General Navigation

01 The Solar System

Everything in navigation that involves time, daylight and the Sun goes back to two facts: the Earth spins on a tilted axis, and it moves round the Sun on a slightly elliptical orbit.

Kepler and the orbit

• Planets move in ellipses with the Sun at one focus (Kepler's 1st law).
• A line from the Sun to the planet sweeps equal areas in equal times (2nd law), so the Earth moves fastest at perihelion and slowest at aphelion.
• Perihelion (closest, ≈ 147 million km): about 3 January. Aphelion (furthest, ≈ 152 million km): about 4 July. Distance does not cause the seasons — the northern winter happens near perihelion.

Axial tilt and seasons

The Earth's axis is inclined 66½° to the plane of its orbit, which is the same as saying the equator is inclined 23½° to the ecliptic (the Sun's apparent yearly path). This obliquity is constant through the year, and it causes the seasons and the changing length of day and night.

Declination and the special parallels

The Sun's declination is its angular distance north or south of the celestial equator. It swings between 23½°N (June solstice) and 23½°S (December solstice), passing 0° at the equinoxes, when it changes fastest.

Daylight

• At the equinoxes day ≈ night ≈ 12 h almost everywhere — latitude has its smallest influence.
• Day length changes fastest around the equinoxes and slowest around the solstices.
• With northerly declination it is summer in the north: days are longer in the northern and shorter in the southern hemisphere.
• Refraction lifts the Sun's image by about 34′, so sunrise is seen earlier and sunset later than geometry alone would predict.
• All heavenly bodies appear to move east to west, because the Earth rotates west to east (counter-clockwise seen from above the North Pole).

Years

02 The Earth: Position & Distance

This is the largest chapter of the exam. Master five tools — d.lat, d.long, departure, convergency and conversion angle — and most "position" questions become two-line calculations.

Shape of the Earth

• The Earth is an oblate spheroid (ellipsoid), flattened at the poles. Compression ≈ 1/298 (≈ 1/300).
• Equatorial radius 6 378 km, polar 6 357 km — the polar diameter is ≈ 43 km (≈ 23 NM) shorter. Mean diameter ≈ 12 700 km.
• ICAO coordinates are referenced to WGS-84.
• Geodetic latitude (from the local vertical) and geocentric latitude (from the centre) differ most at about 45° (≈ 11.6′), and agree at the equator and poles.
• Because the Earth is flatter near the poles, 1° of latitude is slightly longer at the poles (≈ 60.3 NM) and shorter at the equator (≈ 59.7 NM). 1′ equals exactly 1 852 m at about 45°.

Circles and lines

A parallel of latitude (other than the equator) is a small circle and a rhumb line, but not a great circle. A meridian is half a great circle, running true north–south from pole to pole. Longitude runs 0–180° E or W; the 180° meridian is the Greenwich anti-meridian.

Distance

• d.lat: same hemisphere → subtract, different hemispheres → add. Distance along a meridian = d.lat in minutes = NM.
• d.long: same → subtract, different → add; if the sum exceeds 180°, subtract it from 360° and reverse the direction.

Departure is the east–west distance along a parallel. It is greatest at the equator and zero at the poles. For two different latitudes use the mean latitude.

Great circle versus rhumb line

Convergency and conversion angle

• Convergency is the angle between two meridians — equal to the change in GC direction between them.
• CA is the angle between the GC and the RL at either end.
• GC initial + convergency = GC final; RL = GC initial ± CA.
• Convergency is zero at the equator and equals d.long at the poles.

Vertex, antipodes and paths over the pole

• A GC crossing the equator at track θ reaches a maximum latitude of 90° − θ (a GC on 062° tops out at 28°).
• When the two longitudes differ by exactly 180°, the GC runs over the pole: distance = (90 − lat₁) + (90 − lat₂) degrees.
• Antipode of (φ, λ): opposite latitude, longitude 180° − λ named the other way.

03 Time & Time Conversion

Time questions are pure arithmetic once you have the arc-to-time table in your head and always pass through UTC.

