Definition of "nap"

I took thee napping, unprepared.

1662, [Samuel Butler], “[The First Part of Hudibras]”, in Hudibras. The First and Second Parts. […], London: […] John Martyn and Henry Herringman, […], published 1678; republished in A[lfred] R[ayney] Waller, editor, Hudibras: Written in the Time of the Late Wars, Cambridge: University Press, 1905

I tell thee, Jack Cade the clothier means to dress the commonwealth, and turn it, and set a new nap upon it.

1591 (date written), William Shakespeare, “The Second Part of Henry the Sixt, […]”, in Mr. William Shakespeares Comedies, Histories, & Tragedies. […] (First Folio), London: […] Isaac Iaggard, and Ed[ward] Blount, published 1623, (please specify the act number in uppercase Roman numerals, and the scene number in lowercase Roman numerals)

On his long, gaunt body, he carried no spare flesh, no superfluous beard, his chin having a soft, economical nap to it, like the worn nap of his broad-brimmed hat.

1851 November 14, Herman Melville, “16”, in Moby-Dick; or, The Whale, 1st American edition, New York, N.Y.: Harper & Brothers; London: Richard Bentley

There were low bookshelves, there was a thick pinkish Chinese rug in which a gopher could have spent a week without showing his nose above the nap.

1939, Raymond Chandler, The Big Sleep, Penguin, published 2011, page 37

THEY CALL IT the "nap of the Earth," that area from the ground to the level of surrounding trees and hills, the thin rug of foliage and rock folds at the Earth's skin line that has become all-important to the United States Army.

1961, Skyline, page 9

If incorporated in automatic guidance, this practical pursuit adjustment will enhance pilot acceptance of automatic guidance in following nap-of-the-earth profiles with precision.

1987, Some Data Processing Requirements for Precision Nap-Of-the-Earth (NOE) Guidance and Control of Rotorcraft

Instead of grinding the pistons straight around the axis, they are ground diagonally with a special-built machine. As a result, the “nap” of the metal is turned in such a way that, when it meets the “nap” of the cylinder wall, both surfaces quickly develop a high finish which removes the danger of scoring a piston.

1969, Classic Car, volumes 17-19, page 32

4. Races run on English, Welsh or Scottish racecourses. This criterion was included so that media tipsters [sic] nap selections in general could be analysed; the source of naps, The Racing Rag 'tipster table', summarises the nap selections of newspaper tipsters, who restrict their selection to horses running at racecourses in these countries.

2005, Leighton Vaughan-Williams, The Economics of Gambling, page 71

Vanilla ice cream topped with a poached or canned pear half, napped with chocolate sauce, and garnished with toasted sliced almonds.

2006, Wayne Gisslen, Mary Ellen Griffin, Professional Cooking for Canadian Chefs