Air navigation: charts, dead reckoning and radio aids

In short

Air navigation is the practice of fixing an aircraft's position and steering it from departure to destination within a known accuracy and time. It rests on three legs: charts (how the curved Earth is drawn on paper and how directions and distances are measured on it), dead reckoning (computing position from heading, airspeed, wind and time), and radio/satellite aids (VOR, DME, NDB, ILS, GNSS) that give independent position fixes. In India it is examined in B.Sc Aviation navigation papers and in the DGCA CPL/ATPL "Air Navigation" paper, and used daily by pilots, flight dispatchers, ATC and AAI/airline operations staff. Employers such as IndiGo, Air India, Air India Express, Akasa, AAI, Airports Authority CNS/ATM branches and ground-handling firms test exactly this material in technical rounds.

Explained

The Earth, position and direction

• Great circle: a circle on the Earth's surface whose plane passes through the centre; it gives the shortest distance between two points but its direction changes continuously.
• Rhumb line (loxodrome): a line cutting all meridians at the same angle - constant direction, longer than the great circle except along a meridian or the Equator.
• Latitude is measured 0-90° N/S from the Equator; longitude 0-180° E/W from the Greenwich meridian. Change of latitude (ch.lat) and change of longitude (ch.long) are the differences between two positions.
• Departure = east-west distance in nautical miles = ch.long (minutes) × cos(latitude). 1 minute of latitude = 1 NM (1 NM = 1,852 m); 1° of latitude = 60 NM.
• Direction references: True north (geographic), Magnetic north (Earth's magnetic field), Compass north (what the aircraft compass reads).
• Variation = angle between true and magnetic north (E variation added to true to get magnetic? - remember the rule below). Deviation = compass error from aircraft magnetism, listed on a compass deviation card.
• Working rule: "Variation east, magnetic least; variation west, magnetic best" - this applies when converting true to magnetic, i.e. Magnetic = True − East variation, Magnetic = True + West variation; reverse the signs going magnetic → true, so True = Magnetic + East variation and True = Magnetic − West variation. Isogonals join points of equal variation; agonic line has zero variation. Variation over India is small (roughly 0-2° E in the west to about 1° W in the far east, changing slowly) - always read the current value off the chart or AIP.
• Speeds: IAS (indicated), CAS (IAS corrected for instrument and position error), EAS, TAS (CAS corrected for density/compressibility), groundspeed (TAS corrected for wind). Mach number = TAS / local speed of sound.

Charts and projections

• A chart must ideally show correct shape (conformality), correct bearings, correct distances, correct areas and straight great circles - no flat chart can do all, so each projection trades one for another.
• Mercator (cylindrical): meridians and parallels are straight and perpendicular; rhumb lines are straight; scale expands as sec(latitude), so areas and distances distort badly towards the poles; great circles curve towards the nearer pole. Used for ocean plotting charts and low-latitude work.
• Lambert conformal conic: cone cutting the Earth at two standard parallels; great circles are very nearly straight, scale almost constant over the chart band, convergence of meridians represented correctly. This is the workhorse for en-route and plotting charts in mid-latitudes.
• Polar stereographic: used above about 70° latitude; grid navigation is used because meridians converge sharply.
• Transverse Mercator / oblique Mercator: narrow strips along a chosen great circle.
• Chart convergence = ch.long × sin(parallel of origin) for Lambert, = ch.long × sin(mean latitude) approximately on Earth; on a Mercator it is zero, which is why a great-circle track must be converted using conversion angle = ½ × convergence.
• Scale: 1:500,000 means 1 cm on chart = 5 km on Earth. Scale = chart length / earth length. A larger denominator is a *smaller* scale with less detail.
• Aeronautical charts in Indian use: ICAO 1:500,000 topographical, World Aeronautical Chart 1:1,000,000, en-route high/low charts, SID and STAR charts, instrument approach charts, aerodrome charts - all published for India in the AIP India (Aeronautical Information Publication) by AAI's AIS, with amendments, supplements and NOTAMs. ICAO Annex 4 governs chart standards; Annex 15 governs aeronautical information.

