Stability Wars: Why Did Relaxed Lose?

[Winnerhofer]

Speed stabilty (Boeing); vector stability (Airbus); relaxed stability (MD).
If relaxed is the most natural form of stability, why is it that Airbus chose vector stability, Boeing speed stability and not MD's relaxed stability which never became a trend let alone norm.

[warmkiter]

Dont compare fly by wire with conventional aircrafts. The beloved and hated MD11 has so far MAC that with 32% it's almost indifferent. With longer fuselage and tailstrike tendency towards DC10 it needs LSAS to help the pilot. Automatic nose lowering, pitch rate dampening etc were necessary to keep it within requirements. Still it has a crappy accident rate and everybody who flies it knows it can bite if you don't pay attention. Relaxed stability is nothing else than indifferent stability due rear CG to meet fuel economy promised to early customers

[clunckdriver]

Warmkiter, its not "Sheeps", its "Sheep", likewise its "Aircraft", not "Aircrafts!"Sorry, but if I had a nickle for every CV which came to my desk with this on it I would be a rich man, none of them were hired by the way!

[NSEU]

Warmkiter, its(sic) not "Sheeps", its(sic) "Sheep",(insert full stop here) likewise its(sic) "Aircraft", not "Aircrafts!" Sorry, but if I had a nickle (sic) for every CV which came to my desk with this on it I would be a rich man,(insert full stop here) none of them were hired by the way!

"People in glass houses...."

[safetypee]

Winnerhofer, you attempt to compare differing (incomparable) aspects and seek judgement of an ideal solution.
Relaxed static stability in achievable in conventional aircraft; incorrect loading, aft cg will create a sensitive aircraft. In most situations this would be flyable but increasingly require above average skills and moderation of manoeuvres up to a point of loss of control
Certification requirements for cg and handling characteristics provide an adequate safety margin; but where modern aircraft are designed to be operate with adverse (relaxed) stability for economic reasons, then the safety margin for flight handling has to be provided by other means.
This is achieved with computed flight control laws and systems (ideally FBW) negating the need for enhanced skill or limiting manoeuvres.

The choice of ‘speed’, ‘vector’, or ‘attitude’ as the primary parameter in the flight control computation depends on many parameters; aircraft type, role, degree of relaxation, etc. There may be no one best solution.

The use of FBW (computational control) enables other protections to be replaced – stick force per ‘g’ for structural protection, speed (alpha) limit for low speed, similar for high speed, the need to trim, and perhaps the need for ‘feel’.
It could be questioned if the implementations of these other aspects are ideal, particularly if the skills in their use and mechanisation are not fully understood.
How might we train in a Cessna 172 with ‘vector’ control and no trim?
Would such an aircraft be comparable to a modern airliner?

[galaxy flyer]

gums will be here shortly, but "relaxed" stability implies lots of maneuverability and pitch authority which isn't needed in transport category planes. AF 447 might have hit tail first with it.

[Microburst2002]

Clunckdriver wrote

Warmkiter, its not "Sheeps", its "Sheep", likewise its "Aircraft", not "Aircrafts!"Sorry, but if I had a nickle for every CV which came to my desk with this on it I would be a rich man, none of them were hired by the way!


Hahaha, Clunckdriver, tell us in which company is your desk, so that I make certain that I will never ever apply.
:yuk:

[Microburst2002]

How might we train in a Cessna 172 with ‘vector’ control and no trim?
Would such an aircraft be comparable to a modern airliner?

Safetypee: Why not?

Imagine a planet with a civilization so highly developed that they never needed to fly, because they had star trek like teletransportation, but one day they decide to make planes just to have fun.

They could use a fbw system like that of Airbus, and that would be the conventional way. Airplanes have to be stable, and trimmable. Airbii are trimmable by releasing the sidestick. Other airplanes use other methods.

Airbii are intuitive to fly, easy to fly. If that is what you are destined to fly, why not have initial training in a Cessna with a flight path stable fbw?

