WASHINGTON, DC - SEPTEMBER 10: Estelle Parsons poses for a photograph on the set of "The Velocity of Autumn," being staged at Arena Stage. (Katherine Frey/The Washington Post)

In its march to the big time, “The Velocity of Autumn” was forced to decelerate. An announcement of Eric Coble’s drama coming to Broadway last spring had been widely publicized, along with the news that Estelle Parsons and Stephen Spinella were cast as the play’s estranged mother and son, and that Arena Stage’s Molly Smith would occupy the director’s chair.

It wasn’t to be. The commercial producer, Washington-based Larry Kaye, failed to secure a suitable Broadway house in the hugely competitive seasonal rush for theaters — a lesson in not counting your tickets until your lease is signed. But rather than scuttling the project, as sometimes happens after Broadway dreams go plop, the parties involved rapidly regrouped and settled on an obvious and convenient Plan B.

So, with the Oscar-winning Parsons (“Bonnie and Clyde”) and the Tony-winning Spinella (“Angels in America”) still attached, the geography of “Velocity” shifted to Washington and Arena Stage’s Kreeger Theater, where the two-character play began performances Sept. 6 and has its official opening this week. Smith remains the director, for her umpteenth go-round at Arena, instead of her first on Broadway. And because no one involved seems to have gotten the Big Apple out of his system, Arena is marketing the production as an “exclusive, pre-Broadway engagement.”

“I’m still hoping that we can bring the play to Broadway,” said Kaye, whose Hop Theatricals is listed among the many producing entities of recent Broadway mountings of “American Idiot” and “How to Succeed in Business Without Really Trying.” His production had, in fact, been offered a theater on Broadway, he said, “but it would have been way too big. We’ve taken the opportunity to change course a little bit, to have it fit into the Arena schedule for the fall.”

Whether by coincidence or some slightly more deliberate effort, Arena seems to have developed a Broadway bug of late. Two other shows that have passed through the company’s shiny complex on the Southwest Washington waterfront have formal openings 10 days apart on Broadway next month: “A Night With Janis Joplin,” the concert-style jukebox musical that at Arena bore the title “One Night With Janis Joplin,” opens at the Lyceum Theatre on Oct. 10. And “A Time to Kill,” a crime drama based on a John Grisham novel that had its world premiere at Arena in 2011, is to formally open Oct. 20 at Broadway’s Golden Theatre.

WASHINGTON, DC - SEPTEMBER 10: Playwright Eric Coble poses for a photograph on the set of his latest play, "The Velocity of Autumn," being staged at Arena Stage. (Katherine Frey/The Washington Post)

Although Arena was a pioneer in the movement of plays from nonprofit regional theaters to commercial runs on Broadway — its stellar “The Great White Hope” made that segue in 1968 — the transfers happen only sporadically. The uptick might be attributable, in part, to the presence of Arena’s managing director, Edgar Dobie, an experienced Broadway hand. Before his turn to nonprofit theater with a job at Trinity Repertory Company in Providence, R.I., Dobie was Andrew Lloyd Webber’s chief executive in New York, overseeing the musicals produced on Broadway by Lloyd Webber’s Really Useful Group.

In the cases of “Joplin” and “A Time to Kill” — and, if a move comes to pass, “Velocity” — Arena receives royalty checks from the Broadway incarnations. “We love it,” Dobie said. “It’s a nice little surprise for us. It becomes like found money.”

The arrangements that lead to commercial runs for plays and musicals that begin at nonprofit theaters are varied and a sensitive issue, with some murky implications for companies whose status entitles them to more favorable tax provisions. “Joplin” arrived at Arena, Dobie said, with no clear trajectory for Broadway. But “A Time to Kill” and “The Velocity of Autumn” already had Broadway producers involved, and they provided to Arena what’s known in the business as “enhancement” money: They invest substantial amounts in the nonprofit production, reaping the benefits of a trial run and the chance to hone the material. (Sometimes, they even take the set.)

“There are certain physical costs, and you can quantify those costs and arrive at a number. We just ask that we be reimbursed for those costs,” Dobie said of enhancement deals. He added that later, “there is an opportunity for us to participate with a royalty and a profit share.” Other sorts of arrangements are fashioned when nonprofit companies enter the for-profit arena. For example, the Kennedy Center put up a goodly portion of its own money to transfer its revival of “Follies” on Broadway and thusly became the musical’s lead producer.

Kaye wouldn’t say how much enhancement money he gave to Arena. It seems clear, though, that he believes deeply in the piece, which he first saw in a 2012 production in Lakewood, Ohio, a Cleveland suburb. “For me, I just think it’s a beautiful play that should be seen on Broadway.”

Coble, a Cleveland-based playwright in his mid-40s who has had work produced regionally but never on Broadway, says the shift from New York to Washington, an admittedly lower-visibility next step for “Velocity,” was not a concern. “That’s not my job,” he said, sitting in a handsome common room on Arena’s ground level, with views of the harbor. “My job is to make sure the script is as strong as it could be.”

His script is the account of an 80-year-old woman living in Brooklyn, who, under pressure from her children to give up her home, barricades herself inside, rigging the brownstone with molotov cocktails. It becomes the task of an estranged son she hasn’t seen in 20 years to break into the house and try to talk her down.

“I was particularly drawn to it because she was going to blow up the house — she was feisty,” said Parsons, who at 85 seems not to have lost any of her gusto; just four years ago, she tore up the Kennedy Center’s Eisenhower Theater stage with her galloping portrayal of drug-addled Violet Weston in “August: Osage County.” She says she “spends my life” reading bad plays that portray older characters as kindly or weak-willed or mere wallpaper. “The old people are usually passive,” she said, sounding as if she might have been provoked to toss a molotov or two at some of those scripts. “And I always want to play the kind of character I never played before.”

“Velocity” is part of a trilogy Coble has dreamed up: three plays about the same woman at vastly different stages of her life but all taking place at the same point in time. This play is that woman at the latest age, and it seems to touch an extremely topical nerve, having to do with the struggle over autonomy in the years of one’s decline, when the painful decision is debated over whether Mom or Dad should be persuaded to leave familiar surroundings for housing with more aggressive supervision.

“When I read the play, I thought, ‘Oh, my God, this is an important thing that people are dealing with in living rooms all over America,’ ” said Smith, Arena’s artistic director. “What’s this thing called control, and how long do we get to keep it?”

Spinella said that as a son, he related to the tension at the heart of the piece. “My mom is in a nursing home,” he explained, “and I understand to a certain degree what the anxieties about all these issues are.” Given the high proportion of older people who make up theater audiences these days, “The Velocity of Autumn” may satisfy the dramatic need for catharsis in a disproportionate number of ticket buyers.

The extremes to which Parsons’s Alexandra takes her battle for control did not seem farfetched to the focus group of one on whom Smith tested out the credibility of the character’s actions: her 91-year-old mother. Smith recounted, “When I described it to her, she said, ‘I can understand how she feels.’ ”

Who knows? Maybe “The Velocity of Autumn” will ride a wave of octogenarian revolutionary fervor, all the way north to Times Square.

The Velocity of Autumn

by Eric Coble. Directed by Molly Smith. Through Oct. 20 at Arena Stage, 1101 Sixth St. SW. Call 202-488-3300 or visit www.arenastage.org.