DGCA General Navigation – Chapter 1: Direction, Latitude & Longitude

1

The Shape of the Earth

The Earth is not a perfect sphere. Its official shape is described as an oblate spheroid — a sphere slightly flattened at the poles due to centrifugal forces acting during its formation from a rotating gas cloud.

Oblate Spheroid: A sphere flattened at the poles and bulging at the equator. The flattening is called compression.

🔑 Key Values to Memorise:
Compression ≈ 0.3% (1/300th)
Polar diameter is 23 NM or 43 km less than equatorial diameter
Earth is also slightly pear-shaped — max diameter south of Equator
(Southern hemisphere distortion is in metres, not km)

Shapes and Their Cross-Sections

Shape	Cross-Section	Math Complexity
Perfect Sphere	Circle	Simple
Oblate Spheroid	Ellipse	Moderate
Real Earth (Geoid)	Irregular	Complex

✈ DGCA Exam Rule For EASA / DGCA exam calculations, treat the Earth as a perfect sphere with:
Circumference = 21,600 NM or 40,000 km

Fig 1.1 — Four views of Earth's shape. For exams, use the sphere model.

2

Geodosy & Geoid Models

Geodosy is the science of measuring and modelling the Earth's shape. Different countries and agencies have created their own geoid models, each optimised for accuracy over a specific region.

Major Geoid Models

Model	Used By
WGS 84	USA / GPS / ICAO (World Standard)
OS36	UK Ordnance Survey (survey of 1936)
NTF 1970	France (Nouvelle Triangulation de France)
ED50	European Datum 1950 (other EU countries)

⚠ Important: Using different geoid models for the same position can produce errors of up to 200 metres (between ED50 and OS36 extremities). This matters for GPS and FMS accuracy!

Why WGS 84 Became the World Standard

GPS (24 satellites) — accuracy to tens of metres globally. Differences between geoids become significant at this precision.

FMS (Flight Management System) — uses IRS + DME ranging. If DME positions are stored in different datums (UK = OS36, France = NTF70), large position errors occur crossing the English Channel!

✅ ICAO adopted WGS 84 as the world standard. Modern navigation computers auto-correct for Earth shape distortions.

3

The Poles

The Poles are the extremities of the axis about which the Earth spins (the polar axis).

🔑 Key Fact: The polar axis is tilted at 23½° to the axis of Earth's orbit around the Sun. This tilt causes the seasons! (Covered fully in the "Time" chapter.)

Rotation as Seen from the Poles

View from above	Rotation appears
North Pole	ANTI-CLOCKWISE (Counter-clockwise)
South Pole	CLOCKWISE

✈ Exam Favourite "When viewed from above the North Pole, the Earth rotates anticlockwise." This appears frequently in navigation exam questions.

Fig 1.2 — Earth's rotation seen from above each pole

4

Basic Direction on the Earth

Direction is defined starting from a datum — the direction of the Earth's spin, defined as East (hence, "sunrise in the East"). From this, all four cardinal directions follow:

Cardinal Points

N North
Towards North Pole

E East
Direction of spin

S South
Opposite North

W West
Opposite East

Quadrantal Directions (midway between cardinal)

NE

SE

SW

NW

💡 Note: Cardinal & Quadrantal directions were used in maritime navigation but are too imprecise for air navigation. Aviation uses the Sexagesimal system instead.

Fig 1.3 — Cardinal (N,E,S,W) and Quadrantal (NE,SE,SW,NW) points

5

Sexagesimal System / True Direction

The Sexagesimal system measures direction as degrees of a clockwise rotation from North, giving a full 360° circle. This provides the precision required in air navigation.

000° North

090° East

180° South

270° West

🔑 True Direction: When measured from the geographic North Pole, direction is called True direction, suffixed with (T).

N = 000°(T) | E = 090°(T) | S = 180°(T) | W = 270°(T)

⚠ Always use 3-figure groups!
Write 090°(T) NOT 90°(T).
Write 027° NOT 27° — a 2-digit bearing is ambiguous and should be treated as suspect.

Reciprocal Directions

The reciprocal of any bearing is the direction exactly 180° opposite.

Rule: Add or subtract 180° from the given bearing.
If result > 360°, subtract 360°. If result < 0°, add 360°.

Worked Examples

Given Direction	Reciprocal	Working
060°(T)	240°(T)	060 + 180 = 240
353°(T)	173°(T)	353 − 180 = 173
020°(T)	200°(T)	020 + 180 = 200
270°(T)	090°(T)	270 − 180 = 090

💡 Runway Designators: Runways are named at 10° intervals using the magnetic bearing divided by 10 (rounded). A runway at 273° magnetic = RW 27. Its reciprocal end = RW 09. Note: Runway directions use Magnetic North, not True North.

