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

Great circle distance: d = 60 × arccos(sin φ1 sin φ2 + cos φ1 cos φ2 cos Δλ), with d in nautical miles when the angle is in degrees.

Departure (nm) along a parallel = 60 × Δλ(°) × cos φ; use mean latitude for short rhumb-line legs.

Rhumb line maintains constant track; great circle is the shortest path but its track changes continuously unless along a meridian or the equator.

Conversion angle between great circle and rhumb line ≈ ½ × Δλ × sin φ (mean latitude of the leg).

Initial great circle track: tan θ = sin Δλ / (cos φ1 tan φ2 − sin φ1 cos Δλ); quadrant resolved from the sign of Δλ and the relative latitudes.

1 minute of arc of latitude = 1 nm; 1 minute of arc of longitude = cos φ nm.

Mercator chart: rhumb lines plot as straight lines, scale increases with latitude as sec φ, great circles plot as curves concave toward the nearer pole.

Lambert conformal conic: straight-line great circles when the chart is not standard; scale is constant along any given parallel of latitude.

True heading = true course ± drift; magnetic heading = true heading − easterly variation (or + westerly variation).

Compass heading = magnetic heading ± deviation; deviation is aircraft-specific and read from the compass swing card.

Track made good (TMG) = heading ± drift; drift angle = arcsin(crosswind component / TAS).

Wind triangle: GS = TAS cos drift ± wind component along track; headwind reduces GS, tailwind increases it.

E6B/CRP-5: set TAS under the index, place wind dot at wind direction/speed, rotate to true course, read drift and GS.

Time en route = distance / GS; fuel required = (fuel flow × time) plus fixed reserve plus contingency.

Point of no return (equal-time point): distance = (total endurance × GS outbound × GS inbound) / (GS outbound + GS inbound).

Critical point (equal-fuel point) uses fuel flow and safe endurance rather than pure time; recalculate whenever wind or TAS changes.

VOR: CDI centred with TO/FROM flag gives the selected radial/QDM; the ambiguity is resolved by the TO/FROM flag, not by the OBS alone.

VOR radial vs bearing: the radial is the magnetic bearing from the station; your magnetic bearing to the station is the reciprocal.

NDB/ADF: relative bearing + magnetic heading = magnetic bearing to the station; QDM = MB, QDR = MB ± 180°.

DME gives slant range; ground distance ≈ √(slant range² − altitude²), negligible error beyond about 1 nm per 1,000 ft at long range.

ILS localiser gives course guidance (QDM), glide path gives vertical guidance; both are sensitive to false signals beyond the protected area.

GNSS: RAIM needs at least 5 satellites for fault detection and 6 for exclusion; check RAIM prediction before an approach.

Position fix from two VORs: plot both radials; the intersection is the fix. Three lines give a triangle whose size indicates fix quality.

1:60 rule: an error of 1 nm off track over 60 nm equals 1° of track error; use it to compute closing angle and heading correction.

Track error angle = (distance off track / distance flown) × 60; closing angle = (distance off track / distance to go) × 60.

Heading correction = track error + closing angle; apply to the current heading to regain track at the destination.

1 in 60 applies to a 60 nm leg; scale the ratio for other distances (e.g. 30 nm leg: 1 nm off = 2°).

Descent planning: required rate of descent (ft/min) = ground speed (kt) × gradient (%) × 100 / 60, or use 5 × GS for a 3° path.

3° glide path ≈ 318 ft per nm; top of descent distance ≈ altitude to lose / 318 (nm) at a 3° angle.

Pilotage uses visible ground features; dead reckoning uses heading, TAS, wind and time; both should be cross-checked with radio navigation.

ISA: temperature 15 °C and pressure 1013.25 hPa at MSL; lapse rate 1.98 °C per 1,000 ft up to the tropopause at 36,090 ft.

Pressure altitude = indicated altitude with subscale set to 1013.25 hPa; true altitude = pressure altitude corrected for temperature error.

True altitude error ≈ 4 ft per 1,000 ft per °C of ISA deviation; cold air makes the aircraft lower than indicated.

Transition altitude/level: altimeters set to local QNH below the transition altitude and to standard 1013.25 above the transition level.

QNH gives altitude above MSL; QFE gives height above the aerodrome reference point; QNE (1013.25) gives flight level.

Density altitude = pressure altitude + 120 × (OAT − ISA temperature at that pressure altitude), in feet.

1 hPa pressure difference ≈ 30 ft near MSL; a 1 hPa error causes an altimeter error of about 30 ft.

True airspeed increases about 2% per 1,000 ft for a constant IAS at constant temperature, or use TAS = IAS × (1 + altitude/1,000 × 0.02).