Plane sailing (also, colloquially and historically, spelled plain sailing) is an approximate method of navigation over small ranges of

latitude In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pol ...

and

longitude Longitude (, ) is a geographic coordinate that specifies the east– west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek lette ...

. With the course and

distance Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). ...

known, the difference in latitude Δ''φ_AB'' between ''A'' and ''B'' can be found, as well as the departure, the distance made good east or west. The difference in longitude Δ''λ_AB'' is unknown and has to be calculated using meridional parts as in

Mercator __NOTOC__ Mercator (Latin for "merchant") may refer to: People * Marius Mercator (c. 390–451), a Catholic ecclesiastical writer * Arnold Mercator, a 16th-century cartographer * Gerardus Mercator, a 16th-century cartographer ** Mercator 1569 ...

sailing. Both spellings ("plane" and "plain") have been in use for several centuries,''Oxford English Dictionary 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". The expressions "plane sailing" (or more commonly "plain sailing") has, by analogy, taken on a more general meaning of any activity that is relatively straightforward.

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