Fig 1.4 — Sexagesimal compass. Directions measured clockwise from North.

🎯 Reciprocal Calculator: Enter a bearing (0–360):
Bearing: 060° → Reciprocal: 240°

6

Position Reference Systems & Circles on the Earth

Position Reference System: A system that defines any position accurately and unambiguously on Earth's surface. For a sphere, linear (x,y) Cartesian co-ordinates are replaced by angular co-ordinates: Latitude and Longitude.

Great Circle vs Small Circle

Feature	Great Circle	Small Circle
Centre & Radius	Same as Earth's	Different from Earth's
Size	Largest possible circle	Smaller than Great Circle
Navigation use	Shortest path between 2 points	Parallels of latitude
Example	Equator, Meridians	All parallels except Equator

🔑 Critical Definition:
A Great Circle is a circle on Earth's surface whose centre and radius are those of the Earth itself.

The shortest distance between two points on Earth is the shorter arc of the Great Circle joining them.

Given two points, there is only ONE Great Circle joining them (unless they are diametrically opposite).

Fig 1.5 — Great Circle arc = shortest path between A and B

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Equator, Meridians, Parallels & the Graticule

The Equator

The Great Circle whose plane is at 90° to the polar axis. It lies East-West and divides Earth into two equal hemispheres. The Equator is the datum (origin) for measuring Latitude.

Latitude origin = 0°

Meridians

Semi-Great Circles joining the North and South poles. Every Great Circle through the poles forms a meridian and its anti-meridian. All meridians indicate True North-South direction and cross the Equator at 90°.

The Prime (Greenwich) Meridian

The meridian passing through Greenwich, London. This is the datum (origin) for measuring Longitude.

Longitude origin = 0°

Parallels of Latitude

Small circles whose planes are parallel to the Equator. They lie East-West and indicate position North or South of the Equator.

Exception: The Equator itself is the only parallel of latitude that is also a Great Circle.

The Graticule

The network formed by the Prime Meridian + all meridians + Equator + all parallels of latitude. It is the spherical equivalent of the x-y grid on graph paper. Position is defined in degrees/minutes/seconds, not by distance.

Fig 1.6 — The Graticule: Meridians (vertical) + Parallels (horizontal) + Equator

9

Latitude

Latitude of any point is the arc (angular distance) measured along the meridian through that point, from the Equator to the point.

Expressed in degrees, minutes, and seconds of arc.
Annotated N (north of Equator) or S (south of Equator).

Range of Latitude Values

Location	Latitude Value
Equator	0° (neither N nor S)
North Pole	90°N
South Pole	90°S

Angular Measurement System

Unit	Subdivision	Symbol
Degree	1/360th of circle	°
Minute of arc	1/60th of degree	ʹ
Second of arc	1/60th of minute	ˮ

✈ Key Exam Distinction Position is measured in degrees, minutes, and seconds.
Direction is measured in degrees and decimal degrees.

How to Find a Parallel of Latitude

From Earth's centre, construct a line with an elevation angle (for N latitudes) or depression angle (for S latitudes) equal to the desired latitude.
Where this line touches the Earth's surface = that parallel of latitude.

Interactive: Latitude Finder

Drag to explore a latitude (°N): Latitude: 28°N (approx. New Delhi, India)

Fig 1.7 — Latitude is the angle at Earth's centre between the Equator and the point

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Geocentric & Geodetic Latitude

Two Types of Latitude

Type	Definition	Used on Charts?
Geocentric	Angle between the line from point to Earth's centre and the Equatorial plane	No
Geodetic (Geographic)	Angle between the normal (perpendicular) to the spheroid surface at the point and the Equatorial plane	YES ✓

🔑 Important Difference:
For a perfect sphere, these two would be identical. Because Earth is an oblate spheroid, the "normal" at a surface point does not pass through Earth's centre.

⚠ Maximum Difference:
Geocentric vs Geodetic latitude differs most at approximately 45°N/S and the maximum difference is about 11.6 minutes of arc (~11.6 NM on the surface — significant for precision navigation!).

💡 Navigation charts use Geodetic latitude. Modern navigation computers (GPS, FMS, IRS) automatically account for this.

