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Which production fighter was the first designed on purpose to be aerodynamically unstable?

Short answer

It was the F-16, with one qualification of scope: the first production fighter deliberately designed to be slightly unstable from an aerodynamic standpoint, known as relaxed static stability (RSS), in order to reduce drag and improve manoeuvrability. The scope is production fighters.

Which production fighter was the first designed on purpose to be aerodynamically unstable?
A USAF F-16 pilot breaking right on final approach over northern Las Vegas

Instability built in on purpose

The F-16 was the first production fighter deliberately designed to be slightly unstable aerodynamically, a characteristic known as relaxed static stability (RSS), adopted both to reduce drag and to improve manoeuvrability. The result is a highly agile fighter, the first built expressly to sustain 9 g manoeuvres and capable of exceeding Mach 2.

From theory to the prototype competition

The conceptual starting point was energy-manoeuvrability theory, which Colonel John Boyd developed together with the mathematician Thomas Christie to model a fighter's combat performance, drawing on his experience in the Korean War and as a fighter tactics instructor in the early 1960s. Northrop's YF-17 prototypes first flew on 9 June and 21 August 1974. During the fly-off, the YF-16s completed 330 sorties and 417 flight hours, compared with 288 sorties and 345 hours for the YF-17s. The YF-16 moved from one manoeuvre to the next significantly faster and was the unanimous choice. Another advantage of the YF-16, unlike the YF-17, was the Pratt & Whitney F100 turbofan, the same one used by the F-15. The YF-17 was later developed into the YF-18 for the Navy.

A cockpit built around manoeuvring

The pilot sits at an unusual reclined angle of 30°. Instead of the traditional centre stick, the aircraft uses a side-stick controller mounted on the armrest.

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