Kinds of time

Arc and time

The International Date Line

The date line follows the 180° meridian, bending round island groups. Crossing it westbound (from the east, e.g. USA → Japan) the date increases by one; crossing eastbound it decreases. Standard-time questions handle this automatically if you work through UTC.

Sunrise, sunset and twilight

• The Air Almanac tabulates sunrise, sunset and twilight in LMT for each latitude — the LMT is practically the same at every longitude on that latitude for a given date. Convert to UTC with longitude.
• Sunrise/sunset: the Sun's upper limb on the visible horizon for a sea-level observer. At altitude the Sun rises earlier and sets later.
• LMT of sunrise depends on date, latitude and elevation — not longitude.

Twilight lasts longer at high latitudes, where the Sun crosses the horizon at a shallow angle. ICAO night: from the end of evening civil twilight to the beginning of morning civil twilight (or as prescribed by the authority).

04 Direction & Terrestrial Magnetism

Directions are only meaningful with a reference: true, magnetic, compass or grid. The heading chain from compass to true is the most-tested routine in the exam.

The Earth's magnetic field

• The Earth behaves like a magnet with a blue pole in northern Canada (it attracts the red, north-seeking end of a compass). Classic exam position of the magnetic north pole: about 73°N 100°W (it has since moved towards Siberia).
• Lines of force run from the red pole to the blue pole: in the northern hemisphere they point down into the ground.
• Total field T splits into a horizontal component H (the directive force for compasses) and a vertical component Z.

Variation

Variation is the angle between true north and magnetic north, named east (+) or west (−). It can reach 180° (between the geographic and magnetic poles) and it changes slowly over time because the magnetic poles wander — the annual change can increase or decrease the value depending on where you are.

Isogonals converge at the magnetic poles (and the geographic poles, where all meridians meet).

Deviation

Deviation is the angle between magnetic north and compass north, caused by the aircraft's own magnetism. It changes with heading and is recorded on the compass deviation card.

The heading chain

Radio bearings and variation

• VOR radials are magnetic at the station: use the variation at the VOR.
• NDB/ADF bearings are measured at the aircraft using its heading: use the variation at the aircraft.
• QDM = magnetic bearing to the station; QDR = magnetic bearing from it (the radial).

05 Compasses

The direct reading compass is simple and independent of electrics, but its errors in turns and accelerations are a favourite exam topic. The remote indicating compass fixes most of them.

Direct reading compass (DRC) — requirements

Acceleration errors

The magnet's CG sits on the equator side of the pivot (offset by dip). Speed changes on east/west headings swing it, giving a false turn. No error on north/south headings, and none at the magnetic equator.

Turning errors

Turning errors are greatest when turning through north and south, and grow with magnetic latitude; nil through east and west.

Aircraft magnetism and deviation

• Hard iron: permanent magnetism acquired mainly during construction (hammering/riveting in the Earth's field); also changed by lightning strikes, heavy shocks, long storage on one heading. Deviation from hard iron ∝ 1/H, so it decreases at lower magnetic latitudes.
• Soft iron: induced magnetism that changes with heading and latitude; cannot be removed by degaussing.
• Hard-iron components: P (fore–aft), Q (athwartships), R (vertical). +P = blue pole forward, +Q = blue pole in the right wing, +R = blue pole below the compass.

Coefficients and the compass swing

• A (constant on all headings, e.g. lubber line misalignment) is corrected by rotating the compass in its mount.
• B and C are corrected with compensating magnets.
• Swing with engines running and normal electrical/radio load on, using a landing (datum) compass to find the magnetic heading.
• Swing when: a compass is fitted or replaced, after major modifications, lightning strikes or heavy shocks, magnetic cargo, long storage, a large permanent change in magnetic latitude, or at scheduled intervals.

Remote indicating (gyro-magnetic) compass

• A flux valve (detector unit), usually in a wingtip or fin away from aircraft magnetism and wiring, senses the direction of H rather than seeking it — more sensitive, with no moving magnet.
• A directional gyro gives short-term stability; a torque (precession) motor slaves it slowly to the flux valve, so turning and acceleration errors are largely removed.
• The annunciator shows synchronisation between gyro and detector and helps achieve it.
• In a turn the detector signal and the signal selsyn rotor change together, so the system stays synchronised.
• Read on a dial, so parallax is least.

