Longitudinal Stability

[Darth_Bovine]

Hi,

This maybe the wrong place to post this but I've had a look at the other forums and think it best here.

My problem is with understanding longitudinal stability. I know it results from the wing/tail couple, but my problem is this:

When a gust upsets the 'plane, upwards for example, the angle of attack is increased on both the wing and tail. Both will increase in lift assuming airspeed is constant. The longer moment arm of the tail means it has a greater turning moment than the wing.

But if we started from equilibrium then surely the moment from both the wing and tail will increase proportionately and a new equilibrium, with the aircraft climbing, will be reached and the aircraft will not return to level?

Maybe I'm over complicating things but I've been thinking about this for a while and my Google searches have not helped much. Maybe what really happens is that the aircraft will continue to climb until the disturbance is removed, then it returns to level flight??

Any help with this is greatly appreciated.

[JeroenC]

Forget the tail.
Think about Center of Gravity and Center of Pressure. In natural stable airplanes CoP is behind CoG.
An upset induces a pitching moment about the CoG. This increases lift, which affects CoP. So this creates CoP vector creates a turning (pitching) moment about the CoG, negating the initial upset pitching up moment.

[BOAC]

Darth - in VERY simple terms, think of the moment due to change in pitch of the wing as zero so the tail moment always wins, in this case pitching the nose back down again. Think where the wing moment will act? You said it yourselfThe longer moment arm of the tail means it has a greater turning moment than the wing. No doubt there will be lots of complicated answers coming, but this one should do.:)

[Turbavykas]

Hello Darth,

I think wing and tail usually work at different angles of attack. Say we have 5 for the wing and 1 for the tail. Ratio is 5/1. Lets say airplane is displaced by 2 degrees. So the ratio will be 7/3. You can see that lift for the tail increased 3 times but only 1.25 times for the wing. Basic math. As adding is not the same as multiplication :)

[Lightning Mate]

I think wing and tail usually work at different angles of attack

Too right they do.

The tailplane generates a downforce.

[Turbavykas]

But if we started from equilibrium then surely the moment from both the wing and tail will increase proportionately and a new equilibrium, with the aircraft climbing, will be reached and the aircraft will not return to level?

Lift will increase for tail and wing but NOT proportionately. And there will be no equilibrium.

[Smilin_Ed]

Remember that gusts are of short duration so that when the gust is gone, you are back to the original situation. Of course, there probably will be another gust shortly, but again of short duration.

[gums]

Jero and BOAC have it.

Think about the lift acting behind the center of gravity(CoG). Call that distance center of pressure (CoP). So normally, we have a pitch down moment that is counteracted by the horizontal tail. As stated, it usually exerts a downward force to counteract the main wing CoP.

All that is for a plane with normal, or positive, static longitudinal stability. Move the CoG closer to the CoP and the plane gets harder to control. At some point you get "neutral" stability, and it's a bear to handle - like trying to dance on a pinhead that is wobbling.

So if we get a disturbance, lift increases or decreases, and the pitch moment changes. With positive stability, an increase in the AoA/lift will drive the nose back down, and vice versa. Sure, the CoP will move slightly, but the main driver is the change in lift.

I was fortunate to fly the first jet with "relaxed static stability", so our CoG was very close to the CoP of the main wing. Our "stabilators" were almost neutral thru most of the envelope, but the FBW system moved the stabs very quickly and we didn't realize how close we were to losing control, heh heh. At high AoA our tail actually moved opposite of most planes, they were trying to keep the nose/AoA down. This improved many things such as pitch rates, trim drag when cruising, better turn rate because the tail wasn't fighting the main wing, and so forth. Just thot I'd throw that in.

[Darth_Bovine]

Thanks all for taking the time to type replies- I appreciate it.

So in my mind I now have this:

With the CoP aft of CoG for stability, if lift increases (a gust, say) that will tend to cause a restoring nose down rotation.

For the same gust: the proportion of the increase in lift generated by the tail will be larger than the increase from the main wing. Due to the longer momement arm of the tail, this will also cause a restoring nose down tendancy.

Am I missing anything fundamental? I expect to be quizzed on stability in the near future so want to understand it.

I may be back if I run into a brick wall for Lateral, Directional and Spiral stability.

[Ozlander1]

Since the tail is pushing down, you'd want less down force on the tail to enable the tail to raise.

[gums]

Darth!! Think more about CoP and CoG.

Distance of the tail is not nearly as important, although "short-coupled" planes are more of a handful and can have more PIO problems.