[Winnerhofer]

By T.S.
This is bad terminology.
Vector stability and speed stability are control laws.
Relaxed stability is an aerodynamic property.
You can have relaxed stability with speed stability (e.g. F-16) or with vector stability (e.g. A340).
Relaxed stability is just a measure of how far the CG is from the CP.
It has nothing to do with which pitch control law you use.

[Microburst2002]

Yes, that is the idea I had. You can extend the CG aft limit by means of some form of stability augmentation. Wether mechanical or electronic.

[safetypee]

Micro ‘why not’ … indeed why not.
I suspect that one view would terminate with cost effectiveness; others debate the extent and nature of training. As for the type of control system in a training aircraft the differences might only be similar to those between FD formats and the nuances of implementation (FDs use a range of different control laws).

One (military) argument was that irrespective of future aircraft characteristics, the handling qualities / characteristics for all types could be identical with the use of ‘FBW’ and thus eliminate the need for extensive differences training. This of course falls down when considering different roles – fighter vs transport (would they use different control parameters), and again cost effectiveness, particularly when considering how much of military training is situational and decision oriented – an extensive range of experiences and mental skills.
Perhaps current civil operations should take note; ‘FBW’ can reduce the need for a range of manual skills, thus reducing training duration, differences and cost, but this could be at the expense of experience and mental skill. Neither type of control law will replace those.
A Cessna with FMS, a full Flight Guidance system, ECAM, in a realistic operating environment … a pointless debate.

If comparisons are to be made, look at the implementation (training) and use of these systems. Consider operators’ and individual attitudes and assumptions.
Modern aircraft are easy to fly, to be enjoyed, but to operate they require greater, different standards of professionalism, particularly at the extremes of normal conditions.
These are the aspects which could be equated and judged, but there is no such thing as an ideal or best practice, as these are always in the eye of the beholder.

[gums]

Yeah, Galaxy, we gotta define terms and laws.

The F-16 was not statically stable below 0.95 mach. That'a aerodynamic "stability". So the plane would not go to a trimmed AoA if you let off the stick. In fact the tail actually produced "up" lift in most flight conditions, so we had an extra bit of lift , and much reduced trim drag cruising. At very high AoA, the leading edge of our stabilators were full up ( trying to keep AoA under the limit).

We had a gee command for pitch like the 'bus, and the result of the control laws was neutral speed stability. Neither jet trimmed to an AoA in normal laws. But it looks like the 'bus has speed stability in Direct Law, from FCOM's I got from the folks here. And it apparently has enough tailplane to maintain a very high AoA and pretty good directional control as we have seen at least once.

BTW, you can have a FBW system AND static stability in fighters, too - the Hornet is a good example.

I don't think you will ever see "relaxed static stability" implemented on a commercial airliner.

[DozyWannabe]

Airbii are intuitive to fly, easy to fly. If that is what you are destined to fly, why not have initial training in a Cessna with a flight path stable fbw?
Because it helps you to understand what the technology is assisting in the event that one day it might fail to operate as designed.

[FCeng84]

The FARs dictate pitch handling qualities including certain levels of pitch stability as experienced by the flight deck crew when flying manually. For airplanes without augmentation in the form of feedback control laws that increase stability, the FARs translate into fore/aft limits on the CG range. Moving the CG further aft would reduce stability and in the context of this discussion thread constitute "relaxed static stability". The motivation for doing so is the resultant improved fuel economy as the horizontail tail carries less down load (or if you move CG far enough aft, actual positive lift).

A key reason for Boeing to introduce FBW on the 777 was to enable relaxed static stability by allowing the cg to be moved further aft than would have been possible without the C*U pitch control law augmentation. Augmentation allows tuning of the response characteristics independent of the basic, open-loop configuration stability deriviatives. Pitch damping was also added to the backup, reversionary modes to yield adequate handling characteristics for failure conditions. This basic control concept served as the baseline for 787 configuration definition.

