Longitudinal Stability -
gums' last post highlighted the relationship of stick force/stability/CG. That is carried on in the Boeing paper cited by PJ2.
Casting the Boeing words a little differently, it is worth keeping in mind that longitudinal static stability is all about what stick forces the pilot "feels" when the aircraft is not on speed so far as trim speed is concerned.
At the trim speed the stick force should be at or very near zero.
If the aircraft slows down (for whatever reason) and the pilot desires to hold that lower speed, acceptable static stability requires that the pilot MUST hold on a PULL force of some measure. Furthermore, the further away from the trim speed, the HIGHER the pull required
If the aircraft speeds up etc we are looking at a PUSH force etc
As the CG moves aft the slope of this line (stick force against off trim speed delta) reduces and the aircraft gets progressively twitchier.
In an ideal world, the line would be straight and extend well away from trim speed. In reality sometimes the line does strange things and we need additional add ons (such as SAS) to adjust forces so that the pilot is fooled into believing that all is well. In small aircraft, this might be something as simple as a fancy spring arrangement bolted onto the elevator control circuit - typically seen in GA piston to turboprop conversions.
As CG moves aft we eventually get to a point where the static stability is unacceptable and we enter the region of static instability. The aircraft is still flyable (if you know what you are doing). The technique is tiring and stressful and consists of making an input, freezing the controls, assessing the response, making an input .. etc.. etc. A pilot in the know might manage to get the aircraft around the circuit for a landing .. but an extended flight recovery is a big ask. Hence the need for fancy electronic stuff to do the hard work.
Further CG aft movement eventually gets into a region of dynamic instability and the aircraft is beyond the ability of the human pilot altogether ...
Whatever the AF guys had in front of them in the cockpit, they had their hands well and truly full ... one way or the other .. not a situation any of us would wish on any pilot.