Remember that the tail is usually a symmetricl airfoil and it is at a slightly negative AoA compared to the main wing. So a nose up distubance decreases its AoA, and it exerts less downward force. And vice versa.

If you freeze the tail and just bump the stick, the plane will try to get back to whatever AoA you had it trimmed for. Some planes will take longer than others, but big deal. Dampening can be a complex issue, but that's a whole diferrent story.

Just go out and try it.

[Pugilistic Animus]

With gusts it's not undampened longitudinal stability that's important...what's important is operating strength limitations...the topic of `gusts` is very conplex it's best to refer to CFR14 part 25

[TURIN]

Remember that the tail is usually a symmetricl airfoil and it is at a slightly negative AoA compared to the main wing. So a nose up distubance decreases its AoA, and it exerts less downward force. And vice versa.
.
Interesting. I've never seen a symmetrical tailplane. All the airliners I've had dealings with have distinctly flat upper surfaces and highly cambered lower.
Got any examples?

Apart from that, absolutely spot on.

[barit1]

Remember that longitudinal stability is linked to speed stability.

The difference in AOA between wing and tail provides a stabilizing couple to restore the trimmed airspeed; it is then up to the phugoid or the automatic pilot to restore the desired attitude.

[Volume]

I think wing and tail usually work at different angles of attack
Too right they do.
The tailplane generates a downforce.
All the airliners I've had dealings with have distinctly flat upper surfaces and highly cambered lower.
If the wing has positive camber and the stabilizer has negative, then they may very well operate both at the same angle of attack, and the wing will still produce lift while the satbilizer produces downforce.
Anayway, as the satibilzer operates in the downwash of the wing, it will always see a lower angle of attack, with reference to the local airflow. But maybe you were talking about different angles of incidence?

Angle is not the key to longitudinal stability, it might be a required byproduct.
Longitudinal stability is determined by CG position, momentum arm of wing and stabilizer around CG and wing/stabilizer area. Aspect ratio has a bit of an impact as well.

[gums]

Good corrections to my assertion about symmetrical airfoils for the horizontal stab.

Angle of incidence would be lower for same downforce, so might reduce trim drag somewhat.

My experience was with light planes and fighters. Even some lights had all-moving tails like my fighters.

I think the main lesson for the questionor is it's all about the CoG versus the CoP, and what happens to a "trimmed" plane if you have an "upset". Moment arm of the tail due to distance has an impact, but not as much as the CoG versus CoP, IMHO.

Good discussion.

[phiggsbroadband]

Hi Darth, if you want to learn everything about flying and have a couple of weeks spare time, I recommend you read the following set of articles by John S Denker....

See How It Flies (http://www.av8n.com/how/#contents)

Section 6 is relevant (with 6.1.14 an interesting article on Phugoids.)
Also see Section 10.1 on stability.

btw. I have tried the Phugoid Oscillations on a Cessna 172, and the period works out at about 18-20 seconds, for each up or down.

[Darth_Bovine]

@ phiggsbroadband: thanks for the link. I'm reading through that in my spare time! :ok:

From the link provided by phiggsbroadband, I have a question:

Can we say that Angle of Attack stability is equivalent to Longitudinal stability?

From what I've read so far: when we hit a gust (up, increasing angle of attack) the 'plane will naturally want to pitch back nose down - due to the longitudinal stability. But my (rather limited) experience seems to suggest that the aircraft will want to pitch up and climb whenever we hit a gust.

Both can't be correct, surely? Unless I've mixed up 2 different concepts.

[john_tullamarine]

Useful to keep in mind that, for a conventional aeroplane, positive (desirable) static stability means that, with the trim adjusted to a particular speed, the pilot has to

(a) apply and maintain a pull stick force to maintain a lower speed with the force increasing as the speed delta increases, and

(b) apply and maintain a push stick force to maintain a higher speed with the force increasing as the speed delta increases.

Whether this is an attribute of the basic aeroplane or fudged by springs, bells and whistles, or computer wizardry is all transparent to the pilot .. who just feels a pull/push load on the stick which makes conventional sense.

[Lightning Mate]

I think you are referring here to stick force stability, not aeroplane stability.

[john_tullamarine]

I think you are referring here to stick force stability, not aeroplane stability.

Negative .. refer, for instance, to FAR25.173 (http://www.ecfr.gov/cgi-bin/retrieveECFR?gp=&SID=39323f47e1b6ec3fc8d14e5ab3f6fe6c&r=SECTION&n=14y1.0.1.3.11.2.158.27) and FAR 25.175 (http://www.ecfr.gov/cgi-bin/text-idx?SID=39323f47e1b6ec3fc8d14e5ab3f6fe6c&node=14:1.0.1.3.11.2.158.28&rgn=div8).

