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.
Football: The Toon Origami Is Plane Sailing for Iain; Newcastle 0 C Palace 0 Palace Refuse to Fold as Newcastle Fall Flat.Again
May 02, 2005; Byline: By SIMON BIRD IAIN DOWIE never thought Crystal Palace's relegation battle would be plane sailing - but that's exactly...
PLANE SAILING FOR BLUES; LEEDS UTD 1 CHELSEA 5 QUARTER FINAL ACTION FROM ELLAND ROAD; No Jet Lag and Chelsea Power Home
Dec 20, 2012; Byline: NEIL McLEMAN email@example.com RAFA BENITEZ'S Chelsea needed 45 minutes to get back on to GMT last night and...