Achieving perfection, in athletics as in any other arena, never occurs overnight. It’s the product of a work ethic, a mentality and, at times, an anxiety that compels a person to push himself beyond the point at which the typical person stops.

It’s this alter ego of the athlete, the obsessive-compulsive reality behind the heroic public image, that “The Flying Scotsman” depicts in fascinating detail. After an hour or so of sticking faithfully to the sports film playbook, screenwriters John Brown, Declan Hughes, and Simon Rose turn those rules upside down in a third act that is less a celebration of celebrity than a sobering look at the costs that accompany it.

For audiences, it leads to a disorientating sensation, as we reach what we believe to be the conventional climax of the standard sports story, only to watch it erode into something less glorious.

The Scotsman in question is Graeme Obree (Jonny Lee Miller), who stunned the cycling world in 1993 when he walked into a Norway stadium and smashed the world one-hour record. An unemployed amateur cyclist, Mr. Obree had remained relatively unknown while riding in smaller Scottish races, when he was first inspired to assemble the prototype of a new racing bike, working with a veritable junk pile of scrap metal and a deconstructed washing machine. Riding his contraption, he took the world stage by storm, alarming a cycling establishment that saw the rag-tag rider as a threat and earning the adulation of his countrymen.

In so many ways, the story seems too good to be true — the kind of magical sports moment that invites movie references. So it’s no surprise in this movie when Graeme, who has practiced day and night on winding dirt paths and rural country roads, is suddenly and inexplicably inspired to flip his bike handles around in search of a design that will cut down on wind resistance.

He takes to modifying other parts of his bike, too, stripping some metal here and there to make it lighter, ripping apart his wife’s (Laura Fraser) washing machine in search of more perfect bearings, and devising a nighttime exercise routine with a stationary bike that he places in front of a clock and rides until his legs give out.

Graeme is helped by those who recognize the commitment of a man hell-bent on achieving what many deem the impossible: breaking a record that has remained in place for nearly a decade, and doing it with technology that is not developed in a wind tunnel.

While most sports movies tend to fall apart in their final movements, as character development and plot twists are jettisoned in favor of a parade of melodrama and feel-good jubilation, “The Flying Scotsman” works in the opposite order. The movie’s earlier segments are what feel slight and underdeveloped, with Graeme, his wife, and his friend Malky (Billy Boyd) reduced to caricatures as the story moves clumsily from Graeme’s sudden inspiration to construction, road tests, and then the Norway trials.

It’s in the aftermath of his world record triumph that “Scotsman” takes an unexpected diversion, first revealing the power struggle between this common champion and a scared establishment and then revealing the inner struggles of an athlete entering the depths of depression, unable to reconcile his public success with his private anguish. Graeme, as shown here, started riding to overcome his childhood fears, and as those fears have mutated through the decades into feelings of inadequacy and failure, his battle for the world championship sends him into a dismal spiral of despair.

As a whole, it’s difficult to judge “Flying Scotsman” because its second half is so much more interesting than the familiar, underdog-takes-all formula that dominates the early segments. But in parts, there are flashes of brilliance here. Director Douglas Mackinnon’s racing footage, which cuts between a telescopic technique that offers the vantage point of the spectators and a closely mounted camera that shows Graeme’s tunnel vision from the racetrack, is riveting. And Mr. Miller, who must balance the chiseled façade of the fearless athlete with the more fractured mind-set of the emotionally unstable, helps us make the late transition from a familiar sports film to a more affecting character study.

“The Flying Scotsman” is the rare film that stays with its hero after the gold metal is placed around his neck and the chase for glory has come to an end.