The film begins in 1947 at the Muroc Army Air Field in California, with civilian and military test pilots flight-testing high-speed aircraft, including the rocket-powered Bell X-1. Death is a part of their life. After privateer Slick Goodlin demands $150,000 (equivalent to $1,718,000 in 2019) to attempt to break the sound barrier in the X1, World War II hero Captain Chuck Yeager is given the chance. While horseback riding with his wife, Glennis, Yeager falls and breaks his ribs, an injury which inhibits his ability to lock the door on the X-1. Worried that he might not fly the secret mission, he confides in friend and fellow pilot Jack Ridley, who solves the problem by giving Yeager the stump of a broom handle to use as leverage. Though the X1 bucks like a wild bronco, and pushes him to his limit, Yeager goes supersonic and becomes an international hero – a role he is uncomfortable in.
Six years later, Muroc, by then Edwards Air Force Base, remains a beehive of danger, competition, and risky behavior. Major Yeager and friendly rival Scott Crossfield repeatedly break each other’s speed records. They often visit the Happy Bottom Riding Club run by pioneering aviatrix Pancho Barnes for raucous nights of drinking. Loud and vulgar, she favors the pilots at Edwards who fly the best equipment, such as Yeager and Crossfield, whom she dubs “prime”, over green “pudknockers” who only dream about it. Newly arrived United States Air Force captains Gordon “Gordo” Cooper, Virgil “Gus” Grissom, and Donald “Deke” Slayton hope to prove that they have “the Right Stuff”. Publicity has replaced secrecy to generate continued funding, adding further pressure to the pilots. Cooper’s wife, Trudy, and other wives fear becoming widows as the ever more gripping competitions of man versus machine, man versus Nature, and man versus man grow, but cannot change their husbands’ powerful ambitions and what they lead to.
In 1957, the launch of the Soviet Sputnik satellite triggers a crisis for the United States government. Politicians such as Senator Lyndon B. Johnson and military leaders demand America wage and win an emerging Space Race. NASA is founded, and seeks to develop the first U.S. astronauts. In spite of his proven abilities Yeager is excluded because he lacks a college degree. Grueling physical and mental tests select an initial roster of gentlemen officers drawn from the U.S. Air Force and naval aviation. These include Alan Shepard, Wally Schirra, Scott Carpenter of the United States Navy, John Glenn from the United States Marine Corps, and Cooper, Grissom and Slayton. Dubbed the “Mercury Seven”, the men immediately become national heroes. In spite of repeated launchpad and in-flight explosions of the booster rockets which will carry them, the ambitious competitors all hope to be the first in Space as part of Project Mercury. Early U.S. test flights include a chimpanzee to test G-forces and other loads upon animal life. NASA engineers view the astronauts basically similarly, as mere passengers on pre-programmed flight paths. Insulted, the men insist that the Mercury spacecraft at least have a window, a hatch with explosive bolts, and pitch-yaw-roll controls to give them some role in its piloting. However, Russia beats them into Space on April 12, 1961 with the launch of Vostok 1 carrying Yuri Gagarin. U.S. efforts redouble.
Shepard is the first American to reach space on the 15-minute sub-orbital flight of Mercury-Redstone 3, on May 5, 1961. After Grissom’s similar flight of Mercury-Redstone 4 on July 21, the capsule’s hatch blows open upon splashdown and quickly fills with water. Grissom escapes, but the spacecraft sinks. Many accuse him of opening the hatch prematurely and panicking, a personal smirch, not on the program. Glenn, boosted on Mercury-Atlas 6, becomes the first American to orbit the Earth on February 20, 1962. He survives a possibly loose heat shield and receives a ticker-tape parade. The entire Mercury Seven and their families become celebrities, and are feted at a gigantic celebration to announce the opening of the Manned Space Center in Houston.
Although test pilots at Edwards mock the Mercury program for sending “Spam in a can” into Space, they recognize the courage it takes, irrespective of flying skill. Yeager states that “it takes a special kind of man to volunteer for a suicide mission, especially when it’s on national TV.” While attempting to set a new altitude record at the edge of space in the new Lockheed NF-104A, Yeager’s aircraft spins out of control and he is nearly killed in a high-speed ejection. Seriously burned, Yeager simply gathers up his parachute upon landing and walks to the ambulance, proving that he still has the “Right Stuff.”
On May 15, 1963, Cooper has a successful launch on Mercury-Atlas 9, ending the Mercury program. As the last American to fly into space alone, the narrator notes he “went higher, farther, and faster than any other American … for a brief moment, Gordo Cooper became the greatest pilot anyone had ever seen.”