What would induce the U.S. military to consider flying saucer/aircraft designs?

Flying saucer/disk configurations were relatively rare in science fiction stories prior to Kenneth Arnold’s 1947 sighting.

But there was a documented patent for a lenticular flying machine (according to Wikipedia) submitted by Romanian inventor Henri Coanda, who created a functional scale model in 1932, patenting his conception in 1935.

 A flying disc craft called the Discopter was patented by Alexander Weygers in 1944 (Wikipedia also tells us).

And in films, flying saucers were not depicted until 1950’s The Flying Saucer, and others in the 1950s time-frame.

So why were there efforts by the Army, Air Force, and even the Navy to come up with a flying saucer engineered/designed flying craft?

Did the military have access to films that showed such craft flying in the skies?

Did they actually recover a downed flying disc in Roswell, which spurred the military to try to come up with own versions?

What would cause even the slightest interest in the round flying craft design, except for some evidence that such things were extant after 1947?

RR