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On which aircraft did the first early-warning radar fly?
Short answer
The first airborne early-warning radar flew on a modified Grumman TBM Avenger: the TBM-3 converted into the XTBM-3W, which debuted the AN/APS-20 on 5 August 1944. It grew out of Project Cadillac, commissioned by the US Navy to MIT in February 1942. It did not enter service until 1946.

The Project Cadillac commission
On 2 February 1942 the US Navy commissioned the Radiation Laboratory of the Massachusetts Institute of Technology to explore an airborne radar design dedicated to searching for aircraft, under Project Cadillac. The team grew from 37 people, ten of them officers, in May 1943, to 138 by the end of the war. MIT's work to develop a usable system led, in February 1944 and under Project Cadillac, to a prototype system that was built and flown in August on a modified TBM Avenger. The production radar was made by General Electric and Hazeltine.
The converted Avenger
The first aircraft equipped with the AN/APS-20 was a converted TBM-3 Avenger, designated XTBM-3W, which first flew on 5 August 1944. That early-warning Avenger carried a crew of just a pilot and a radar operator. In 1944 the US Navy introduced airborne early warning at sea, installing the AN/APS-20 radar in TBF Avenger aircraft.
From evaluation to service
About 40 TBM-3W conversions were made. The system was still under evaluation when the war in the Pacific ended and did not enter service until 1946. Even so, it was the very first airborne early warning aircraft. Project Cadillac II began in 1944 with the aim of developing a flying command centre.
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