Plane sailing (also spelled plain sailing) is an approximate method of navigation over small ranges of latitude and longitude. With the course and distance known, the difference in latitude ΔφAB between A and B can be found, as well as the departure, the distance made good east or west. The difference in longitude ΔλAB is unknown and has to be calculated using meridional parts as in Mercator Sailing.
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".
The expression "plane sailing" has, by analogy, taken on a more general meaning of any activity that is relatively straightforward.
Famous quotes containing the words sailing and/or plane:
“There’s precious little to say between day and dark,
Perhaps a few words on the implacable will
Of time sailing like a magic barque
Or something as fine for the amenities....”
—Allen Tate (1899–1979)
“As for the dispute about solitude and society, any comparison is impertinent. It is an idling down on the plane at the base of a mountain, instead of climbing steadily to its top.”
—Henry David Thoreau (1817–1862)