Dead reckoning and the triangle of velocities

• Dead reckoning (DR): computing a future or present position from a known departure point using heading, TAS, wind velocity and elapsed time. It needs no outside reference and is therefore the fallback when all aids fail.
• Triangle of velocities - three vectors:
  1. Air vector: heading (true) and TAS - where the aircraft points and how fast it moves through the air.
  2. Wind vector: wind direction (the direction wind blows *from*) and speed.
  3. Ground vector: track (true) and groundspeed - the resultant, what happens over the ground.
• Drift = track − heading (starboard/right drift is positive). Wind correction angle (WCA) is the angle applied to heading to make the aircraft follow the desired track; drift and WCA are equal and opposite.
• Headwind/tailwind component = wind speed × cos(angle between wind and track); crosswind component = wind speed × sin(that angle).
• Three standard DR problems: (a) given heading, TAS and wind → find track and groundspeed; (b) given desired track, TAS and wind → find heading and groundspeed; (c) given heading, TAS, track and groundspeed → find wind velocity.
• Solved with the Dalton-type navigation computer (CRP-5/E6B) or trigonometrically; modern FMS does it continuously from inertial and GNSS data.
• Position fixing: a fix is a position from two or more independent observations; a running fix transfers an earlier position line along the DR track. DR error grows with time, so it is regularly updated by a fix.
• Pilot navigation (map reading): matching features to the chart - rivers, rail lines, coastlines, towns - still part of the syllabus and of VFR cross-country flying.
• Track error and correction: use the 1 in 60 rule (below) for closing angle and track-error angle.

Ground-based radio aids

• NDB / ADF: a non-directional beacon transmits in 190-1750 kHz (LF/MF); the airborne ADF needle points to it, giving a relative bearing. Magnetic bearing to station = relative bearing + magnetic heading. Cheap and long-range over sea, but subject to night effect, static (thunderstorm) interference, coastal refraction, quadrantal error and mountain effect; no distance information. Being progressively withdrawn worldwide.
• VOR: VHF omnidirectional range, 108.0-117.95 MHz, transmits 360 radials; the receiver measures the phase difference between a reference and a rotating variable signal to give a magnetic bearing from the station. Accuracy about ±1-2°; line-of-sight only, so range depends on altitude. Cone of confusion overhead; scalloping from reflections. A DVOR (Doppler VOR) is the common modern installation at Indian airports because it is less site-sensitive.
• DME: ultra-high frequency (960-1215 MHz) secondary radar; the aircraft interrogates, the ground transponder replies after a fixed 50 µs delay, and the set measures round-trip time to give slant range in NM plus groundspeed and time-to-station. Slant range ≠ ground distance - the error matters near the station at height.
• VOR/DME together give a one-station rho-theta fix; collocated VOR/DME or VORTAC is the classic en-route aid.
• ILS: precision approach aid - localizer (108.1-111.95 MHz, odd tenths) for azimuth, glide path (328.6-335.4 MHz) typically 3°, plus marker beacons (75 MHz) or DME. Categories: CAT I (DH 200 ft, RVR 550 m), CAT II (DH 100 ft, RVR 300 m), CAT IIIA/B/C (progressively lower/no DH and lower RVR). Delhi (IGI) has CAT IIIB runways, and several Indian airports have CAT II/III capability - the current list is in AIP India. Note that sensitive and critical areas must be protected from vehicles and aircraft.
• Other aids in the syllabus: marker beacons, radar (primary surveillance, secondary SSR with Mode A/C/S, precision approach radar), radio altimeter, transponder/ADS-B, and GBAS/GLS at a few airports.
• Terminology: QDM (magnetic bearing to station), QDR (magnetic bearing from station), QTE (true bearing from station), QUJ (true bearing to station).