All the usual stories about balls in teacups and such are fine but, at the end of the day, it comes back to off trim speed stick forces. Indeed, I always find the ball and teacup confusing .. unless we are talking about HOLDING the ball somewheres up the side of the teacup ... but that might just be me, I guess.

[phiggsbroadband]

Hi Darth, you say...

'From what I've read so far: when we hit a gust (up, increasing angle of attack) the 'plane will naturally want to pitch back nose down - due to the longitudinal stability. But my (rather limited) experience seems to suggest that the aircraft will want to pitch up and climb whenever we hit a gust.'

I think what it really means is that it will want to pitch back down -AFTER THE GUST- has occurred.

If you have gained height in the gust, you will have also lost speed, so the plane will be flying slower and producing less lift... hence it descends to increase speed, back to the previous level, and so the start of a phugoid oscillation... see chapter 6.1.14

For my Cessna 172 a stick induced pull up of 200ft resulted in a loss of 20 knots. Then when I released the stick the plane dived 300ft in 18s and regained 30 knots, then it climbed 200ft and lost 20kts in the next 18s, then dropped about 100ft and was just about back where we started from.

The relationship between speed and height is mentioned in chapter 1.2.1... Try to remember the conversion formula. It is very near 10ft/kt/100kts i.e. one division of the altimeter is equal to one division of the ASI at 100kts... but only at 100kts (it is half that at 50kts.). As one goes up the other goes down.

[HazelNuts39]

phiggsbroadband,

I think you're comparing apples and oranges.

A stick-induced pull-up results in an exchange of kinetic and potential energy at more-or-less constant total energy.

An upward gust adds energy, increasing height at constant speed.

[phiggsbroadband]

Hi John, you quote...

Negative .. refer, for instance, to FAR25.173 (http://www.ecfr.gov/cgi-bin/retrieveECFR?gp=&SID=39323f47e1b6ec3fc8d14e5ab3f6fe6c&r=SECTION&n=14y1.0.1.3.11.2.158.27) and FAR 25.175 (http://www.ecfr.gov/cgi-bin/text-idx?SID=39323f47e1b6ec3fc8d14e5ab3f6fe6c&node=14:1.0.1.3.11.2.158.28&rgn=div8).

If you notice these refer to Transport Category Aircraft. The stick only controls a piston in the Hydraulic Servos, which move the flying surfaces. The stick forces are all engineered feedback, much the same as power steering on modern cars... Its all artificial feedback, and on some cars can be switched high or low, or even a different sensitivity at different speeds.

[Darth_Bovine]

Hi,

I understand if we lose speed we loose lift from L = Cl.1/2.rho.V2.S

That would result in pitch down due to main wing loosing lift. What if the gust means that airspeed is constant (maybe highly theoretical...)?

The restoring force is only coming from the turning moment of the tail in that case? In that case lift from both wings (main and tail) is only modified by the relative change in AoA of both.

Maybe I'm getting out of my depth by getting too technical. I guess my question now is this:

If an upward gust causes a aeroplane to pitch up (consider speed to be constant), will the restoring effect of stability cause it to pitch back toward level, by pitching nose down slightly, even before the gust is removed? Or does the restoring pitch down only happen when the gust is removed?

My instinct leans toward the latter, which means the extra down pitch moment of the tailplane will not be present (gust removed at this stage, so the larger proportion of AoA increase on the tail, and hence larger turning moment, is removed). So the balance of forces will return to the pre-gust situation.

Is the tendency during the gust (constant speed) to start to recover to level, but this will be achieved fully once gust is removed? Maybe there is no such thing as a gust where speed remains constant??

[jimjim1]

But my (rather limited) experience seems to suggest that the aircraft will want to pitch up and climb whenever we hit a gust.

How would you know the direction of the gust? Surely gusts must by definition come from every direction?

Anyway:

The CoG ahead of the CoP is the first thing to think about. In this sense the aircraft is like a dart. There is nothing else to worry about in the first instance. Get some darts and throw then backwards, sideways, everyway you like. Watch the flight.

Don't worry about the direction of the gusts or anything else.

The aircraft is flying along in a certain direction and a perturbation in the air changes its attitude. It is STILL moving through the air in the same direction. In the case of pitch and yaw, the 'dart' stability restores the aircraft so that it regains its orientation pointing in the direction of travel. Roll stability is different.