06 Units, Speed & Altitude

Conversion questions are free marks if the factors are memorised and the flight computer is used carefully. Keep the units straight before you calculate.

Distance and length

ICAO units: horizontal distance in m, km and NM; heights and altitudes in ft or m; speed in kt (or km/h); vertical speed in ft/min or m/s.

Speed, time, distance

Volume and mass of fuel

Airspeeds and Mach

• IAS → (instrument/position error) → CAS → (compressibility) → EAS → (density) → TAS.
• Below about 10 000 ft and 200 kt, TAS ≈ CAS + 2 % per 1 000 ft.
• Climbing at constant CAS, both TAS and Mach number increase. At constant Mach in a climb (ISA, below the tropopause), TAS decreases.

Ram rise: a total-air-temperature probe reads warm. Rise ≈ (TAS/100)² °C, so COAT ≈ IOAT − (TAS/100)².

Altimetry for navigation

• Pressure altitude = elevation + (1013 − QNH) × 27 ft.
• Density altitude ≈ PA + 120 ft per °C of ISA deviation.
• True altitude: ≈ 4 % of height above the station per 10 °C off ISA — warm air: true higher than indicated; cold air: true lower ("from high to low, look out below").

07 Chart Principles & Scale

No flat chart can show a sphere without distortion. The chart-maker chooses which property to keep; for aviation that is almost always correct angles (conformality).

Desirable properties

• Conformal (orthomorphic): angles and bearings correct, shapes correct locally. The most important property for navigation — scale is the same in all directions at any point, and meridians and parallels cross at 90°.
• Constant scale, great circles as straight lines, rhumb lines as straight lines — no single chart achieves all of these.

Projection surfaces

Charts with straight meridians and scale varying with latitude, and curved rhumb lines: Lambert and polar stereographic.

Scale

A larger scale (1:250 000) shows more detail than a smaller one (1:1 000 000).

Chart features

• Contour lines join points of equal elevation above MSL.
• Isogonals on the chart show variation; isogrivs (on gridded charts) show grivation.
• The exact scale varies slightly across every chart, even a conformal one.

08 Mercator Projections

On a direct Mercator chart, a straight line is a rhumb line. That one property explains the chart's strengths (constant-track plotting) and its weaknesses (scale expansion, no poles).

Direct Mercator

• Cylindrical projection, tangent at the equator, made conformal mathematically.
• Scale ∝ sec lat: correct at the equator, doubling at 60°, infinite at the poles (the poles cannot be shown).
• Chart convergency is zero everywhere — correct only at the equator.
• Every parallel is drawn the same length as the equator.
• Radio bearings (great circles) must be converted to rhumb lines with the conversion angle before plotting.

Transverse Mercator

• Cylinder tangent along a chosen central meridian; scale correct along it and treated as constant within ≈ 300 NM.
• Used for countries with large north–south extent (topographical maps, e.g. the UK OS grid).
• Parallels (except the equator) appear as ellipses; a straight line at 90° to the central meridian is a great circle.
• Convergency correct at the central meridian and the equator.

Oblique Mercator

• Cylinder tangent along any chosen great circle (the "false equator"); used for strip charts along a selected great-circle route.

09 Lambert Conformal Conic

The Lambert conformal conic is the standard en-route chart for mid-latitudes. A straight line is very nearly a great circle, and the chart's convergence is fixed by one number: the constant of the cone, n.

Construction

• Conic, conformal. Meridians are straight lines converging at the cone's apex; parallels are arcs of concentric circles.
• Scale is correct along the two standard parallels (the quoted/nominal scale), smallest at the parallel of origin, and varies only with latitude — constant along any parallel.
• Parallel spacing reduces between and expands outside the standard parallels.
• Great circles are curves concave to the parallel of origin; within the chart they are treated as straight lines. Only meridians are exactly straight GCs.
• Rhumb lines are curves concave to the pole.

