Chapter 1
Direction, Latitude & Longitude

1. The Shape of the Earth

The Earth's shape is commonly described as an oblate spheroid — a sphere slightly flattened at its poles. The flattening (called compression) is approximately 0.3% (1/300th), meaning the Earth's polar diameter is 23 NM (43 km) less than its equatorial diameter. Recent satellite surveys also show a slight pear-shape, with maximum diameter south of the Equator (measured in tens of metres — far smaller than the polar compression).

Because the Earth is not a perfect ellipse, the only accurate descriptor is "geoid" (from Greek — Earth-shaped). Different agencies have modelled the geoid for their own regions; the main ones are:

• UK Ordnance Survey — OS36
• France — NTF 1970
• Europe — ED50
• USA / World — WGS 84

Why ICAO Adopted WGS 84

Two developments forced standardisation:

1. GPS — global, ~tens-of-metres accuracy; adopted WGS 84 from the outset.
2. FMS/DME position updating — the FMS data base stores DME station positions in lat/long. Mixing geoids (UK DMEs in OS36, French DMEs in NTF70) would cause large discontinuities when crossing the English Channel.

ICAO therefore mandated WGS 84 as the world standard. Modern navigation computers automatically correct for Earth-shape distortions.

The Poles

The Poles are the extremities of the Earth's spin axis. The polar axis is inclined to the plane of the Earth's orbit at 23½°. For this chapter, the polar axis is drawn upright (the seasonal effects are covered in the chapter on Time).

2. Basic Direction on the Earth

Cardinal and Quadrantal Points

The primary datum for direction is the Earth's spin direction (East = sunrise). From this:

• North — direction of the North Pole
• South — opposite of North
• East — direction of Earth's spin
• West — opposite of East

Midway between these are the Quadrantal directions: NE, SE, SW, NW.

Viewing from the Poles

A frequent exam question — when viewed from above the North Pole, the Earth rotates anticlockwise. Viewed from above the South Pole, it rotates clockwise. The direction of East and West does NOT change — it is always the direction of (and opposite to) the Earth's rotation.

The Sexagesimal System / True Direction

Air navigation uses the Sexagesimal system: direction measured in degrees clockwise from North (000° to 360°).

• North = 000°(T) or 360°(T)
• East = 090°(T)
• South = 180°(T)
• West = 270°(T)

When the North datum is the geographic North Pole, the direction is True direction, written with the suffix (T).

Reciprocal Directions

The reciprocal of a direction is direction ± 180°.

3. Position Reference Systems & Circles on the Earth

Navigation requires a Position Reference System to define location unambiguously on the Earth's surface. On a flat surface, Cartesian coordinates (±x, ±y) work perfectly. On a sphere, angular coordinates replace linear ones: Longitude (Y-axis equivalent) and Latitude (X-axis equivalent).

Great Circle

A Great Circle is a circle on the Earth's surface whose centre and radius are those of the Earth itself. It divides the Earth into two equal hemispheres. Key property:

The Equator

The Great Circle whose plane is perpendicular (90°) to the Earth's polar axis. It divides the Earth into Northern and Southern Hemispheres and is the datum for Latitude (equivalent to the X-axis).

Meridians

Meridians are semi-Great Circles joining 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 through Greenwich is the Prime Meridian — the datum for Longitude (equivalent to the Y-axis).

Small Circles & Parallels of Latitude

A Small Circle is a circle on the Earth's surface whose centre and radius are not those of the Earth. Parallels of Latitude are the most important small circles: they are parallel to the Equator, lie in an East–West direction, and indicate position North or South of the Equator.

4. The Graticule & Angular Measurements

The Graticule

The Graticule is the network formed by the Prime Meridian, all meridians, the Equator, and all parallels of latitude — the spherical equivalent of a Cartesian x–y grid.

Angular Measurements

Position in the Graticule is expressed in angular rather than linear units:

For direction, degrees and decimal degrees are used. For position, degrees, minutes (and seconds where needed) are standard.

5. Latitude — Definition & Types

Definition of Latitude

The latitude of a point is the arc along the meridian through the point, measured from the Equator to the point. Expressed in degrees, minutes (and seconds) of arc, annotated N or S.

• Equator = 0°
• North Pole = 90°N
• South Pole = 90°S

Geocentric vs Geodetic (Geographic) Latitude

Because the Earth is an oblate spheroid (not a perfect sphere), two definitions of latitude exist:

• Geocentric Latitude — angle between the line from the point to the Earth's centre and the Equatorial plane.
• Geodetic (Geographic) Latitude — angle between the normal (perpendicular) to the spheroid surface at the point and the Equatorial plane. This normal does not necessarily pass through the Earth's centre.

6. Special Parallels of Latitude

7. Longitude, Difference in Longitude & the Anti-Meridian

Definition of Longitude

The longitude of a point is the shorter arc along the Equator between the Prime Meridian and the meridian through the point. Annotated East (E) or West (W), measured up to 180°E or 180°W.

Giving position: Latitude is always quoted first, longitude second — e.g. New York 41°N 074°W.

Difference in Longitude (Ch Long)

The Greenwich Anti-Meridian (180°E/W)

The 180°E and 180°W meridians are coincident — known as the Greenwich Anti-Meridian. A famous source of exam confusion: at 180° longitude, the Eastern Hemisphere is to your West and the Western Hemisphere is to your East. The direction of East and West has not changed — only which hemisphere is in each direction relative to where you stand.

Latitude vs Longitude — Key Difference

• Parallels of latitude — always parallel to each other (like slicing a pineapple)
• Meridians of longitude — emanate from the North Pole, reach maximum separation at the Equator, converge to the South Pole (like orange segments)

8. Converting Lat/Long to Distance & Resolution Accuracy

The Nautical Mile — Defined by Arc

The nautical mile is defined so that 1 minute of arc on a Great Circle = 1 NM. The mean Earth radius gives 6 080 ft per minute. ICAO definition: 1 NM = 1 852 metres.

Resolution Accuracy — Summary Table

9. Great Circle Vertices

Definition

The Northern vertex is the most northerly point on a Great Circle; the Southern vertex is the most southerly point. Key properties:

• Vertices are antipodal — directly opposite each other on the Earth, on a common meridian/anti-meridian
• Their latitudes are equal in magnitude but opposite in sign
• GC distance between them = 10 800 NM (= 180° × 60 NM)
• At either vertex the GC direction is exactly 090°(T) (East) or 270°(T) (West)

Vertex Longitude — Finding the South Vertex

South vertex longitude = North vertex longitude ± 180° (take the value ≤ 180).

Equator Crossings — Longitudes

The GC crosses the Equator at two points, each 90° of longitude from either vertex:

Equator Crossings — Track Angles

The track angle at each equator crossing depends on the vertex latitude and the direction of travel:

• First crossing eastbound (from north vertex going East): track = 90° + vertex latitude
• Second crossing eastbound (after south vertex, still East): track = 90° − vertex latitude
• Westbound crossings: take the reciprocals of the eastbound values

Special Cases

• A meridian (vertices at 90°N/S) crosses the Equator at 000°(T) or 180°(T)
• The Equator itself (vertices at 0°N/S) has direction 090°(T) or 270°(T)