Fig 1.8 — Geocentric (red) vs Geodetic (green) latitude

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Special Cases of Parallels of Latitude

Four special parallels are defined based on Earth's 23½° axial tilt. They relate to the seasons and periods of daylight throughout the year.

Arctic Circle

66½°N

= 90° − 23½°. At summer solstice, sun never sets above this line.

Antarctic Circle

66½°S

= 90° − 23½°. At winter solstice (NH), sun never rises above this line.

Tropic of Cancer

23½°N

Sun is directly overhead on June 21 (NH mid-summer / summer solstice).

Tropic of Capricorn

23½°S

Sun is directly overhead on Dec 21 (NH mid-winter / winter solstice).

Fig 1.9 — The four special parallels of latitude (not to scale)

✈ Memory Aid 66½° = 90° − 23½° (Earth's tilt). Notice that Arctic/Antarctic and Tropic values are complementary (add up to 90°). Also: Cancer is North (C-N), Capricorn is South (C-S).

12

Longitude

Longitude of any point is the shorter arc along the Equator between the Prime Meridian and the meridian through the point.

Measured in degrees and minutes of arc.
Annotated E (east of Greenwich) or W (west of Greenwich).

Range of Longitude Values

Location	Longitude Value
Prime Meridian (Greenwich)	000°
Maximum East	180°E
Maximum West	180°W
Anti-Meridian (coincident)	180°E = 180°W

🔑 Key Comparison — Latitude vs Longitude:
Latitude lines are all parallel to each other. Think: "slicing a pineapple"
Longitude lines fan from N Pole, max separation at Equator, converge at S Pole. Think: "segmenting an orange"

Reversal at 180°E (Anti-Meridian)

⚠ Confusing but Exam-Tested!
At the Greenwich Meridian: Eastern longitudes are to your East.
At the 180° meridian: Eastern longitudes are now to your WEST and Western longitudes to your EAST!

The direction East (090°T) has NOT changed — it is still the direction of Earth's spin. Only the apparent position of E/W hemispheres reverses.

Fig 1.10 — Longitude viewed from above North Pole. Point B is at 040°E.

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Difference in Longitude (Ch Long)

Rules for Calculating Change of Longitude (Ch Long)

RULE 1 — Same side (both E or both W):
Ch Long = Larger − Smaller

Example: 100°W and 080°W → 100 − 80 = 20°

RULE 2 — Different sides (one E, one W):
Ch Long = E value + W value

Example: 020°W and 010°E → 20 + 10 = 30°

⚠ Special Case near 180° Anti-Meridian:
When positions straddle 180°, the calculated total may exceed 180°.
ALWAYS take the SHORTER arc.

Example: 163°E and 152°W
163 + 152 = 315° (this is the long way round!)
Ch Long = 360° − 315° = 45°

Worked Examples

Position 1	Position 2	Ch Long	Method
040°E	070°E	030°	Same side: 70−40
030°W	100°W	070°	Same side: 100−30
020°E	050°W	070°	Diff sides: 20+50
163°E	152°W	045°	360−(163+152)=45
170°E	160°W	030°	360−(170+160)=30

Fig 1.11 — Calculating Ch Long. Red arc = same side (30°). Purple arc = short way round 180° (45°).

Ch Long Calculator:

to

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Positions in Latitude & Longitude

🔑 Rule: Latitude ALWAYS comes first, then Longitude!

New York: 41°N 074°W
Delhi (IGI) ARP: 28°34'N 077°07'E

Formats for Expressing Position

Format	Example	Precision
Degrees only	41N 074W	~1°
Deg + Minutes	4100N 07400W	~1 NM
Decimal minutes	5150.2N 00119.3W	0.1 NM
Deg/Min/Sec (DMS)	515013N 0011912W	~100 ft
DMS decimal	515000.28N 001924.45W	<1 metre

Indian Pilot Locations (Examples)

Location	Approx Position
Delhi (Indira Gandhi Intl)	2832N 07708E
Mumbai (CSIA)	1906N 07251E
Bangalore (Kempegowda)	1314N 07732E
Chennai (MAA)	1300N 08010E
Kolkata (CCU)	2238N 08826E

Fig 1.12 — Major Indian airport positions (approximate)

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Conversion of Latitude & Longitude to Distance

Nautical Mile (NM): Defined so that 1 minute of arc on a Great Circle = 1 NM.