The constant of the cone

• Chart convergence equals earth convergence only at the parallel of origin.
• The angle between departure and arrival directions of a straight line = chart (map) convergence.
• The rhumb line between the two ends ≈ straight-line initial track ± half the chart convergence.

Measuring distance

Measure distance with the latitude scale near the middle of the line, or use the quoted scale between the standard parallels.

10 Polar Stereographic & Grid

Near the poles meridians converge so quickly that true direction becomes useless for steering. The polar stereographic chart and a grid overlay give a direction that stays constant along a straight line.

Polar stereographic projection

• A plane tangent at the pole, projected from the opposite pole (azimuthal, conformal).
• Meridians are straight lines radiating from the pole; parallels are concentric circles.
• Scale is correct at the pole and expands away from it (∝ sec² of half the co-latitude) — it gets smaller towards the pole.
• Convergence factor n = 1: chart convergence = d.long (correct at the pole).
• Great circles are almost straight lines (slightly concave to the pole, straighter at higher latitude); rhumb lines are curves concave to the pole.

Grid navigation

Gridding a chart = choosing a datum meridian and drawing lines parallel to it. Grid north is the direction of the datum meridian towards the North Pole. A straight line then keeps a constant grid track even though its true track changes.

For a datum other than Greenwich, use the longitude difference from the datum. In the southern hemisphere the signs reverse.

Grivation

• Grivation is the angle between grid north and magnetic north. "Grivation west, magnetic best": MH = GH + griv W.
• Isogrivs are lines of equal grivation.

11 Dead Reckoning & Wind

Dead reckoning is the triangle of velocities: what the aircraft does through the air, what the air does over the ground, and the result over the ground. Every wind question is one of three unknown sides.

The triangle of velocities

Quick trigonometry (or the CRP-5)

Maximum drift occurs with the wind at 90° to the heading (not the track); maximum drift angle = sin⁻¹(W/TAS).

Air plot and ground plot

• Air distance / ground distance = TAS / GS → GD = AD × GS / TAS.
• A multi-drift wind finding uses three headings and their drifts: the wind that satisfies all of them.

12 In-Flight Navigation

In-flight navigation is about correcting the plan with what the aircraft actually does: track errors, revised ETAs, speed changes to meet a time, and descent planning. The 1-in-60 rule does most of the work.

The 1-in-60 rule

A heading error from using the wrong variation sign (2°E instead of 2°W = 4°) gives an off-track distance of 4/60 × distance (200 NM → ≈ 13–14 NM).

Revised ETA and required groundspeed

Losing time: speed reductions

Work in groundspeed, convert to TAS (GS − wind component), then to IAS or Mach.

Climb and descent

Position lines from radar, NDB and VOR

• Weather radar: target X° left/right of the nose → bearing from aircraft = HDG(T) ∓ X. Plot from the target = reciprocal.
• NDB: QDM = MH + relative bearing; convert to true with the aircraft's variation. VOR: radial = QDR from the station; use the station's variation.
• Radio bearings are great circles; on Mercator apply the conversion angle, on Lambert the chart convergence.
• Running fix / doubling the angle: when the relative bearing changes from 45° on the bow to abeam (90°), the abeam range equals the distance flown.
• Bearing-change rule: range ≈ 60 × distance flown / change of bearing (for small changes near abeam).
• DME gives slant range: ground range = √(slant² − height²), height in NM (6 076 ft per NM).

Visual navigation

• Uncertain of position: keep visual contact, log the time, and head for a large line feature (coast, river, motorway), then identify your position along it.
• Two parallel line features crossed at 90° give a groundspeed check.
• White-out: snow cover merges with an overcast sky, removing the horizon and surface definition.

13 PET & Point of Safe Return

Two points answer two different questions. The PET (point of equal time, or critical point) tells you where going on and turning back take the same time. The PSR/PNR (point of safe return) tells you how far you can go and still get back with the fuel you have.

Point of Equal Time (PET / CP)

D = total distance, O = groundspeed onward (continuing), H = groundspeed home (returning). Both GS are those that apply after the decision — e.g. with one engine out, use the reduced TAS for O and H, but use the normal GS to work out the time taken to reach the PET.

