turnpike

noun

1. A frame consisting of two bars crossing each other at right angles and turning on a post or pin, to hinder the passage of animals, but admitting a person to pass between the arms.

   “1626, Ben Jonson, The Staple of News, Act III, Scene 1, Yale Studies in English Vol. 28, New York: Henry Holt, 1905, p. 58, I moue vpon my axell, like a turne-pike, / Fit my face to the parties, and become / Straight one of them.”

2. A gate or bar set across a road to stop carriages, animals, and sometimes people, until a toll is paid.

   “1722, Daniel Defoe, A Journal of the Plague Year, London: E. Nutt et al., pp. 9-10, […] it was rumour’d that an order of the Government was to be issued out, to place Turn-pikes and Barriers on the Road, to prevent Peoples travelling;”

   “[…] Pope Pelagius, then Bishop of Rome […] thereupon assum'd the Power of opening and shutting Heaven's Gates; and he afterwards setting a Price or Toll upon the Entrance, as we do here at passing a Turn-pike […]”

3. (Scotland)A winding stairway.
4. A beam filled with spikes to obstruct passage; a cheval de frise.
5. (US)A toll road, especially a toll expressway. In some places the clipped version, pike, is used for roads without tolls.

   “Eleven Pair of Mills ſtand within Four Miles of the Place, which bring a great Trade to it: But the Road is by this means ſo continually torn, that it is one of the worſt Turnpikes about London.”

   “[T]here is a bundle of pawnbrokers' duplicates, those turnpike tickets on the road of poverty ...”

6. A trajectory on a finite time interval that satisfies an optimality criterion which is associated with a cost function.

   “In the monograph we discuss a number of results concerning turnpike properties in the calculus of variations and optimal control which were obtained by the author in the last ten years.”

verb

1. To form (a road, etc.) in the manner of a turnpike road, or into a rounded form, as the path of a road.