Lockheed XFV-1 Salmon

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It took off vertically, landed vertically as well, ripped out engines, and some of the Army's original ideas came to fruition thanks to Lockheed's huge budget.
Grumman X-29
In the 1980s and 1990s, the U.S. Air Force acquired the Grumman X-29 aircraft, whose forward-swept wings were more aerodynamic but impossible to fly: the digital flight computers allowed it to correct its trajectory as many as 40 times per second, making it impossible to do so without computers.