• In still air the PET is at the midpoint. A wind moves the PET into wind: a headwind outbound moves it beyond the midpoint.
• Reducing TAS (e.g. engine failure) makes the wind relatively stronger, moving the PET further into wind.
• The PET does not depend on fuel. The descent is ignored because it occurs whichever way you go.

Point of Safe Return (PSR / PNR)

E = safe endurance (usable fuel excluding reserves, expressed as time). The PSR depends on fuel and groundspeeds, not on the distance to destination.

• Any wind brings the PSR closer to the departure point than in still air.
• For a given wind strength, a pure crosswind reduces the radius of action least.
• Radius of action: the same formula, with E the time available (e.g. return before sunset).

Multi-leg and fuel-based PNR

When wind or fuel flow changes along the route, work leg by leg: subtract the fuel used out-and-back on each whole leg from the usable fuel, then find how far into the next leg the remaining fuel takes you out and back (fuel per NM out + fuel per NM home).

14 Inertial Navigation & FMS

Inertial systems navigate with no external signals at all: they measure acceleration, integrate it into velocity and then into distance. In the current ATPL structure this material sits mainly under Radio Navigation, but it appears throughout these General Navigation banks.

Principle

• The sensors measure acceleration. GS comes from the first integration, distance from the second.
• The platform (real in an INS, mathematical in an IRS) must stay level and aligned: corrections for Earth rotation, transport wander (movement over the curved Earth) and Coriolis.
• Schuler tuning: an undamped 84.4-minute period keeps the platform on the local vertical — used in both gimballed and strap-down systems.
• TAS (from the ADC) is needed only to compute the wind.

INS versus IRS

Alignment and modes

• Mode selector (B737): OFF – ALIGN – NAV – ATT. Alignment happens in ALIGN, or by selecting NAV directly.
• Levelling uses the accelerometers; gyrocompassing finds true north by sensing Earth rate (east gyro / horizontal accelerometers). Only possible on the ground: in flight the system cannot separate aircraft accelerations from misalignment.
• The system computes latitude itself, so it rejects a large latitude error in the entered position but cannot check longitude.
• Present position is entered as latitude/longitude (the format every system accepts). NAV must be selected before the aircraft moves.
• IRS positions are set only during alignment; after that the IRS is not updated (the FMC is).
• Lost in flight (power off/on): no re-alignment — only ATT mode (attitude plus manually entered heading) remains.

Errors

• Azimuth gyro drift at a constant rate: heading error ∝ t; position error ∝ t². Example: 0.01°/h for 12 h at 500 kt → ½ × 500 × 0.000175 × 144 ≈ 6 NM.
• Triple-fit systems compute positions independently, so they normally differ slightly. If one INS disagrees, at least one is drifting.
• INS flies great circles between waypoints: track changes continuously; at a waypoint on the same parallel the track changes by the convergency.

FMS (B737 type)

• Main units: FMC and CDU (MCDU). Start-up pages: IDENT → POS INIT → RTE; SIDs/STARs on DEP/ARR.
• Navigation database: 28-day AIRAC cycle, one active and one inactive.
• Radio position from DME/DME (and VOR/DME); messages are alerting or advisory.
• Magnetic variation tables are stored in the IRS and applied to true heading.
• Created waypoints: place-bearing/distance, place-bearing/place-bearing, along-track displacement, lat/long.

15 Related Subjects

These questions appeared in the General Navigation sources but belong to other ATPL subjects (031 Mass & Balance, 033 Flight Planning, 062 Radio Navigation, 022 Instruments). They are kept here for completeness.

Mass and traffic load

The maximum traffic load is the smallest of: MZFM − DOM; MTOM − DOM − take-off fuel; MLM − DOM − landing fuel; MRM − DOM − ramp fuel.

A forward CG increases longitudinal stability and reduces manoeuvrability (more elevator force needed).

Radio aids

• DME accuracy: ±0.25 NM ± 1.25 % of range.
• GNSS ionospheric delay depends on frequency, so dual-frequency receivers remove most of it.
• Coastal refraction: the same angular error gives a larger position error from the more distant beacon.