What is "plane sailing"

Plane \Plane\, a. [L. planus: cf. F. plan. See Plan, a.] Without elevations or depressions; even; level; flat; lying in, or constituting, a plane; as, a plane surface.

Note: In science, this word (instead of plain) is almost exclusively used to designate a flat or level surface.

Plane angle, the angle included between two straight lines in a plane.

Plane chart, Plane curve. See under Chart and Curve.

Plane figure, a figure all points of which lie in the same plane. If bounded by straight lines it is a rectilinear plane figure, if by curved lines it is a curvilinear plane figure.

Plane geometry, that part of geometry which treats of the relations and properties of plane figures.

Plane problem, a problem which can be solved geometrically by the aid of the right line and circle only.

Plane sailing (Naut.), the method of computing a ship's place and course on the supposition that the earth's surface is a plane.

Plane scale (Naut.), a scale for the use of navigators, on which are graduated chords, sines, tangents, secants, rhumbs, geographical miles, etc.

Plane surveying, surveying in which the curvature of the earth is disregarded; ordinary field and topographical surveying of tracts of moderate extent.

Plane table, an instrument used for plotting the lines of a survey on paper in the field.

Plane trigonometry, the branch of trigonometry in which its principles are applied to plane triangles.

alt. (context nautical English) A technique for navigation using planar geometry. n. (context nautical English) A technique for navigation using planar geometry.

Plane sailing (also, colloqually and historically, 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 Δφ between A and B can be found, as well as the departure, the distance made good east or west. The difference in longitude Δλ 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 expressions "plane sailing" (or more commonly "plain sailing") has, by analogy, taken on a more general meaning of any activity that is relatively straightforward.