Little Eagles, Hampstead, London<br/>King James Bible, Shakespeare's Globe, London<br/>David Mamet Double Bill, Arcola, London

The story of the scientist behind the Sputnik space programme will never get off the launch pad in this underpowered production

To go where no man has gone before, or no leading British playwright anyway: that was Rona Munro's mission on penning Little Eagles, a biodrama about Sergei Korolyov, a hitherto "unsung hero", according to the pre-publicity for this premiere, launching an RSC season in Hampstead.

Everyone has heard of Yuri Gagarin and his Earth-orbiting voyage, 50 years ago this month. Korolyov was the Russian mastermind and chief designer who oversaw both the Sputnik and Vostok programmes in the space race, until he died prematurely in 1966.

Little Eagles begins with Korolyov's career in a near-fatal early dip. Imprisoned in a grey Siberian labour camp, Darrell D'Silva's Korolyov is half-frozen and beaten by vicious guards, but proves to be survivor with a dream and tenacious drive.

Re-employed by the authorities, he develops Cold War ballistic missiles, then dares to advocate a space-conquering programme instead. Impressing Brian Doherty's swaggering Khrushchev, he becomes the top dog in this enterprise, ousting the colleague who formerly denounced him, John Mackay's twitchy Valentin Glushko, for a while at least.

Post-Khrushchev, as Korolyov struggles to remain in favour, Little Eagles portrays him as tragic hero, doomed, in part, because he's stand-out figure in a system that swears by mass, egalitarian levelling. A Red Army commanding officer, Greg Hicks's Geladze, asks suspicious questions and – getting hot-headed responses – turns into Korolyov's potential nemesis. Yet the scientist is his own enemy, too, working himself to death to maintain safety standards in the face of slashed funding – dreading the death of a cosmonaut.

Some of this is gripping, but the narrative struggles to keep its multiple balls in the air. There are bemusing gaps, sketchy subplots and a scene introducing us to Gagarin (an eager, confident Dyfan Dwyfor) which looks confusingly like a flashback to Korolyov's youth. The dialogue, veering into the semi-poetic, has a scattering of vivid descriptive images. But in Roxana Silbert's production, even the aerial choreography is underwhelming. Little Eagles is, alas, no high flyer.

A spirit of epic adventure has taken hold, more winningly, at Shakespeare's Globe. Artistic director Dominic Dromgoole hasn't beamed himself up to the Starship Enterprise quite yet, but he'll be going truly global in 2012, playing host to 38 international companies. Meanwhile, throughout Easter week, the timber-framed theatre has been presenting a cover-to-cover recitation of the King James Bible – the seminal translation of 1611.

The session I caught was certainly going to test just how good a book this is, for it included Joshua and Judges, with chunks that are just lists detailing which cities were divvied up to which clans, as the "children of Israel" tried to secure a foothold. That these passages proved mesmerising in performance was a little short of a miracle. I speak as a committed atheist, but there is an enchanting simplicity and intimacy to Jacqueline Somerville's staging, with a handful of actors taking turns, not preaching from a tome, but wandering across the bare wooden stage as they address us directly, as storytellers (one earphone in, playing them the text).

Daniel Langley – an accomplished newcomer – even managed to make the interminable lists seem gently teasing, and magically conjured up glimpses of a distant land – the curve of coastline in a tiny sweep of his hand. Elsewhere among the cast there was some fluffing. But dramatically hair-raising stories suddenly emerge. ("Then Jael Heber's wife ...went softly unto him, and smote the nail into his temples.") And while this translation's lyrical repetitions ("Libnah with her suburbs, and Jattir, and Eshtemoa, with their suburbs ...") are as soothing as a 17th-century shipping forecast, what emerges from this Old Testament reading is a disturbing, still topical portrait of unending tribal conflicts and religious fundamentalism justifying slaughter.

In the Arcola's double bill of David Mamet's rarely aired Lakeboat and Prairie du Chien, the latter is a creepy and elusive short, set on a 1910 night train, where guns may be pulled in a poker game being played in parallel with a spooky tale told about a murder. Lakeboat is an early play in which an explosively moody crew on a cargo boat reveals flashes of sensitivity and despair, confiding in college boy Dale. He, roughing it as their cook, believes that his predecessor met a nasty end.

This collection of motor-mouthed snippets is shot through with misogynistic anecdotes, which can get wearisome. Director Abbey Wright doesn't always get the pacing right, but Helen Goddard's corroded, studded-iron set is terrific, and Wright has assembled an impressive cast.

'Little Eagles' (020-7722 9301) to 7 May; Recital of the King James Bible (020-7401 9919) today and tomorrow; 'Lakeboat' and 'Prairie du Chien' (020-7503 1646) to 7 May

Next Week:

Kate Bassett relives The Passion, a three-day event in Port Talbot, with Michael Sheen as Christ

Theatre Choice

Wife to James Whelan is an overlooked gem by Irish playwright Teresa Deevy, whose career ended when in 1937 the Abbey, Dublin, turned down this play, a portrait of love and friendship among small-town lads and lasses. Gavin McAlinden's London fringe premiere boasts an admirable young ensemble at the up-and-coming New Diorama, to Sat.