Stability Wars: Why Did Relaxed Lose?
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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?
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?
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Boeing Normal Mode with split columns
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.
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.
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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.
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.
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Boeing FBW Pitch Feel
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.
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.
Last edited by FCeng84; 6th Feb 2015 at 19:07. Reason: Correct misleading final statement
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Originally Posted by Winnerhofer
Vector stability and speed stability are control laws.
.
Last edited by roulishollandais; 28th Feb 2015 at 18:25. Reason: ref
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Long term target = what a control chooses to regulate
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.
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.
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By Tom S.
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.
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.
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Boeing Direct Mode includes Augmentation
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.
"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.
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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.
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.
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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.
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.
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Pitch Trim - Stab/Elevator vs. All Flying Tail with Trim Tab
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.
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.
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A Direct Question
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.
In degraded modes, Boeing tries to keep the normal handling characteristics by essentially guessing at some parameters.
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A Direct Answer
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.
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.
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Explanation Please ...
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.
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.
Last edited by FCeng84; 4th Mar 2015 at 02:54.
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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?
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?
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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!
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!
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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.
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.
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Stability vs. Damping
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).
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).