# Can the fly-by-wire system of a modern airliner handle an unstable condition?

According to this answer airliners/large passenger aircraft such as an A320 are designed such that they are longitudinally, statically stable under normal flying conditions.

What if, for some reason, the c.g. would suddenly shift just aft of the neutral point? Could the FBW system of (for example) an Airbus handle this, just like the FBW of a fighter jet which is unstable by design?

Of course I'm not talking about a situation where the c.g. ends up so far back that the aircraft enters a deep stall, but a condition just "after" neutral stability, where the aircraft has just become "slightly unstable".

• If the reaction time of the FCS is significantly shorter than the short period mode of the aircraft, then yes. – Peter Kämpf Feb 5 '18 at 1:13
• Which will probably be the case, right? Or is it not possible to generally assume this? – Daniel Feb 5 '18 at 1:15
• The very first implementation of the fly by wire system in a real air craft was the X31 which was an experimental fighter jet. en.wikipedia.org/wiki/Rockwell-MBB_X-31 Since fighters need agility they are aerodynamically unstable to enable high turn and gear rates. – Timothy Truckle Feb 5 '18 at 6:25
• Yes, even when the aircraft is in the positive static stability region, there are constant disturbances that would change the aircraft pitch attitude and AOA away from the desired/programmed pitch. In the F-4 we had attitude augmentation systems in all three axis, pitch, roll, and yaw, which, when they detected small deviations, would input flight controls to correct for them. They were effectively eliminated attitude wandering.. FBW systems would work similarly, and be even more effective, in any static stability region, regardless of the dynamic stability characteristics of the aircraft – Charles Bretana Feb 5 '18 at 14:31
• Usually we call this "robustness", basically the ability for a control system to control something out of spec. Like what if your target is over weight, under power, or unbalanced, or more or less stable than expected. Some system are designed to be super robust, some are less so. It all depends on all kinds of tradeoffs. – user3528438 Feb 5 '18 at 22:56

Yes it can - to an extent, depending on:

• amount of CG shift;
• airspeed;
• aircraft weight (actually Moment of Inertia);
• maximum deflection rate of elevators/ailerons.

If the airframe has aerodynamic static stability, a disturbance in Angle of Attack Creates aerodynamic forces that return the aircraft attitude back to neutral. If the Centre of Gravity shifts aft of the neutral point, the airframe becomes statically unstable - the aerodynamic forces now want to amplify the disturbance. The rate gyro's in the fly-by-wire system sense that the attitude deviates from the commanded attitude, and deflect the elevators/ailerons such that the aircraft is brought back.

Amount of CG shift The ability of the Flight Control System to correct for unstable equilibrium depends on the degree of instability: the curvature of the right cup in the picture above.

Airspeed Deflection of the elevators and ailerons generates aerodynamic moments proportional to $V^2$. At high airspeeds, a small deflection results in a large moment about the CoG - the critical situation is low airspeed, which mostly occur close to the ground. At low airspeeds large deflections are required.

Aircraft weight If the aircraft is at a high gross weight, and if this weight is distributed away from the CoG, larger control deflections are required to correct disturbances in AoA. A heavier bowling ball in above picture makes for higher required forces.

Maximum deflection rate of elevators/ailerons The frequency response of the flight control systems is a function of how fast the control surfaces can be brought to the required position, and this is a function of hydraulic fluid supply rate: the added capacity of all the operational hydraulic pumps.

The F-16 is designed to rapidly correct for any disturbance from the commanded attitude, in any flight situation. All systems are dimensioned such, that artificial stability can still be provided at the lowest airspeed and the highest MOI that the aircraft can encounter. The A320 is not designed with a flight critical FBW system - if all systems fail, the aircraft returns to a state with aerodynamic static stability. If the FBW system fails in an F-16, the pilot must eject.

• "The A320 is not designed with a flight critical FBW system - if all systems fail, the aircraft returns to a state with aerodynamic static stability." However, what happens if an unstable condition occurs due to a shift in c.g. at the same time as a failure of the FBW system? Could the pilot then still hand-fly it? – Daniel Feb 5 '18 at 11:41
• That's a gradual thing as well, depends on the degree of instability. A pilot can provide active corrective inputs if the instability is not too rapid and violent, like the instability in a hovering helicopter which has a typical time period of tens of seconds. It takes getting used to though, and it would be tiring to do it for longer periods. – Koyovis Feb 5 '18 at 14:02

The word handle here is quite loaded. I think your question is whether a commercial transport category FBW aircraft capable of maintaining level flight for statically unstable CG. A better interpretation is, whether a pilot can safely fly the said aircraft if the CG is unstable, or nearly unstable (aft of the published CG envelope)? The answers to all of them, I would argue, are no.

First of all, to stabilize a statically unstable aircraft an AOA feedback is required in the pitch loop (see B.L. Stevens and F. Lewis, Aircraft Control and Simulation). For the commercial FBW transport category aircraft I've worked with, only pitch rate and pitch angle are fed back. AOA and other measurements are used for gain scheduling, but not directly in the pitch loop. I suspect this is the case for all commercial FBW. Pitch rate, with gain scheduling, is usually sufficient to increase the handling quality for relaxed stability configurations (static margin < 5%). I suspect a lot of this has to do with failure tolerance: if your AOA measurement is miscompared or disabled, the plane must keep flying. So pitch unstable aircraft is a no-go for Part 25.

Second, even if the CG is stable, but sufficiently aft of the CG envelope, the FBW would likely not be tuned to achieve the necessary handling quality for safe flight. The longitudinal modes would not be sufficiently damped, and you are more prone to control sensitivity. The situation worsens as you approach neutral stability.

• But the A320 also measures the accelerations, otherwise how could you fly a C* law? It also has and angle of attack protection, though I don't think it actually uses the AOA to fly it (have another question ongoing on that) - I think it is a pitch and speed control loop (with dv/dt) as well... – Jan Jul 2 '19 at 5:29
• I would like to think the C* as a tracking command, and outside of the stability augmentation (SAS). However, without understanding the A320 laws in depth, I don't want to surmise its feedback and its effect on statically unstable configurations. – JZYL Jul 2 '19 at 14:58