1 NM = 6080 feet = 1852 metres (ICAO standard)
This arises because Earth's mean radius ≈ 20.9 million feet.

🔑 Converting Latitude Difference to Distance:
Since all meridians are Great Circles:
1 minute of latitude change = 1 NM
1 degree of latitude change = 60 NM

Example: 50°00'N to 50°05'N = 5 NM

⚠ Longitude is DIFFERENT!
This 1 minute = 1 NM rule applies to longitude ONLY at the Equator (because the Equator is the only parallel that is also a Great Circle). At all other latitudes, parallels are Small Circles and the formula is different.

Quick Reference

Angular Change	Distance on Meridian
1 second (1")	≈ 101 feet ≈ 30 metres
0.1 minute (0.1')	≈ 608 feet ≈ 185 metres
1 minute (1')	1 NM = 6080 feet = 1852 m
1 degree (1°)	60 NM = 111.1 km
90°	5400 NM (Equator to Pole)
360°	21,600 NM (circumference)

Fig 1.13 — On any meridian, 1 minute of arc = 1 nautical mile

16

Resolution Accuracy Using Latitude & Longitude

The number of decimal places used when writing a position declares the accuracy (resolution) being claimed. Each format corresponds to a real-world precision:

FORMATACCURACYTYPICAL APPLICATION

5321N 1 NM = 6080 ft En route navigation (FPL)

5321.3N 600 ft / 185 m INS, IRS, FMS, GPS cockpit displays

53°21'17"N 100 ft / 30 m Airfield diagram chart, AIP entries

53°21'17.3"N 10 ft / 3 m Location of precision navaid (ILS)

53°21'17.32"N 1 ft / 30 cm Calibration of precision navaid (ILS)

🔑 Two ways to express sub-minute positions:
1. Decimal minutes: 5150.2N (1 decimal place = 0.1 NM = 608 ft = 185 m)
2. DMS: 51°50'12"N (1 second = ~101 ft = ~30 m)

💡 Practical Note: Modern cockpit systems (INS, IRS, FMS, GPS) use decimal minutes. Large-scale charts use DMS. The system can express position from 1 NM (en route) to 50 cm (ILS calibration) — same format, just more digits!

✈ DGCA MCQ Tip "A position given as 5321N implies an accuracy of approximately 1 NM."

"A position entered into an FMS/GPS is to the nearest decimal minute, implying accuracy of 0.1 NM = 600 feet."

"The ARP of an aerodrome quoted in the AIP as 515013N 0011912W is accurate to the nearest second of arc = 100 feet = 30 metres."

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Great Circle Vertices

Vertex: The most northerly (or southerly) point of a Great Circle. Every Great Circle has a Northern Vertex and a Southern Vertex, which are antipodal (diametrically opposite).

🔑 Key Properties of Vertices:
1. Vertices are antipodal — same latitude, opposite longitude (±180°)
2. Distance between vertices = 10,800 NM (half Earth's circumference)
3. At either vertex, the Great Circle direction is 090°(T) or 270°(T) — i.e., the GC runs East-West at the vertex
4. Vertices lie on a meridian and its anti-meridian

Finding the Other Vertex

If Southern Vertex = 63°S 170°W
Then Northern Vertex = 63°N and longitude = 170° − 180° = −10° = 010°E

Rule: Same latitude number, opposite N/S. Longitude ± 180°.

Equator Crossing Points

A Great Circle crosses the Equator at two points, each at a longitude 90° Ch Long from either vertex.

Example: Northern vertex at 63°N 010°E
→ Crosses Equator at: 010°E ± 90° = 100°E and 080°W

Track Angle at Equator Crossing

At the Equator crossing, the angle = latitude of the vertex.

Travelling East from N vertex:
First crossing: Track = 090° + vertex_lat
Second crossing: Track = 090° − vertex_lat

Travelling West from N vertex: Use reciprocals (+180°)

Worked Example (63°N vertex, tracking East)

Crossing	Longitude	Track °(T)	Working
1st (southbound)	080°W	153°	090+63=153
2nd (northbound)	100°E	027°	090−63=027

Two Special Cases

Vertex Latitude	Type of GC	Equator crossing angle
90°N/S	Meridian	180° or 000°
0°N/S	Equator itself	0° (it IS the Equator), direction 090° or 270°

Fig 1.14 — Great Circle vertices, crossing points, and track angles at Equator

Fig 1.15 — Track angles at first and second Equator crossings (tracking East)

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Practice Questions & Answers (DGCA Style)

Solved Practice Questions

Q1 What is the approximate compression of the Earth?
a) 3% b) 0.03% c) 0.3% d) 1/3000

Q2 A Graticule is the name given to:
a) A series of lines drawn on a chart
b) A series of Latitude and Longitude lines drawn on a chart or map
c) A selection of small circles as you get nearer to either pole

Q3 A great circle has its North vertex at 70°N 130°E. What is the position of its South vertex?