All future Boeing commerical airplanes will include relaxed static stability as a core feature.

[Owain Glyndwr]

Pitch damping was also added to the backup, reversionary modes to yield adequate handling characteristics for failure conditions. This basic control concept served as the baseline for 787 configuration definition.
Interesting!
So if I have read you correctly the 777/787 handling with aft CG is inadequate without stability augmentation. This goes further than all the AI aircraft I have been involved with from A310 to A340 where the aircraft has to be satisfactorily flyable without any augmentation even with aft CG - i.e. direct law for A320 onwards. Several PPRuNers have posted to the effect that this is so.

[gums]

Yeah, OG.

I cannot imagine a certification nowadays for a commercial jet that does not have positive static stability once in the so-called "direct law". You know, the one that relies upon the natural aero of the jet to seek a trimmed AoA.

Our problem, and this shows up in last paragraphs of the AF447 report, is the Airbus has neutral "speed" stability until in "direct" law. And then the basic design is primary and you have something close to what all the planes since the mid-fifties have had with hydraulic flight control systems.

[FCeng84]

One thing to be careful with is terminology regarding control system modes. The Boeing 777 and 787 have three basic modes for manual control: Normal, Secondary, and Direct. All three involve pitch stability augmentation.

Normal Mode is provided unless failures result in insufficient equipment availability to support the full-up suite of functionality. Most pilots will only ever experience this mode as the other two are for rather remote failure conditions.

Secondary and Direct Modes are activated in the event of failures that preclude Normal Mode. These two reversionary modes share the same level of augmentation and thus the same handling qualities. Secondary Mode is activated if sensor input data required to support Normal Mode are no longer available. Direct Mode is activated if control system computational resources required to support Normal or Secondary Mode are no longer available.

Both Secondary and Direct Modes involve pitch rate feedback to improve pitch stability. Because these are reversionary modes and Normal Mode has sufficient availability, the handling qualities provided by Secondary and Direct Modes are permitted to be degraded. These response characteristics would not be sufficient for certification for every day use.

It turns out that the limitation as to how far the stability can be relaxed is the acceptability of the reversionary mode handling qualities, not what the full-up Normal Mode system can provide. Making it handle well when all of the resources are available is one thing, having it handle acceptably when the stuff has hit the fan is something else.

[john_tullamarine]

Another point of critical interest, presuming OG's observation to be correct, relates to system reliability. That is, the level of confidence that the operator/crew can have that the crew won't be left with a degraded mode where the LSS is grossly inadequate ?

While an aircraft can be so flown (even if it be statically unstable - providing that the pilot knows the tricks of the trade) the workload, as LSS reduces, becomes progressively intolerable and prolonged flight associated with recovery becomes impossible.

[Owain Glyndwr]

@FCeng84


It is not easy, apart from the use of Secondary rather than Alternate, to see any substantive difference between the two sets of logic. In both cases progressive loss of system resources (computers, sensors) is accompanied by a loss of stability augmentation.


Again if I have read you correctly, the main differences seem to be that in the Boeing design the first step after a failure is to drop to a level of stability augmentation that is pitch damping only whereas the Airbus design retains the essentials of the C* function, albeit sometimes with compromise gains. The next step to "Direct" law has no change of augmentation in the B777/787 but no augmentation at all on the AI designs.


Your comment that the allowable level of relaxed stability depends on the "bottom level" of handling qualities available and JT's comment that this is linked to reliability are both spot on. This implies that Boeing have convinced themselves and the FAA that the probability of losing all pitch damping is less than 10^-9 per flight hour.


It may well be that in the long gap between the appearance of the A320 and the B777 computer technology (and sensor technology - do not forget the sensors!) had improved to the point where it was possible to construct a mathematical case to prove that this was so, but realistically, when talking of "proof" at that level of probability one is as much in the realms of faith, engineering judgement and faith in one's engineering judgement as in the arithmetic.


