It Kind of Worked...
A couple of weeks ago, I ran a history blurb on the A-10A Thunderbolt II and it's impressive GAU-8 Avenger gun system. The system was wildly successful, and provided a massive amount of damage to an enemy element with little cost (bullets are substantially cheaper than missiles and bombs). Both the A-10 and the F-16 entered design during the Vietnam War, with both aircraft taking to the skies on the tail end of American involvement in Southeast Asia. The United States had taken what it had learned in the war and applied it to its Research, Development, and Engineering (RDE) processes. The A-10 first flew in 1972, and the F-16 followed two years later in 1974. The A-10 was designed to be a close-air-support (CAS) aircraft that directly aided ground forces. The F-16, however, was designed to replace many of the smaller century (100) series aircraft as an air superiority fighter. The A-10 entered service in 1977, with the F-16 following the year after.
The success and appreciation of the weapon system of the A-10 was so popular, that the Air Force and the Army wanted to employ it on a larger assortment of aircraft. The F-16, by nature, was originally only fitted with a smaller M61A1 20 mm Vulcan gun system. It was too light to carry a full scale GAU-8, and any attempt to modify the airframe to carry such a weapon ruined it's maneuverability. The demand and mission seeking a smaller system that was able to be fitted to the external hardpoints on the F-16 initiated the same year it was introduced.
General Electric was the one who ultimately won the bit for the prototype "Pod, Lightweight, 30 mm, Airborne, Cannon" (Standard Nomenclature). The system was contracted through Wright-Patterson Air Force Base in Ohio and saw subsequent testing from Eglin Air Force Base in Florida. The F-16 was the primary aircraft, but other aircraft, such as the F-15 Eagle, were also candidates to carry the weapon system. The development of the 30 mm pod, as well as the main GAU-8 was merged after Fiscal Year (FY) 1975. The pod version of the weapon was to be called the GAU-13, as part of the Improved Aircraft Gun Systems (IAGS) program.
The GE pod was officially unveiled to Air Force officials in September of 1977, weighing only 1,500 lbs and capable of firing up to 2,400 rounds per minute. It was not nearly as rapid firing or heavy as the native GAU-8 system, but it did provide a complementary barrage to the F-16's onboard M61A1.
The gun was seen as satisfactory, and it did serve on the F-16 through the early 1990s. Poor accuracy was its demise, since the pod had to be carried in such a way that the Heads-up Display (HUD) in the plane's cockpit could not compensate for the correction. As a result, in 1991 - after only a day in combat during Operation Desert Storm (ODS), the pods were removed from all F-16's. They only remained on exported F-5 Tiger II's until about 2005 when they were removed from foreign service as well. The F-16's of today retain the M61A1 20 mm gun system.
The GAU-13 was an example of attempting to downsize the GAU-8, but as history has shown, that is difficult if not impossible.