United States Army Air Forces
The United States Army Air Forces (USAAF) was the aviation division of the United States Army during the 1940s. 

In July 1947, the Air Forces retrieved a Ferengi shuttle which had crash landed in Roswell, New Mexico, after the shuttle had traveled back in time from the year 2372 via time warp. Air Forces Lieutenant General Denning oversaw the interrogation of the vessel's three inhabitants, whom he believed to be alien invaders. The three Ferengi were eventually able to escape with the assistance of two helpful Humans, retrieve their ship, and return to their own time by recreating the time warp. The Air Forces subsequently covered up the incident, issuing an official statement claiming that only a weather balloon had been recovered in Roswell. ()

Less than three months later, the Army Air Forces became a separate military branch, the United States Air Force, which was quickly followed by Chuck Yeager's first successful supersonic test flight. ()

In the alternate reality, two USAAF badges were displayed behind the bar of the Riverside, Iowa Shipyard Bar. ()

United States Army Air Forces personnel

Named
Denning (Lieutenant general)
Garland (Nurse)
Jeff (attached civilian professor)
Wainwright ()

Unnamed
MP guards
MP #1
MP #2
Major

Appendices

Background information 
While teleplay writers Ira Steven Behr and Robert Hewitt Wolfe consistently refer to the service branch of the United States military encountered in "Little Green Men" as the "Army Air Corps", and to Denning as an "Army Air Corps general" in the script, both they and the Star Trek fact checkers had overlooked that this constituted an anachronism: the "" (USAAC) had been renamed to "United States Army Air Forces" (USAAF, and plural to indicate the proliferation of specialized departments within the service) on 20 June 1941, six years prior to the events depicted in the episode. However, the USAAC designation was neither seen nor heard even once in the episode. Meanwhile, the wardrobe department of Star Trek had, unwittingly or not, paid closer attention to the actual historical development, as the uniforms of the American soldiers were endowed with the proper, time-period correct USAAF service emblems (the USAAC emblem lacked the birds/wings), which were prominently featured in the episode.

As the original name already suggested, the service started out as a branch of the US Army, but was by the time of World War II already a full-fledged, de facto independently operating military service on its own. In order to reflect this, and just two months after the events depicted in "Little Green Men", the service was again renamed to "United States Air Force" (USAF, and singular to emphasize its separate status) on 18 September 1947, which is the name it still holds to date. However, one other anachronism did appear on screen, whereas an older, incorrect roundel – one that was replaced in January 1947 – appeared on the plane parked outside the base warehouse. 

The two badges seen in the 2009 film Star Trek have been identified as having belonged to the World War II-era  and  respectively. 

Real world Star Trek affiliated USAAF enlistees included Creator Gene Roddenberry and Art Director Matt Jefferies, both serving as bomber pilots during World War II with Roddenberry serving in the Pacific Ocean theater, whereas Jefferies flew over North-Africa and southern Europe. Other known Star Trek cast and crew with USAAF ties included producer Fred Freiberger (serving as a reserve at the time in which the Star Trek episode was set, one year after he was taken off the active list pursuant his war service as a bomber navigator, in the 8th USAAF incidentally), and performers DeForest Kelley, David Sharpe and Anthony Zerbe, the first two during World War II.

External links 
 
 
 

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Earth military organizations