It was designed in 1916 by Frederick Koolhoven who was the chief engineer at Armstrong Whitworth as a single-engine two-seat fighter. He opted for the quadruplane configuration that was also chosen for other anti-zeppelin fighter like the Pemberton-Billing P.B.29E, Supermarine Nighthawk and the Wright Quadruplane, all of that when Sopwith were designing and building their successful Sopwith Triplane fighter.
The first prototype, named Armstrong Whitworth F.K.9 was built and flown for the first time in the summer of 1916 and was powered bya a 110hp Clerget 9Z engine. It had a shallow fuselage with the wings joined by a plank-like interplane struts. It was unarmed and, after being evaluated at the Central Flying School in late 1916 an order of 50 for the improved version, the F.K.10 even if it wasn't produced yet.
The F.K.10 featured a new and deeper fuselage, a new tail and held the wing configuration of the F.K.9. It was armed with a forward firign synchronised 0.303 Vickers machine gun and with another one mounted in the observer cockpit. It was powered by either a 130hp Clerget 9B or LeRhône 9J engine. However it showed inferior performance than the Sopwith Strutter, which was already in service at the frontlines performing the two-seat fighter role, even if it wasn't it's initial one. That's why only five of them were built for the RFC and three more for the RNAS and they weren't employed operationally and it wasn't developed further.
Sources:
1. https://en.wikipedia.org/wiki/Armstrong_Whitworth_F.K.10
2. Salamander Books - The Complete Book of Fighters
