Smooth and easy progress.
'Plain sailing', along with the variants 'smooth sailing' and 'clear sailing', which are more common in the USA than elsewhere, is a nautical phrase that has the literal meaning of 'sailing that is easy and uncomplicated'. All of these variants of the expression are now used figuratively to describe any straightforward and trouble-free activity. There might seem to be be little more to say about 'plain sailing', if it weren't for the existence of the phrase 'plane sailing'.
'Plane sailing' is a simplified form of navigation, in which the surface of the sea is considered to be flat rather than curved, that is, on what mathematicians call a 'plane surface'. The plane method of approximation made the calculations of distance much easier than those of 'Mercator's sailing', in which the curvature of the earth was taken into account.
These days we are pretty unequivocal in our spelling - 'plain' means 'ordinary and uncomplicated' and 'plane' means 'flat'. The vagaries of spelling in the 17th century made no such distinction and 'plain' and 'plane' were used interchangeably. It is the 'plain' spelling that is found first in print, in Adam Martindale's A Collection of Letters for Improvement of Husbandry & Trade, 1683:
A token for ship boys, plain-sailing made more plain and short than usually, in three particular methods.
The first known use of the 'plane sailing' spelling isn't found until much later, in James Atkinson's Epitome of the Art of Navigation, 1749:
Plane Trigonometry applied in Problems of Sailing by the Plane Sea-Chart, commonly called Plane-Sailing.
The spelling is variable but there can be no doubt that whoever coined 'plain sailing' meant 'navigating the sea as though it were completely flat', that is, what we now call 'plane sailing'.
In recent years the introduction of the phrase 'clear sailing' as an alternative to 'plain sailing' may have cleared things up a little. This was used to good, if rather poignant, comic effect in The Simpsons' cartoon The Simpsons Bible Stories, 1999:
Milhouse: Well, Lisa, we're out of Egypt. So, what's next for the Israelites? Land of milk and honey?
Lisa: [consulting a scroll] Hmm, well, actually it looks like we're in for forty years of wandering the desert.
Milhouse: Forty years! But after that, it's clear sailing for the Jews, right?
Lisa: [nervously] Uh-huh-hum, more or less.
See other Nautical Phrases.