Basics of Navigation: The Earth, Coordinates, Direction and Distance
The model of the Earth
Questions in this domain test whether you can move confidently between the idealised Earth and the numbers used operationally. The Earth is approximated by an oblate spheroid (ellipsoid): polar radius about 6357 km, equatorial radius about 6378 km, flattening about 1/298.3. A sphere is used for most flight-planning formulae; the ellipsoid matters when precision is claimed. Great circles are the intersection of the surface with a plane through the centre; rhumb lines cross every meridian at a constant angle. Only the equator and meridians are both.
Coordinates and distance
Latitude runs 0–90° N/S from the equator; longitude runs 0–180° E/W from Greenwich. Remember that a degree of latitude is close to 60 NM everywhere, while a degree of longitude shrinks as the cosine of latitude (about 60 cos lat NM). Departure = change of longitude in minutes × cos latitude. A common trap is mixing up departure with great-circle distance, or forgetting to convert minutes of arc into nautical miles.
Direction
True direction is referenced to the geographic (true) north pole, magnetic direction to the magnetic pole, and compass direction to the aircraft's own compass after deviation. Variation is the angle between true and magnetic north at a position (east variation: magnetic north lies east of true north); deviation is caused by the aircraft's own magnetic fields. Isogonals join equal variation; the agonic line joins zero variation. Another trap is applying variation and deviation in the wrong order, or with the wrong sign.
Worked example
An aircraft at 60°N flies due east along the parallel through 2° of longitude. Departure = 120 min × cos 60° = 120 × 0.5 = 60 NM. If the question instead asks for the great-circle distance, the answer is smaller than the departure would suggest on a globe, because the great circle curves poleward of the parallel.
Rule of thumb
"Variation east, magnetic least" when converting true to magnetic; reverse the rule going magnetic to true. Always sketch a north arrow with true and magnetic north before applying signs.