Satellite navigation, RNAV and PBN

• GNSS constellations: GPS (USA), GLONASS, Galileo, BeiDou and India's regional NavIC (IRNSS). A receiver measures pseudo-ranges to at least four satellites to solve for latitude, longitude, altitude and clock error.
• Augmentation: ABAS/RAIM (onboard integrity monitoring), SBAS - India's is GAGAN (GPS Aided GEO Augmented Navigation, ISRO + AAI), the first SBAS certified for the equatorial region, supporting LPV approaches; GBAS (local, at an airport).
• PBN (Performance Based Navigation) replaces "which box do you carry" with "what performance must you achieve": RNAV specifications (RNAV 5, RNAV 1/2) and RNP specifications (RNP 4, RNP 1, RNP APCH, RNP AR) - RNP includes on-board performance monitoring and alerting; RNAV does not. The number is the lateral accuracy in NM achieved 95% of the time.
• Approach classifications: 2D (LNAV, VOR, NDB) and 3D (LNAV/VNAV, LPV, ILS). RNP APCH with LNAV minima is now widely available in India, and GAGAN-based LPV approaches have been commissioned at several airports.
• Inertial systems: INS/IRS use accelerometers and gyros - fully self-contained, no external signal, but position drift grows with time (typically a couple of NM per hour), so they are blended with GNSS and DME in the FMS Kalman filter.
• Indian regulatory frame: the Bharatiya Vayuyan Adhiniyam, 2024 (which replaced the Aircraft Act, 1934) and the Aircraft Rules; DGCA is the regulator and issues CAR Section 8 (operations) and airworthiness requirements; AAI provides CNS/ATM services and publishes the AIP; ICAO Annexes 4, 5 (units), 10 (radio navigation aids), 11 and 15 and Doc 8168 (PANS-OPS) and Doc 9613 (PBN Manual) are the international references. India's airspace reorganisation and the flexible use of airspace and GAGAN mandate timelines are revised periodically - check the current DGCA CAR/AIC rather than relying on a remembered date.

Time, flight planning interface and units

• UTC is the universal reference; IST = UTC + 5:30. Indian flight plans, NOTAMs and ATC clearances use UTC.
• LMT: 1° of longitude = 4 minutes of time; 15° = 1 hour.
• Standard units (ICAO Annex 5 as applied in India): distance in NM, short distance/runway and visibility in metres, altitude in feet, speed in knots, vertical speed in feet per minute, wind in knots, pressure in hectopascals, mass in kilograms.
• Altimetry references: QNH (altitude above mean sea level), QFE (height above aerodrome), standard 1013.25 hPa for flight levels. India's transition altitude is commonly 4,000 ft at many aerodromes but is specified per aerodrome in the AIP - read the chart.
• Convergency and departure feed into great-circle flight planning; detailed fuel and mass computations belong to the flight-planning topic.

Key points

• Nautical mile - 1,852 m, equal to 1 minute of latitude; the basis of all navigation distance work.
• Great circle vs rhumb line - shortest path with changing direction vs constant direction but longer path.
• Departure - east-west distance = ch.long in minutes × cos(lat).
• Variation - true-to-magnetic angle; deviation - compass error in the aircraft; both must be applied in the right order.
• Compass → Magnetic → True - add deviation, then variation (east positive).
• Mercator - straight rhumb lines, sec(lat) scale expansion, great circles concave to the Equator.
• Lambert conformal - near-straight great circles, almost constant scale; standard en-route chart.
• Convergence = ch.long × sin(mean lat); conversion angle = half of convergence.
• Triangle of velocities - air vector + wind vector = ground vector; solves heading, track, groundspeed or wind.
• Drift and WCA - equal in size, opposite in sign; crosswind = V·sin θ, headwind = V·cos θ.
• 1 in 60 rule - 1 NM off track in 60 NM flown ≈ 1° of angular error.
• NDB/ADF - gives bearing only, suffers night effect, static and coastal refraction; no range.
• VOR - magnetic radials, ±1-2°, line-of-sight, cone of confusion overhead; DVOR standard in India.
• DME - slant range, not ground range; also gives groundspeed and time to station.
• ILS - localizer plus 3° glide path; CAT I/II/III minima; Delhi has CAT IIIB.
• GNSS/GAGAN - four satellites minimum; GAGAN is India's SBAS enabling LPV approaches.
• RNP vs RNAV - RNP adds on-board performance monitoring and alerting; the figure is 95% lateral accuracy in NM.
• INS/IRS - self-contained but drifts with time; blended with GNSS and DME in the FMS.