Ther is nothing wrong with that, but we should recognise that it is so.

[FCeng84]

The Boeing FBW Normal Mode has an availability of 10^-7 per flight hour. The system can endure a number of failures of redundant equipment and still provide the full-up, Normal Mode control augmentation.

You are correct that the Direct Mode is better than 10^-9 per flight hour. Very much simplified augmentation is provided by the Actuator Control Electronics (ACE) LRUs. The separate LRUs that host the Normal Mode functionality are bypassed in Direct Mode. The four ACEs are brick walled from each other. In the case of the pitch axis there are four separate pitch rate sensors that feed each of the ACES and elevator actuator control is partitioned among the ACEs. Flight deck column position is measured by separate sensors that feed the respective ACEs. In Direct Mode, two ACEs respond to the left column and drive the left elevator while the other two ACEs respond to the right column and drive the right elevator. The columns are mechanically linked through a breakout element that allows one to move free of the other if sufficient differential force is applied.

[Owain Glyndwr]

Thank you for that explanation. I did wonder whether you had a separate, dedicated pitch damper to meet 25.1309.

[Owain Glyndwr]

A follow up question if I may.


What happens in Normal mode if one pilot demands up elevator and the other demands down elevator? Presumably the yokes become disconnected, but what do the control surfaces do?

[FCeng84]

The mechanical link between the two columns will pop out of its detent allowing relative motion if the force carried by that link exceeds 50 lbs.

The average of the left and right column positions is used as the consolidated input to the Normal Mode control law. Both elevators are commanded to the same position based on this consolidated column position and the other feedback signals that make up the control algorithm.

[Owain Glyndwr]

Thank you once again

[Microburst2002]

FCeng84

Unfortunatelly I haven't had the chance to fly the 777, not even in a sim, so I can't make any experiments, and the FLT CTL chapter in the FCOM is not very detailed. It explains little about how it works.

Airbus uses C* and Boeing C*U, right? What I don't understand exactly is how the artificial feel works in the boeing yoke. Is it only for giving cues to the pilot about overspeed, impending stall and such, or it has some relation with airspeed?

What happens in a 777 if you pull the yoke like 2 or 3º and then keep it there (all automation off). Will the pitch stop at some point like in a conventional airplane? (would that be the pitch damping feature?) Or will it keep pitching up and up? In the airbus it would keep pitching up and up until some protection kicked in.

[FCeng84]

Microburst - glad to take a crack at your questions - feel free to ask follow-ups as you see fit.

When talking of controller feel it is important to distinguish between force generated via changing the force/displacement characteristics of the controller and forces that are generated via the pilot finding it necessary to hold the controller out of detent. Both of these concepts come into play with the Boeing FBW pitch control system.

As you are probably well aware, C* is a combination of pitch rate and the normal load factor increment from that for level flight. To get to C*U, Boeing has chosen to add a third, speed based term. The U in C*U is a command that is a function of the difference between the current airspeed and a reference airspeed. If speed is higher than the reference speed, the U term commands airplane nose up response. Similarly, if the speed is lower than the reference speed, the U term commands airplane nose down response.

The C*U control system forms the sum of measured C*, the U term based on speed, and the C*U command that is a function of column position. In steady state, the C*U control system drives the elevators to command pitch such that the sum mentioned above is zero. If speed is equal to the reference speed, the pilot will find that zero column commands zero pitch rate and normal load factor for constant flight path angle. If speed is higher than the reference speed, the pilot will find that a push displacement of the column is needed to generate sufficient C*U command to offset the system's nose up U term. Similarly, if speed is lower than the reference speed, the pilot will have to pull in steady flight to keep the U term from commanding the nose down. Note that all of this is achieved without changing the force/displacement feel characteristics of the column.