Answer: 70°S 050°W
Same latitude number (70), opposite S. Longitude: 130E − 180 = −50 = 050°W

Q4a GC with N vertex at 70°N 130°E. Equator crossing longitudes (initial direction EAST from N vertex)?

Crossing longitudes: 130°E ± 90° = 040°E and 140°W
Track at 1st crossing (Eastbound): 090 + 70 = 160°(T)

Q4b Same GC, initial direction WEST from N vertex?

Crossings still at 040°E and 140°W
Tracks = reciprocals: 200°(T) and 340°(T)

Q5 Compression = 1/297, semi-major axis = 6378.4 km. Find polar semi-minor axis.

Formula: polar = equatorial × (1 − 1/compression)
= 6378.4 × (1 − 1/297)
= 6378.4 × 0.99663
= 6356.9 km → Answer: b

Additional Practice (DGCA MCQ Style)

Q6: The shortest distance between two points on Earth is along:
→ The shorter arc of the Great Circle joining them

Q7: The Equator is special because it is the only parallel of latitude that is also a:
→ Great Circle

Q8: At a Great Circle vertex, the direction of the Great Circle is:
→ 090°(T) or 270°(T) — East or West

Q9: The difference in longitude between 040°E and 055°W is:
Different sides → 40 + 55 = → 095°

Q10: ICAO has adopted which datum as the world standard for GPS?
→ WGS 84

Q11: 1 minute of arc along a meridian equals approximately:
→ 1 Nautical Mile (1 NM = 1852 m)

Q12: The maximum difference between Geocentric and Geodetic latitudes is approximately 11.6 minutes and occurs at approximately:
→ 45°N/S

💡 Quick Summary Table

Concept	Key Number
Earth compression	0.3% or 1/300
Polar diameter less than equatorial	23 NM / 43 km
Earth circumference (exam)	21,600 NM / 40,000 km
1 NM	1852 m / 6080 ft
1° of Great Circle arc	60 NM
Max geocentric/geodetic diff	11.6' at 45°N/S
Tropic latitudes	23½°N and S
Polar circle latitudes	66½°N and S
Earth's axial tilt	23½°

Chapter 1
Direction, Latitude & Longitude

📋 Contents — Chapter 1

Shapes and Their Cross-Sections

Major Geoid Models

Why WGS 84 Became the World Standard

Rotation as Seen from the Poles

Cardinal Points

Quadrantal Directions (midway between cardinal)

Reciprocal Directions

Worked Examples

Great Circle vs Small Circle

The Equator

Meridians

The Prime (Greenwich) Meridian

Parallels of Latitude

The Graticule

Range of Latitude Values

Angular Measurement System

How to Find a Parallel of Latitude

Interactive: Latitude Finder

Two Types of Latitude

Range of Longitude Values

Reversal at 180°E (Anti-Meridian)

Rules for Calculating Change of Longitude (Ch Long)

Worked Examples

Formats for Expressing Position

Indian Pilot Locations (Examples)

Quick Reference

Finding the Other Vertex

Equator Crossing Points

Track Angle at Equator Crossing

Worked Example (63°N vertex, tracking East)

Two Special Cases

Solved Practice Questions

Additional Practice (DGCA MCQ Style)

Chapter 1Direction, Latitude & Longitude

📋 Contents — Chapter 1

Shapes and Their Cross-Sections

Major Geoid Models

Why WGS 84 Became the World Standard

Rotation as Seen from the Poles

Cardinal Points

Quadrantal Directions (midway between cardinal)

Reciprocal Directions

Worked Examples

Great Circle vs Small Circle

The Equator

Meridians

The Prime (Greenwich) Meridian

Parallels of Latitude

The Graticule

Range of Latitude Values

Angular Measurement System

How to Find a Parallel of Latitude

Interactive: Latitude Finder

Two Types of Latitude

Range of Longitude Values

Reversal at 180°E (Anti-Meridian)

Rules for Calculating Change of Longitude (Ch Long)

Worked Examples

Formats for Expressing Position

Indian Pilot Locations (Examples)

Quick Reference

Finding the Other Vertex

Equator Crossing Points

Track Angle at Equator Crossing

Worked Example (63°N vertex, tracking East)

Two Special Cases

Solved Practice Questions

Additional Practice (DGCA MCQ Style)

Chapter 1
Direction, Latitude & Longitude