Formulas and examples

Example 1 - Departure and distance. Two points lie on latitude 23° N, one at 72° 30′ E (near Ahmedabad) and one at 77° 30′ E (near Bhopal).

• ch.long = 5° = 300 minutes of arc.
• Departure = 300 × cos 23° = 300 × 0.9205 = 276.2 NM (about 511 km).
• Along a meridian the same 300 minutes would be 300 NM - showing how east-west distance shrinks with latitude.

Example 2 - Triangle of velocities (find heading and groundspeed). Desired true track 090°, TAS 150 kt, wind 180°/30 kt.

• Angle between wind direction and track = 180° − 90° = 90°, so the wind is a pure crosswind from the right (starboard).
• Crosswind = 30 × sin 90° = 30 kt; headwind component = 30 × cos 90° = 0 kt.
• WCA = arcsin(crosswind / TAS) = arcsin(30/150) = arcsin 0.2 = 11.5°, applied into wind → true heading 101.5° (say 102°).
• Groundspeed = TAS × cos(WCA) = 150 × cos 11.5° = 150 × 0.9799 = 147.0 kt.
• Time for a 220 NM leg = 220 / 147.0 = 1.497 h = 1 h 30 min.

Example 3 - Compass to true and back. The compass reads 275°, deviation 2° W, variation 1° E.

• Magnetic heading = Compass + deviation (E positive) = 275° − 2° = 273° M.
• True heading = Magnetic + variation (E positive) = 273° + 1° = 274° T.
• If the chart gives a true track of 280° and the same errors apply, the compass heading to steer = 280° − 1° + 2° = 281° C.

Example 4 - 1 in 60 rule. An aircraft flying a 180 NM leg is found 6 NM right of track after 60 NM.

• Track error angle = 60 × 6 / 60 = 6° (right of track).
• Distance remaining = 180 − 60 = 120 NM, so closing angle = 60 × 6 / 120 = 3°.
• Total correction = 6° + 3° = 9° left to reach the destination; a 6° left turn alone would only parallel the original track.

Example 5 - DME slant range and ILS height. An aircraft at 6,000 ft AMSL reads 5.0 NM DME from a station at 1,000 ft AMSL.

• Height difference = 5,000 ft = 5,000/6,076 = 0.823 NM.
• Ground distance = √(5.0² − 0.823²) = √(25 − 0.677) = √24.32 = 4.93 NM - about 0.07 NM of slant error, small here but large close in and high up.
• On a 3° ILS at 4 NM from touchdown, height above threshold ≈ 4 × 318 = 1,272 ft.
• Line-of-sight range for a VOR from 6,000 ft ≈ 1.23 × √6,000 = 1.23 × 77.5 = 95 NM (ignoring the station's own height).

Where it is used

• Airline flight decks and FMS operation: IndiGo, Air India, Air India Express, Akasa and SpiceJet pilots fly PBN routes, RNP APCH and ILS approaches and use DR for contingency when aids are lost.
• Flight dispatch and operations control: great-circle route distances, wind components from significant-weather charts, ETAs and NOTAM/AIP checks for aid outages.
• AAI CNS and ATM engineering: installation, flight-checking and calibration of DVOR, DME, ILS and GAGAN/GBAS ground stations at Indian airports.
• Air traffic control: radar and ADS-B surveillance, PBN route and holding-pattern clearances, separation based on DME distances and RNP capability.
• General aviation, flying clubs and DGCA exams: cross-country VFR navigation with 1:500,000 charts, CRP-5 computer and the "Air Navigation" written paper for CPL/ATPL.
• Drones, UAVs and surveying: GNSS/NavIC positioning, waypoint navigation and geo-fencing under the Drone Rules, 2021.

