Change of latitude and longitude, departure and distance

Navigation · Chapter 2 · DGCA CPL and ATPL

How far apart two places are, north–south and east–west, the shortest way between them, and where you end up after a flight.

Remember

Ch lat: same side subtract, opposite add. Ch long: same side subtract; through 000° add; through 180° add the two gaps to 180°.
1° of latitude = 60 NM. NM ÷ 60 = degrees.
Shortest distance: same meridian ch lat × 60; over the pole (90 − A) + (90 − B); equator ch long × 60; opposite points 10 800 NM.
Departure = ch long (′) × cos(lat); ch long (′) = departure ÷ cos(lat).
Oblique track: north part D × cos(track), east part D × sin(track).

Great circles: try it

The great circle • Slice the Earth through its centre: the cut meets the surface in a great circle • Its whole ring (pink) splits the Earth into two equal halves
Your turn: any two places • Tap any place on the Earth, then tap a second place • The great circle through them appears, with its whole ring round the Earth • Drag to turn the Earth. Try places far apart, then close together
The rhumb line • One steady heading follows a rhumb line (teal, dashed) • London to Vancouver: the great circle swings north over Greenland; the rhumb line stays near 50°N and is longer
Your turn: both lines • Tap two places: you get both lines and both distances • The further from the equator and the more east–west the trip, the bigger the gap
When they are the same line • Along the equator and along a meridian, the rhumb line and the great circle are the same line • Everywhere else the great circle is shorter

What a nautical mile is

Distance from an angle • Latitude and longitude are angles at the centre, so a distance reads straight off an angle • Here: 10° at the centre, along 075°E
Closer: ten degrees • The same arc, close to the ground • Each white tick is 1°; the gold piece is one degree • 1° = 60 NM
Closer still: one degree • One degree split into its 60 minutes • The pink piece is one minute of arc: 1 NM, about 1.9 km • Fly it at 120 kt and you cross it in 30 seconds
Equator to pole • From the equator to a pole is 90° at the centre • 90 × 60 = 5 400 NM
Not exactly the same everywhere • The Earth is slightly squashed: it is flatter near the poles • A minute of arc there is a little longer; at the equator a little shorter