Now to the question of what happens when starting at a trim condition the pilot pulls and holds a small amount of column. The initial response will be nose up pitch rate / increase in normal load factor. As speed bleeds off, the U term will command more and more nose down in an effort to return to the reference speed. Eventually the speed difference will become large enough that the pilot's nose up command due to column pull is balanced by the nose down command due to speed error. If held long enough and allowed to damp out a new equilibrium will be reached where the pilot is holding constant pull force and the airplane is steady at a speed the is the corresponding amount slower than the reference speed. For a push, the converse happens leading eventually to steady flight at a speed higher than the reference speed.

The Boeing system operates with minimum reference speed limit of top of amber band on the speed tape and a maximum reference speed limit at Vmo/Mmo. The C*U reference speed cannot be set outside of those limits.

The system is designed to feel intuitive to the pilot who has learned to fly a conventional, unaugmented airplane. The basic operation is to fly the airplane to the desired condition activating pitch trim as needed to remove steady column force (i.e., the need to hold column out of detent). On an unaugmented airplane the pitch trim input drives the stabilizer (or elevator trim) up/down. With C*U these same inputs command the reference speed down/up (polarity choice here intentional) to yield the same flight deck effect.

Boeing does vary the stiffness of the column feel (i.e., the force displacement relationship) for other purposes, but not as part of the basic C*U control law at a given airspeed. Column feel is stiffened at high speed and softened at low speed to provide better speed awareness and feel similar to an airplane with mechanical linkage between pilot an elevator such that column force is proportional to elevator hinge moment.

[roulishollandais]

Vector stability and speed stability are control laws.Stability is not a control law but a quality -among others- of the control law/closed loop :zzz:.

[FCeng84]

A control law utilizing integral feedback involves a choice of "regulated variable". This is the response parameter whose error (difference between command and response) the control law will drive to zero in steady state. With C* the regulated variable is a mix of pitch rate and normal load factor. With C*U a third parameter is added - speed deviation from a reference.

The Boeing C*U system adjusts pitch attitude (and thus flight path angle) such that, in steady state, speed will match the reference speed. In this way, C*U provides speed stability.

It is important not to confuse speed stability (pertaining to the pitch axis long mode or phugoid mode) and maneuver stability (pertaining to the short period mode). These modes are separated sufficiently in frequency (~.02 Hz vs. ~0.5 Hz) that they can be treated individually. Both the Boeing system using C*U and the Airbus system using C* alone provide augmentation to improve closed loop short period characteristics.

Also keep in mind that with control system feedback augmentation there is a difference between open loop stability and closed loop stability. With the feedback control system operational, the flight crew only experiences the closed loop stability. Allowing the open loop short period stability to be relaxed improves airplane fuel economy performance. Use of feedback control to provide desirable closed loop stability keeps the flight crew happy and reduces their workload.

[Winnerhofer]

Pretty close. The details of exactly how and why you drop from Normal to Secondary or Direct are complicated and subtle. Details of FBW systems are also export controlled by the US so US persons can get in a lot of trouble for discussing them in uncontrolled forums.

However, the 777 FCOM is publically available (e.g. through SmartCockpit) and not export controlled. It’s quite clear that pitch control in Secondary & Direct modes is proportional elevator deflection. I.e. the elevator position is based directly on the column position. However, you can still get some level of augmentation by altering the proportionality constant (the control gain) and, at least in pitch, the computers are never totally out of the loop.

It’s definitely true that handling qualities in degraded modes do not have to meet the same requirements for certification as normal mode; it just has to be safe and flyable by a “reasonably competent pilot”. There’s no requirement that it be nice, or not-fatiguing, or require little attention, to fly in degraded mode.

Aerodynamics is still aerodynamics so, without augmentation, most modern airliners aren’t particularly nice to fly…because they’re so slippery (low drag), the natural damping is low and you get lots of oscillations if you’re not paying attention. This is why yaw dampers were one of the first augmentations ever added.

