Chapter 24: The Sailings
The sailings are the computational methods for relating course, distance, and change of latitude and longitude — from simple plane sailing to great-circle work.
Plane, traverse and parallel sailing
Plane sailing treats a short run as a plane right triangle: difference of latitude is the side along the meridian, departure the side along the parallel, and distance the hypotenuse. Traverse sailing resolves a series of courses into a single equivalent course and distance by summing northings, southings, eastings and westings. Parallel sailing, used when steering due east or west, converts departure to difference of longitude: DLo = p / cos L.
Mid-latitude and Mercator sailing
Mid-latitude sailing uses the mean latitude to convert departure to difference of longitude and is adequate for moderate runs. Mercator sailing is exact for rhumb lines: it uses meridional parts from the traverse tables, tan C = DLo / m where m is the difference of meridional parts, giving the rhumb-line course, and distance = DLat / cos C.
- Plane sailing — short distances, one course
- Traverse — several courses resolved into one
- Mercator — exact rhumb line via meridional parts
Great-circle sailing
A great circle is the shortest path between two points on a sphere, but its course changes continuously, so it is sailed as a series of rhumb-line legs between waypoints lifted from a gnomonic chart or computed. The vertex is the highest-latitude point of the track, where the course is 090° or 270°. Where the great circle passes into unacceptably high latitudes — ice, weather — a composite track is used, following the great circle to a limiting parallel, then that parallel, then a great circle to the destination.
Formula cards
Plane sailing
DLat = D cos C ; departure p = D sin C
Valid for short runs where convergency is negligible.
Mid-latitude sailing
DLo = p / cos(Lm)
Lm is the mid-latitude between the two positions.
Great-circle distance and initial course
cos D = sin L1 sin L2 + cos L1 cos L2 cos DLo
Initial course from the spherical law of sines or the four-parts formula.
Key takeaways
- • DLo = departure / cos(mid-latitude) is the workhorse approximation.
- • Mercator sailing with meridional parts is the exact rhumb-line method.
- • Great-circle savings grow with latitude and with east-west distance; composite sailing caps the latitude reached.
Knowledge check
Immediate feedback with rationales. Answer each question to see the explanation.
Chapter 24 quiz
0 of 3 answered
1.Steering 090° for 60 NM in latitude 60°N, the change of longitude is about:
2.The vertex of a great circle is where:
3.Composite great-circle sailing is used to: