mass.

Fuel burn increases with mass; heavier aircraft require longer take-off and climb and have lower cruise altitude capability.

Density altitude and temperature affect performance; high density altitude reduces climb rate and increases take-off distance.

Loading must keep CG within the certified forward and aft limits for all phases of flight, including fuel burn-off.