Armstrong was involved in several incidents that went down in Edwards folklore or were chronicled in the memoirs of colleagues. During his sixth X-15 flight on April 20, 1962, Armstrong was testing the MH-96 control system when he flew to a height of over 207,000 feet (63 km) (the highest he flew before Gemini 8). He held up the aircraft nose for too long during its descent to demonstrate the MH-96's g-limiting performance, and the X-15 ballooned back up to around 140,000 feet (43 km). He flew past the landing field at Mach 3 at over 100,000 feet (30 km) in altitude, and ended up 40 miles (64 km) south of Edwards. After sufficient descent, he turned back toward the landing area, and landed, just missing Joshua trees at the south end. It was the longest X-15 flight in both flight time and length of the ground track.
On April 24, 1962, Armstrong flew for the only time with Chuck Yeager. Their job, flying a T-33, was to evaluate Smith Ranch Dry Lake in Nevada for use as an emergency landing site for the X-15. In his autobiography, Yeager wrote that he knew the lake bed was unsuitable for landings after recent rains, but Armstrong insisted on flying out anyway. As they attempted a touch-and-go, the wheels became stuck and they had to wait for rescue. As Armstrong told the story, Yeager never tried to talk him out of it and they made a first successful landing on the east side of the lake. Then Yeager told him to try again, this time a bit slower. On the second landing, they became stuck, provoking Yeager to fits of laughter.
On May 21, 1962, Armstrong was involved in the "Nellis Affair". He was sent in an F-104 to inspect Delamar Dry Lake in southern Nevada, again for emergency landings. He misjudged his altitude and did not realize that the landing gear had not fully extended. As he touched down, the landing gear began to retract; Armstrong applied full power to abort the landing, but the ventral fin and landing gear door struck the ground, damaging the radio and releasing hydraulic fluid. Without radio communication, Armstrong flew south to Nellis Air Force Base, past the control tower, and waggled his wings, the signal for a no-radio approach. The loss of hydraulic fluid caused the tailhook to release, and upon landing, he caught the arresting wire attached to an anchor chain, and dragged the chain along the runway.
In April 1962, NASA announced that applications were being sought for the second group of NASA astronauts for Project Gemini, a proposed two-man spacecraft. This time, selection was open to qualified civilian test pilots. Armstrong visited the Seattle World's Fair in May 1962 and attended a conference there on space exploration that was co-sponsored by NASA. After he returned from Seattle on June 4, he applied to become an astronaut. His application arrived about a week past the June 1, 1962, deadline, but Dick Day, a flight simulator expert with whom Armstrong had worked closely at Edwards, saw the late arrival of the application and slipped it into the pile before anyone noticed. At Brooks Air Force Base at the end of June, Armstrong underwent a medical exam that many of the applicants described as painful and at times seemingly pointless.
NASA's Director of Flight Crew Operations, Deke Slayton, called Armstrong on September 13, 1962, and asked whether he would be interested in joining the NASA Astronaut Corps as part of what the press dubbed "the New Nine"; without hesitation, Armstrong said yes. The selections were kept secret until three days later, although newspaper reports had circulated since earlier that year that he would be selected as the "first civilian astronaut". Armstrong was one of two civilian pilots selected for this group; the other was Elliot See, another former naval aviator. NASA announced the selection of the second group at a press conference on September 17, 1962. Compared with the Mercury Seven astronauts, they were younger, and had more impressive academic credentials.