run-in

Derived from the verb run into.
For the meaning "end-phase", it presumably comes a marathon race, where in the final part the runners run into the stadium and complete a lap.

• Audio (US):

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run-in (plural run-ins)

1. An encounter; a scrape or brush, especially one involving trouble or difficulty.
   • 2004, Pamela Morsi, Suburban Renewal, page 95:

     During that time he had two more run-ins with the law. One involved the sale of stolen property. The other was for a series of hot checks.

2. The end-phase of a competition etc.

   Yahoo Sport's Leicester City blogger Helen Nutter gets ready for the Premier League run-in knowing her side - incredibly - still have a great chance of being crowned champions

   • 1951 October, R. S. McNaught, “Lines of Approach”, in Railway Magazine, page 704:

     But despite its plague of tunnels, the run-in on this route is of unusual interest to the locomotive enthusiast: besides the hordes of self-important saddle-tanks shunting in the extensive yards, there was at one time the chance of seeing those slender little North London engines, with their large outside cylinders and no visible storage place for coal, and also an occasional South Eastern locomotive sporting a lot of polished brass.

3. A sudden compression between two coupled railcars when the hinder one is moving faster than the fore one.
   • 1990, F. G. Carlson, Undesired Emergency Brake Applications, Association of American Railroad Research and Test Department:

     Brake pipe pressure reduction rates of over 30 psi/sec lasting for about 15 milliseconds were created by harsh slack run-ins.

   • 2024, Srini Swamy, Graydon F. Booth, Anand Prabhakaran, Very Long Trains: Moving Train Tests, Federal Railroad Administration:

     Researchers noted no unusual events (e.g., knuckle breaks) or notable instances of significant slack action or run-ins/run-outs at the lead locomotive during the test.

Derived from the verb run in.

• Audio (US):

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run-in (not generally comparable, comparative more run-in, superlative most run-in)

1. (participial adjective; editing, typography) (not comparable) Having been run in before or behind previous text.

   Antonym: free-hanging

   These headings are of the run-in type because a free-hanging style would just be a waste of column inches.

2. (participial adjective; mechanical, engineering) (sometimes comparable) Having been run in to seat the parts.

   Synonym: broken in (adjective)

   A well run-in engine is likelier to consume less crankcase oil over the course of its working life.

• inrun, inurn