[FCeng84]

Allow me to correct the following statement from Winnerhofer:

"It’s quite clear that pitch control in Secondary & Direct modes is proportional elevator deflection. I.e. the elevator position is based directly on the column position."

Boeing 777 Direct Mode includes pitch damping as part of the elevator command. Boeing 787 Direct Mode includes rate feedback for damping in all three axes (pitch, roll, and yaw).

Boeing Secondary Mode has the same control law functionality as Direct Mode.

[Winnerhofer]

FCeng84:You're probably privy to more detailed FBW data than I am.
Rate damping would be nearly invisible to the pilot though would require a functional accelerometer so wouldn't need to be explicitly in the FCOM.
You know your stuff inside-out and Boeing pros are rare in any forum.
There are far many more Airbus pros because of the numbers.
Had the B737 had been converted to FBW, then there would've been parity.
Anyway, I rate the B787 streets ahead of the A350.

[Microburst2002]

FCeng84 thanks for your post, although I noticed it a little bit late!

I was aware of the U part of the C*, but I had read something about the pitch damping mode, too, I don't know where (not in the FCOM I believe). I wondered if there were variable forces in the control column for the trimming, but seems not.

So, if the B777 is as you say, and I'm sure it is, when the pilot uses the trim switches to change the reference speed after a change in the equilibrium, he has to release the control column until it is back in neutral. Is that right?

I mean, in a conventional airplane, if you gently pulled the yoke and kept it close to your belly, and let the speed drop, the pitch stabilized shortly after and the airplane reached a new equilibrium at a slower speed, and it required a given force to maintain that situation. Then, with the pitch trim switches you could relieve the force required to keep the column right there, until that force became zero. The yoke remained there thereafter, close to your belly. As I understand it, in the B777, however, you have to ease back the column to neutral as you trim (it is more or less they way that MS FS pilots trim the airlplanes with those unrealistic controls).

In a way, Boeing and Airbus controls are so similar, specially in maneuvers not involving speed changes, with the A/THR in SPEED mode. Pull or push and release to neutral just as the flight path becomes the desired path. Easy!

The U part o the control law, seems to me, is there just to make the pilot feel a bit more like in a conventional airplane, in spite it is not. Far from it. I mean, imitating conventional takes more technology than just embracing innovation. Boeing system may seem simpler to pilots (or so they say, them Boeing pilots) but it is probably more sophisticated than Airbus.

[FCeng84]

Microburst,

Stepping back to examine un-augmented airplanes for a moment, there is a difference between an arrangement with a stabilizer and elevator (most common on large commercial transports) and an all flying horizontal tail with a pitch trim tab.

With a stabilizer / elevator the full horizontal tail (the stabilizer) moves slowly in response to pitch trim inputs. The pilot's primary pitch control input (column or stick) commands the displacement of the fast moving trailing edge surfaces attached to the stabilizer (left and right elevator). The column/stick input defines the position of the elevator relative to the stabilizer. With this arrangement, pitch trim is achieved by trading stabilizer for elevator. As the stabilizer is moved in the direction of the elevator, less elevator is required. The pilot relaxes the column/stick. Pitch trim is complete when the stabilizer has moved to the position where it generates the desired pitching moment with the elevator at its position corresponding to column/stick centered with no force.

With some (typically smaller) airplanes that do not have separate elevator and stabilizer surfaces the pilot's column/stick controls motion of the full horizontal tail. This arrangement usually includes a tab on the horizontal tail that is used for pitch trim. With this arrangement, the pilot relieves steady controller forces by adjusting the trim tab. The column/stick is not moved during the trim process. The tab applies aerodynamic force to the horizontal tail thus relieving the pilot's need to carry force. I believe it is this arrangement that you are describing where pilot controller will be at a variety of positions when in trim depending on how much pitching moment is needed from the tail to balance other sources of pitching moment.

