Traditionally the period drama sweeps the red carpet at the Academy Awards, training the best picture statuette in its sights with the aid of lavish costumes, detailed sets, a casual approach to factual accuracy and important historical figures stuttering or slaying evil kings. In 2017, however, it’s not easy to argue the case for this sort of crowd-pleaser when the rest of this year’s slate boasts largely gritty, groundbreaking and norm-challenging nominees. But Hidden Figures manages to both stay faithful to the genre’s most enjoyable elements while puncturing the boundaries with a knowing kick of its kitten heel.

Theodore Melfi’s biopic tells the previously untold story of Katherine G Johnson (Taraji P Henson), Dorothy Vaughan (Octavia Spencer) and Mary Jackson (Janelle Monáe), a trio of female African-American mathematicians working behind the scenes at Nasa in the early 1960s. These human computers helped to mastermind the launch of astronaut John Glenn into orbit during the great space race at a time when, in Virginia, Jim Crow laws were still in effect, there being two entrances, toilets and coffee pots, to separate white and black Americans. Indeed, it’s still shocking to see the “colored” signs that delineate them on screen.

The civil rights movement gently gathers pace in the background, whether it’s flashes of Martin Luther King on television or Dorothy encountering a protest outside the library. But the focus here is on the three friends’ individual battles within the forcefield of racism and sexism. As a result the film feels contemporary, rather than just a timely reminder of the troubling past. Dorothy faces off with Kirsten Dunst’s prim supervisor about equal pay and promotion; Mary wins the right to train as Nasa’s first female black engineer; Katherine negotiates being the only woman in a room full of fusty white male colleagues with unflattering buzz cuts. These are everyday encounters won out by sassy, headstrong leads, proving that Hollywood films centred on black characters can be positive as well as successful (it is the highest grossing of this year’s best picture nominees).

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Hidden Figures is not without shortcomings. While it’s good to see Kevin Costner in something other than a sports jersey, delivering monologues about how “we all pee the same colour” and dramatically breaks off the sign for the black women’s loos, his fictional character – Katherine’s boss – mines the familiar white saviour trope and did not appear in the book the film is based on. Other critics have called the film out for the distinctly unfleshy backstories given to the main characters, with hardly any time to explore their friendship in any meaningful detail, and for depicting racial tensions with a fairly timid hand, a slap on the wrist instead of an outraged fist.

In spite of its flaws, however, the point of Hidden Figures is to fly the flag for feelgood film-making at a time when celebratory black narratives are growing but still few and far between. It balances the peppy subplots with tear-jerking moments of clarity: at first Katherine’s mission to get across campus to reach the “coloured bathrooms” is presented in comedic fashion, with bursts of Pharrell Williams’s jaunty pop-soul whenever she flings open a door and totters off for a wee. But her impassioned speech delivered later to her all-white office about why she keeps disappearing stings (and hence Costner’s sign smashing commences). Important scenes such as these and the ones where Katherine successfully nails another dizzying calculation so that Glenn can rocket to space are why the film deserves to clean up this year. In the face of yet more macho action-dramas like Hacksaw Ridge, where one white man saves the day as per, Hidden Figures makes it abundantly clear that the all-American hero should be female, gifted and black.