Interview questions

• Q: What is dead reckoning and why is it still taught when GNSS exists? A: It is computing position from a known point using heading, TAS, wind and time; it needs no external signal, so it is the fallback if GNSS or radio aids fail or are jammed.
• Q: Why is a rhumb line a straight line on a Mercator chart? A: Because the projection keeps meridians parallel and straight, so a line of constant direction cuts them all at the same angle and plots straight.
• Q: Why are Lambert charts preferred for en-route navigation? A: Great circles plot almost straight and scale is nearly constant across the chart band, so distances and tracks can be measured directly.
• Q: Difference between variation and deviation? A: Variation is the angle between true and magnetic north at a place, shown on the chart; deviation is the error of that particular aircraft's compass caused by the aircraft's own magnetism, listed on a deviation card.
• Q: What is the difference between drift and wind correction angle? A: Drift is the angle between heading and the resulting track; WCA is the equal and opposite angle applied to heading to achieve the desired track.
• Q: How does a VOR determine bearing? A: It transmits a reference signal and a rotating variable signal, and the receiver measures the phase difference between them to derive the magnetic radial from the station.
• Q: Why does DME read more than the map distance? A: DME measures slant range from aircraft to station, so the aircraft's height above the station adds to the ground distance; the error is largest close to the station at high altitude.
• Q: State the 1 in 60 rule and a use for it. A: One nautical mile off track per 60 NM flown corresponds to about one degree of angular error; it is used to compute track error, closing angle and the correction to regain track.
• Q: What is the difference between RNAV and RNP? A: Both specify required lateral accuracy, but an RNP specification also requires on-board performance monitoring and alerting of the crew when accuracy cannot be met.
• Q: What is GAGAN and what does it enable? A: India's satellite-based augmentation system by ISRO and AAI; it corrects and monitors GPS signals over the Indian region and supports LPV vertically guided approaches without ground ILS.
• Q: Name three errors of an ADF/NDB. A: Night effect from sky-wave interference, static interference from thunderstorms, and coastal refraction as the signal crosses a coastline at an angle (quadrantal and mountain effects also apply).
• Q: What are ILS CAT I, II and III in terms of minima? A: Roughly DH 200 ft with RVR 550 m for CAT I, DH 100 ft with RVR 300 m for CAT II, and progressively lower or no decision height with much lower RVR for CAT IIIA/B/C; the exact values for an aerodrome are in the AIP.
• Q: Why does an INS need blending with GNSS? A: Inertial position drifts with time because accelerometer and gyro errors integrate, so GNSS, DME or VOR updates bound the error.

Common mistakes

• Applying variation and deviation in the wrong direction - always work compass → magnetic → true adding east errors, and reverse the signs going true → compass.
• Confusing wind direction (where it blows *from*) with the direction it blows *towards* when drawing the wind vector.
• Using plain ch.long as east-west distance and forgetting the cos(latitude) factor in departure.
• Treating DME range as ground distance in approach or holding calculations.
• Mixing up QDM and QDR, or adding relative bearing to true instead of magnetic heading.
• Assuming a great circle plots straight on a Mercator chart, or forgetting the conversion angle when transferring a great-circle track.
• Correcting only the track error angle after going off track, and omitting the closing angle - the aircraft then flies parallel to the intended track.
• Quoting ILS category minima or Indian transition altitudes from memory instead of the current AIP and approach chart.

Related topics

Aviation meteorology · Flight planning, weight and balance · Air traffic control and airspace classification · Aircraft instruments and altimetry · Avionics and communication systems · Airport operations and aeronautical information services