With the stab/elevator arrangement pitch trim always occurs with the elevator in the same position. What varies is stabilizer position. As a result, pitch trim always occurs with the column/stick in the same, centered position on the flight deck. In this way, pitch trim on a B777 is very similar to pitch trim on a B737. On the B777 there is no mechanical trim wheel running back and forth on the flight deck when stabilizer motion is commanded, by the coordination between column and pitch trim switch inputs is nearly identical. The biggest difference is that on a B777 pitch trim is only required when steady speed has changed. On a B737 pitch trim is required for other changes affecting pitching moment balance such as flaps, speedbrakes, gear, and thrust in addition to speed.

You are correct to state that implementation of C*U is more complicated than C* alone. Boeing made a design philosophy decision during development of the B777 to provide convensional speed stability and thus speed awareness through through column forces throughout the flight envelope. Pitch trim is required for speed changes and the airplane tends to maintain trim speed. Pilot workload is slightly higher than with C* alone, but it was felt that keeping the pilot more in the loop was worth the effort.

[Winnerhofer]

Boeing "Direct" and Airbus "Direct Law" are not even close to the same thing!
In degraded modes, Boeing tries to keep the normal handling characteristics by essentially guessing at some parameters.

[Winnerhofer]

True, the two direct modes aren't the same.
Boeing doesn't really guess parameters though, it just fixes them at values that are known acceptable rather than adjusting to optimum based on actual flight conditions.

[FCeng84]

Winnerhofer,

I am quite familiar with the Boeing control laws and find myself quite puzzled by your last two posts. Boeing Direct Mode makes use of very simple control law logic that does not involve any reliance on air data of any kind. Please explain what parameters you are referencing.

[Microburst2002]

Thanks FCeng84, that clarifies a lot to me.

One more thing. I used to read lots of aerodynamics like the naval aviators and others, and in the stability and control chapter I got a little lost. Static stability is easy to understand, aerodynamic center I understand, too, but then those graphs about the stick forces and the part of dynamic stability is more complicated. The phugoid mode I understand. The so called second mode not so much. The way I understand it is that as a gust affects the angle of attack, because the cg is in the correct side of the aerodynamic center (stable) the airplane will counteract the pitching moment. Now, in case I pull the control column and create a nose up moment with elevator deflection, this second mode applies too, right? and then the nose up moment I created will be less and less, even if the control is kept at the same deflection, and the pitching rate less and less, until it is totally cancelled, because the airplane is stable in pitch. And this occurs in just a couple of seconds or so. And if the airplane is unstable, the pitch rate would just increase and require reversed stick force to try to control it. If it was neutrally stable it would remain constant, so I guess it would be similar to an Airbus with some pull angle in the sidestick. It will keep pitching up until some protection activates. Except in the neutral airplane there would be no stick forces?

[FCeng84]

Microburst - let me give this a try. I am not familiar with what you to refer to as the "so called second mode". I googled it, but did not get much. Is that another name for the "short period".

The basic longitudinal dynamics of a rigid body airplane are customarily presented as having four states: U (speed), Alpha (angle-of-attack), q (pitch rate), and theta (pitch angle). These four states give rise to two modes: phugoid and short period. Phugoid can be thought of as a constant energy mode where speed and altitude are trading back and forth (tranfer between kinetic and potential energy). Phugoid frequency is usually quite slow with a period of 30 seconds to two minutes. Short period can be though of as a constant speed mode with a much higher frequency with a period of a couple of seconds.

When the elevator is deflected it excites both the short period and the phugoid modes. The short period is much faster so it dominates the initial response. The airplane pitches until the restorative pitching moment generated by a change in angle of attack balances the pitching moment from the elevator (assuming stability). This results in the relationship between stick force and normal load factor as the angle of attack change gives rise to lift change. As you state, this initial response takes only a couple of seconds and hopefully the short period mode has sufficient damping to settle out to a steady load factor quickly.

