Distance in navigation
Aviation uses a clearly defined unit of length: the nautical mile (NM).
Definition of the nautical mile
1 NM = 1852 m exactly — international convention by the IHO (Monaco, 1929), adopted by ICAO (Annex 5).
Historic definition: 1 NM = the arc length of one minute on a great circle of the Earth ("one nautical mile is one minute of arc along the equator or a meridian"). With a mean Earth radius of 6371 km, this gives 1852.2 m — hence the precise definition at 1852 m.
Earth circumference at equator
The circumference of the Earth at the equator is 21 600 NM (= 360° × 60' per degree = 21 600 arc minutes, each = 1 NM). For ICAO chart scaling this is very useful: every 15° of longitude at the equator equals 900 NM, every 1° = 60 NM.
Consequence: 1 minute of latitude = 1 NM
On a meridian line (longitude), 1 minute of latitude (1') = 1 NM, because meridians are great circles.
| Arc | Distance on meridian |
|---|---|
| 1° latitude | 60 NM |
| 1' (minute) latitude | 1 NM |
| 10' (ten minutes) latitude | 10 NM |
| 1" (second) latitude | ≈ 30.86 m |
On a parallel (any latitude other than the equator) this does not hold: distance per minute of longitude shrinks with cos(φ).
- At the equator (φ=0°): 1' of longitude = 1 NM.
- At 60° latitude: 1' of longitude = 1 × cos(60°) = 0.5 NM.
- At the poles: 1' of longitude = 0 NM.
Distance between meridians at the equator
The distance between two consecutive meridians at the equator is 111 km (= 1° × 111.32 km/°). More precisely: 1° = 111.32 km at the equator.
Earth is a sphere — slightly flattened
The Earth is not a perfect sphere, but an oblate geoid (slightly flattened by rotation). Geometry:
- Equatorial diameter: about 12 756 km.
- Polar diameter (pole to pole): about 12 714 km.
- Difference: about 42 km — i.e. the Earth's diameter at the equator is 42 km larger than its diameter from pole to pole.
This flattening is the basis for the WGS-84 reference ellipsoid (semi-axes a = 6378.137 km, b = 6356.752 km).
Great circle vs small circle
| Term | Definition |
|---|---|
| Great circle | Circle on the Earth's surface whose centre coincides with the Earth centre (geocentre). Examples: equator, every meridian. Largest possible radius. The number of possible great circles is unlimited (through every point pair runs exactly one). |
| Small circle | Circle on the Earth's surface whose centre does NOT coincide with the geocentre ("a small circle does not have its central point within the geocentre"). Examples: all latitudes except the equator. |
→ Consequence: the equator is a great circle; it divides the Earth into a northern and southern hemisphere; its plane is exactly perpendicular to the Earth's axis.
→ Meridians are great circles and all the same length (Earth half-circumference, 10 800 NM).
Great circle vs rhumb line (loxodrome)
Great circle (orthodrome): shortest connection between two points on the Earth's surface ("the shortest connection between two places on the surface of the Earth is an orthodrome"). Crosses meridians at varying angles — requires continuous heading correction.
Rhumb line (loxodrome): line that crosses all meridians at the same angle ("a loxodrome intersects with all meridians at the same angle"). A constant compass course is a rhumb line. Longer than the great circle (except on meridians or the equator).
| Leg length | Difference great circle vs rhumb |
|---|---|
| 100 NM mid latitudes | < 0.1 % → negligible |
| 500 NM E-W | ~0.5 % |
| 1000 NM E-W | ~2 % |
| Transatlantic (3000 NM) | up to 10 % depending on route |
For PPL distances (typ. < 200 NM): rhumb ≈ great circle → constant course suffices.
Polar circles and tropics
The Earth has four important parallels besides the equator:
| Parallel | Latitude | Meaning |
|---|---|---|
| Arctic / Antarctic Circle | 23.5° from the pole (= 66.5° N/S) | Separates the polar zones from sub-polar regions. Inside the polar circles there are days with "midnight sun" and days with no sunrise. The Arctic and Antarctic Circles are parallels of latitude at 23.5° distance from the Earth's poles. |
| Tropic of Cancer (north) | 23.5° N | Northernmost zenith of the sun (around 21 June). |
| Tropic of Capricorn (south) | 23.5° S | Southernmost zenith of the sun (around 21 December). |
The tropics lie at 23.5° from the equator and are the lines where the sun apparently changes its direction of motion (solstice).
Other units and conversions
| Unit | Value | Use |
|---|---|---|
| NM | 1852 m | Aviation, maritime |
| km | 1000 m | SI, some VFR AIPs (e.g. Germany) |
| sm / mi (statute mile, US) | 1609.344 m | US sectionals, some METAR visibility |
| ft (foot) | 0.3048 m | Altitude |
| m (metre) | SI base unit | Visibility, runway length in many states |
Conversions (rounded):
- 1 NM = 1.15 sm
- 1 NM = 1.852 km
- 1 sm = 0.87 NM
- 1 km = 0.54 NM
- 1 inch = 25.4 mm (for chart scales)
Rules of thumb for mental conversion in the cockpit
m → ft (altitude conversion)
ft ≈ m × 3 + 10 % — e.g. 500 m × 3 = 1500 + 150 = 1650 ft (true value: 1640 ft).
km → NM (distance conversion)
NM ≈ km / 2 + 10 % — e.g. 100 km / 2 = 50 + 5 = 55 NM (true value: 54 NM).
Both rules give cockpit-ready estimates with ~1 % error.
Speed units
For navigation and horizontal speed, the standard unit is knots (kt) or kilometres per hour (km/h):
- 1 kt = 1 NM per hour (NM/h) — the aviation unit for horizontal speed.
- 1 km/h — rarely in international aviation, more common in national rules (DE GAFOR in km).
Distances in aviation are generally given in NM (exceptions: visibilities in METAR sometimes in m, altitudes in ft).
Application
- PLOG: leg distances in NM, measured with a plotter on the ICAO chart.
- Converging meridians: long E-W flights or polar routes need periodic course correction — barely relevant at VFR distances.
- Chart ↔ world: scaled via map scale (see "scales" lesson).