Without dates it gets too squishy.
From Joe Baugher's web site;
"The saga of the Northrop P-61 Black Widow begins back in August 1940, at the height of the Blitz on London. During this time, the US air officer in London, Lt. Gen. Delos C. Emmons, underwent a briefing in which he was brought up to date on British progress on radar (Radio Detecting and Ranging). Radar had first been developed in Britain in 1936, and British scientists and engineers were at that time working on the early versions of AI (Airborne Interception) radar sets which could be carried aboard airplanes, enabling them to detect and intercept other airplanes in flight without having to rely on ground installations.
At the same time, the British Purchasing Commission that was shopping for aircraft in the USA announced that they urgently required a night fighter that would be capable of stopping the German bombers that were attacking London by night. Such a fighter would have to be able to stay on station above London all night, which meant at least an 8-hour loiter time. In addition, the night fighter needed to have sufficient combat altitude in order to take on the bombers when they showed up.
When General Emmons returned to the USA, he reported that the British had an urgent need for night fighter aircraft, and that American industry might be able to supply that need. A preliminary specification was drawn up by the Emmons Board and was passed on to Air Technical Service Command at Wright Field in late 1940. Because of the heavy weight of the early AI radar and because of the high loiter time required, a twin-engined aircraft was envisaged.
Northrop Chief of Research Vladimir H. Pavlecka happened to be at Wright Field at that time on an unrelated project, and was told of the Army's need for night-fighters. However, he was told nothing about radar, only that there was a way to "see and distinguish other airplanes". He returned to Northrop the next day. On October 22, Jack Northrop met with Pavlecka and was given the USAAC's specification. At this time, no other company was known to be working on night fighters, although at about this time Douglas was starting work on their XA-26A night fighter and the AAC were considering the A-20B as an interim night fighter."
and "The design was revised still further on November 22. The belly turret was deleted, and the crew was changed back to three--pilot, gunner, and radar operator. The pilot sat up front, and the gunner sat immediately behind and above the pilot. The gunner was to operate the turret via remote control, using a special sight attached to a swiveling chair. A "stepped-up" canopy was used to provide a clear field of view for the gunner. The rear fuselage with its clear tail cone provided the radar operator with an excellent rearward view which enabled him to act as a tail gunner if the plane happened to be attacked from astern. Optionally, the dorsal turret guns could be "locked" into the forward-pointing position, so that they could be fired by the pilot. The belly guns were deleted, and four 20-mm cannon were to be fitted in the wings. This design was formalized into Northrop Specification 8A (or NS-8A), dated December 5, 1940."
Now a few mistakes were made but they were basically 'designing in the dark' when it came to the size/volume and weight of the radar equipment, at least for the first few months.
It turns out you could put some of the early radar sets in rather small planes (Defiant) and at least shoot down
something.
Coming up with a compromise between the Defiant's endurance and and
8 hour patrol might have allowed for a smaller aircraft also
Then you have the armament question, how much is
enough? Four 20mm guns with 6-9 seconds worth of ammo figuring you are lucky to get one intercept and firing opportunity per flight?
Lighter guns and more firing time?
Enough ammo to swan about the sky for 8 hours and performing multiple interceptions while waiting for daylight to land?
Mission requirements are going to drive the design, not designing kool plane and seeing what you can stuff into it or get it to do once it is flying.
Adapting an existing design is another story but has it's limitations as the P-70 shows.