Now as time goes on the phugoid comes into play due to the load factor change causing a flight path change and thus a speed change (assuming constant thrust). The phugoid is driven by the pitching moment associated with a change in speed. Note that the phugoid mode for a large transport airplane is usually quite lightly damped. Because it is so slow, however, the pilot is able to add damping without much trouble.

Short period stability is closely related to Cm-alpha (pitching moment due to angle of attack). With the airplane CG well forward, Cm-alpha is large and it will take lots of elevator (i.e., stick force) to hold a target load factor. As CG moves aft, Cm-alpha is reduced and stick force per g goes down. Go far enough and you get neutral stability where a steady pull-up load factor can be achieved with the stick back at zero. Go even farther and you have a whale of a ride on your hands as the short period is unstable. Every little disturbance will push that airplane away from pitch trim and corrective action will be required to bring it back! How would you find only needing a small pull to start the nose up and then having to push to keep load factor for increasing to the point where you either stall or break the wing?!

With C* augmentation the phugoid mode is eliminated by the control system that controls to a target pitch rate / normal load factor maneuver. To get C*U, speed feedback is added to create what is essentially an augmentation phugoid. The period of that augmentation phugoid is determined by how much gain is placed on the speed feedback path. The higher the gain, the shorter the period of the phugoid mode.

Sorry to ramble on, but I enjoy discussions that bring it back to the physics. If you really want to make it interesting start taking the flexible modes of the airplane structure into account!

[roulishollandais]

May I add and recall the definition of "stability" ?
If you change a bit the state of the system, the stable system comes back by itself to the initial state.
The unstable system continues to diverge, or start an oscillation, or stays on the new position. The case of the system oscillating when coming back must be appreciated to the time it needs to come back vs control feedback, and if several oscillations modes may happen.

[FCeng84]

Roullishollandais - good points

I think it is helpful to differentiate between stability and damping. As noted above, if the airplane has a tendency to return when perturbed, that is an indication of stability. If it does not return but settles to a new steady point, it is neutrally stable. If it diverges it is unstable. If it returns with no or minimal oscillation, that shows both stability and good damping. If it returns, but oscillates a lot before it settles back to the trim condition, it is stable but with low damping. If it returns toward trim, but shoots out the other side and begins an oscillation that grows, it has an initial stabilizing moment, but negative damping (i.e., oscillatory instabilty).

Closed loop short period should be both stable and well damped. Closed loop phugoid should not be unstable. With C* there is no phugoid so it is essentially neutral with regard to speed stability. With C*U the phugoid is stable but the damping does not need to be as high as for short period. The phugoid mode is so low in frequency that the pilot has little trouble adding damping through the pitch controller (column/stick).

[Microburst2002]

Wow, you see? Airbus is much simpler! Except you need all those protections and such...

The "second mode of oscillation" is something I must have read in the "aerodynamics for naval aviators" or some similar old book. I think it is the short period, yes.

Yesterday I saw pictures of a Bombardier CS-100 series, and I noticed they have sidesticks. I assume they have a fbw flight control system. I wonder of what type. I would bet for a C* type, but it could be a C*U if it included a trim switch and some stick forces to protect from departing from the envelope.

[FE Hoppy]

As this old thread was referenced in a new one I thought I might add some info.
CSeries is C*U in normal mode. The pitch trim switches are used (inflight) to set the speed reference and a bug is shown on the speed tape.

We do a little exercise in the sim to demonstrated the U function by inducing a speed differential and watching the thing attempt to recover to equilibrium. A couple of oscillations only then the pilot intervenes and recovers much faster than the FBW. Life is too short to watch it do the whole thing.

It's pretty impressive though if you abuse the aircraft and then let go. Assuming you have enough height to play with.

One interesting anomaly is the tuning between AT and FBW. The engines at Higher altitudes are VERY slow to accelerate/decelerate and it's possible for the two systems to become unsynchronised.