Basics of Navigation
by Capt. Pankaj Pahil
Chapter 1
Direction, Latitude & Longitude
📋 Contents — Chapter 1
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.
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 |
Circumference = 21,600 NM or 40,000 km
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) |
Why WGS 84 Became the World Standard
Rotation as Seen from the Poles
| View from above | Rotation appears |
|---|---|
| North Pole | ANTI-CLOCKWISE (Counter-clockwise) |
| South Pole | CLOCKWISE |
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
Towards North Pole
Direction of spin
Opposite North
Opposite East
Quadrantal Directions (midway between cardinal)
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.
N = 000°(T) | E = 090°(T) | S = 180°(T) | W = 270°(T)
Write
090°(T) NOT 90°(T).Write
027° NOT 27° — a 2-digit bearing is ambiguous and should be treated as suspect.
Reciprocal Directions
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 |
Bearing: 060° → Reciprocal: 240°
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 |
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).
The Equator
Meridians
The Prime (Greenwich) Meridian
Parallels of Latitude
The Graticule
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 |
Direction is measured in degrees and decimal degrees.
How to Find a Parallel of Latitude
Where this line touches the Earth's surface = that parallel of latitude.
Interactive: Latitude Finder
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 ✓ |
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.
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!).
Four special parallels are defined based on Earth's 23½° axial tilt. They relate to the seasons and periods of daylight throughout the year.
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 |
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)
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.
Rules for Calculating Change of Longitude (Ch Long)
Ch Long = Larger − SmallerExample: 100°W and 080°W → 100 − 80 = 20°
Ch Long = E value + W valueExample: 020°W and 010°E → 20 + 10 = 30°
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 |
New York:
41°N 074°WDelhi (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 |
1 NM = 6080 feet = 1852 metres (ICAO standard)
This arises because Earth's mean radius ≈ 20.9 million feet.
Since all meridians are Great Circles:
1 minute of latitude change = 1 NM1 degree of latitude change = 60 NMExample: 50°00'N to 50°05'N = 5 NM
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) |
The number of decimal places used when writing a position declares the accuracy (resolution) being claimed. Each format corresponds to a real-world precision:
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)
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."
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
Then Northern Vertex = 63°N and longitude = 170° − 180° = −10° = 010°E
Rule: Same latitude number, opposite N/S. Longitude ± 180°.
Equator Crossing Points
Example: Northern vertex at 63°N 010°E
→ Crosses Equator at: 010°E ± 90° = 100°E and 080°W
Track Angle at Equator Crossing
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° |
Solved Practice Questions
a) 3% b) 0.03% c) 0.3% d) 1/3000
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
Answer: 70°S 050°W
Same latitude number (70), opposite S. Longitude: 130E − 180 = −50 = 050°W
Crossing longitudes: 130°E ± 90° = 040°E and 140°W
Track at 1st crossing (Eastbound): 090 + 70 = 160°(T)
Crossings still at 040°E and 140°W
Tracks = reciprocals: 200°(T) and 340°(T)
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)
→ The shorter arc of the Great Circle joining them
→ Great Circle
→ 090°(T) or 270°(T) — East or West
Different sides → 40 + 55 = → 095°
→ WGS 84
→ 1 Nautical Mile (1 NM = 1852 m)
→ 45°N/S
| 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° |
Reinforce Chapter 22: Basics of Navigation
Test your knowledge and practice actual exam questions for Air Navigation.