RAE Bedford investigated ‘relaxed’ longitudinal stability in their 1-11 (XX 105) – late 70’s. The aft cg was part simulated and part real. For real, it was quite a long way back – the tech log was annotated “do not use aft stairs or doors” !!
The next disconcerting point was that the simulation used an experimental auto control system (autopilot servos?) which had to be programmed by a ‘boffin’ using a computer patch-board (the size of a large Lego board) and covered in wires as if arranged in a cat’s cradle.
Anyway, the system was a delight to fly. The pitch control was attitude demand with auto trim. There was no attitude change with speed change, yet speed control was not onerous.
I can’t recall the stick forces, probably no change from the basic aircraft feel system, but overall the modified ‘speed’ stability did not cause any problems. The auto throttle was used fairly extensively, but manual flight was typically ‘fighter like’; point the aircraft with one hand, adjust the speed with the other.
AFAIK, the control laws were similar to those used by Airbus in their tests / validation work pre A320.
I have a faint recollection that a flight-path demand control law was also flown, where again speed stability was not an issue. Also, (from a weak memory) there were tests of direct lift control where pitch demand resulted in lift change without attitude change – the stick moved the spoilers in / out, the auto system compensated with a pitch-maintaining elevator movement. The majority of this test work was flown independently of the aft cg work and the system was assessed during steep approaches – flight path accuracy and low flare ht.
The pitch demand system was evaluated throughout out the flight envelope (0-2g), excepting stalls (for obvious reason in the 1-11). The only notable problem was during landing where the pitching axis changed from the cg to the main wheels at touch down. The control system adjusted for the resulting nose down pitch with a back stick input which ‘skipped’ the aircraft back into the air. A quick patch-board change fixed that. IIRC one of the FBW fighter projects ‘discovered’ a similar problem.
The BAe owned 1-11 (G AY.. ) flew an experimental fly-by-light control system (alongside the conventional controls) using same/similar control laws as did RAE.
Tests on this aircraft were at ‘real’ aft cg, achieved by moving lead wts in flight. The emergency recovery procedure was for the FTE to pick up two 50 lb wts at the rear of the aircraft and run forward! My recollection from only one flight was that the handling was similar to the RAE tests; low altitude / landing tests were not flown – for other obvious reasons.
With hindsight, … … we did some very serious ‘silly’ things, but safely, and they were great fun.
Many of these tests were addressing the type of question starting this thread; those which were answered positively eventually have been used in aircraft. The process is slow and cautious, with small, safe steps, even if some appear giant leaps.