Plane sailing

# Plane sailing

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Plane sailing is an approximate method of navigation over small ranges of latitude and longitude.

Both spellings ("plane" and "plain") have been in use for several centuries,

Plane sailing is based on the assumption that the meridian through the point of departure, the parallel through the destination, and the course line form a right triangle in a plane, called the "plane sailing triangle".

This is the usual method used to navigate using paper charts and maps.

The expression "plane sailing" has, by analogy, taken on a more general meaning of any activity that is relatively straightforward.

• Rhumb line
Rhumb line
In navigation, a rhumb line is a line crossing all meridians of longitude at the same angle, i.e. a path derived from a defined initial bearing...

Great-circle navigation is the practice of navigating a vessel along a track that follows a great circle. A great circle track is the shortest distance between two points on the surface of a planetary body, assuming a perfect spherical model.-Methods:In order to construct a great circle track,...

Plane sailing versus Parallel Sailing

The art of plane sailing involves traversing diagonally through a rectangle or square formed by the latitudes
Latitude
In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...

and longitudes
Longitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....

of the start and end posiitions, and over a region so vast that it cannot be approximated to a triangle on a flat surface. In comparison, parallel sailing involves traversing through a region which can be approximated to be a triangle as we commonly study in school geometry, formed by latitudes, longitudes and the course line.

Therefore, in parallel sailing, the formulae of Euclidean trignometry
Euclidean geometry
Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these...

that one studies in school, will work. In plane sailing, which is generally taken as spanning over a course line of 500 nautical miles or more, the triangle is spherical. Thus, the known trignometric relations do not work directly. Instead, lessons from spherical trigonometry
Spherical trigonometry
Spherical trigonometry is a branch of spherical geometry which deals with polygons on the sphere and the relationships between the sides and the angles...

have to be applied.

The origin of these two methods of position calculation at sea seem to emerge from the fact that the earliest of human adventure at sea was centred on parallel Sailing method whereby boats navigated 'parallel' to the coastline visible to them. Hence the name, parallel sailing. In this era, the oceanic voyages were not yet taken.
Slowly, human curiosity took them farther from the coast, in search of new knowledge, which led to development of plane sailing. Plane sailing involved knowledge and understanding of 'meridional parts', for its calculations.

Meridional Part

As the knowledge of the spherical shape of the earth came to humans, mathematicians and astronomers divided the earth into latitudes and longitudes. Since the Earth is not an exact sphere, but an oblate spheroid, the distance between two latitudes continues to decrease as one moves towards either of the poles, from equator.
The distance between two adjacent latitudes , when described in terms of number of times an arc of length one minute , as measured at the equator , can fit between those two adjacent latitudes is called Meridional Parts.