Now there is a lot more to aircraft stability as understood by test pilots but I think that this is the place to start and indeed may be sufficient for a beginning pilot. As far as I recall it was for me and I have the advantage of never having progressed beyond being a beginning pilot:-)

I did not know for instance that the tailplane produced downward thrust in normal flight or indeed that a canard produces upward thrust and is therefore more efficient (uses less fuel).

[phiggsbroadband]

Hi Hazelnuts.. you quote..

'An upward gust adds energy, increasing height at constant speed. '

I think you are 30% right. But that ignores the pitch up of the nose caused by the gust, which goes into adding the further 70% of the climb.

The nose of the plane then has to pitch down.. It does slightly too much, so it has to pitch up again, and again overshoots.. etc. ad infinitum.

[HazelNuts39]

Is the tendency during the gust (constant speed) to start to recover to level, but this will be achieved fully once gust is removed? Maybe there is no such thing as a gust where speed remains constant??I really don't know much about stability, but my take on this is:

Let's assume a sharp-edged gust of constant velocity. When an airplane in steady level flight encounters an upward gust, the angle of attack increases. As the angle of attack increases, the lift increases, and when the lift is greater than the weight the airplane will be accelerated upwards at initially the same speed and pitch attitude. A stable airplane tends to return to the angle of attack it is trimmed at, so the airplane will tend to pitch down to regain the initial angle of attack. However, that tendency is not very strong but the angle of attack decreases mainly because the vertical speed increases. When the airplane vertical speed is equal to the gust velocity, the airplane continues to climb, at the trimmed angle of attack and speed, at the same pitch attitude as it had initially in level flight. When leaving the gust the airplane goes through a similar, but reversed sequence but its final altitude will be greater than where it started, by an amount of approximately the gust velocity times the time to traverse it.

[Shawn Coyle]

Doesn't angle of attack stability really mean maneuver stability (no matter how you spell it).
Static stability is the tendency of the aircraft to return to the original trim condition when an disturbance has been encountered and then removed.
Stick force and stick position are two different measures of this. With an irreversible flight control system (i.e. all hydraulically boosted) there is no difference between the two stabilities as the forces on the cockpit control must be artificially generated. With a reversible flight control system, stick free stability is what you get when you release the stick forces (as the friction in the system may prevent the stick from returning to the original trim condition). When you place the stick back at the original condition, that is stick fixed stability.
Confused?? Try teaching this to test pilots and flight test engineers!!!

[bubbers44]

Simply put once stabilized in flight any stick movement upsetting this balance releasing the stick will make the aircraft return to the same stabilized flight.

[bubbers44]

If you are in a J3 cub with no gyros turn to 180 and trim,reduce power and you can safely descend with no gyros through a cloud deck as long as you hold your heading in an emergency. It works for jets too.

[john_tullamarine]

If you notice these refer to Transport Category Aircraft

Indeed.

However, were one to rub out "25" and pencil in "23" one gets much the same story for bugsmashers .. as in FAR 23.173 (http://www.ecfr.gov/cgi-bin/text-idx?SID=ba8deeddb04eb54c686036bb31f78d1a&node=14:1.0.1.3.10.2.64.35&rgn=div8) and FAR 23.175 (http://www.ecfr.gov/cgi-bin/text-idx?SID=ba8deeddb04eb54c686036bb31f78d1a&node=14:1.0.1.3.10.2.64.36&rgn=div8).

The interest is in what the pilot "feels" at the stick, not what wizardy fools him/her into experiencing that perception. You might read up on elevator down springs and bobweights to see the simple ways of making reality morph this way and that ...

A lot of discussion in this thread confuses the two basic stability animals ... "static" (when one applies a load to the stick) and "dynamic" (when one releases it and sees what happens next).

[fly4freedom]

When a gust upsets the 'plane, upwards for example, the angle of attack is increased on both the wing and tail. Both will increase in lift assuming airspeed is constant. The longer moment arm of the tail means it has a greater turning moment than the wing

L=Cl*d*square V*A/2
A is the surface of the airfoil.the surface of the wing is much bigger than the horizontal stabilizer.

[bubbers44]

The tail is not lift, it is a downward force to give the aircraft stability.
The wing is the only surface that counteracts gravity which is lift. The tail down force must be supported by the wing lift force and why some aircraft save fuel by keeping the CG back in cruise. Airbus is one and we figured that ourselves in the Lear Jet by transfering fuel back and being able to reduce cruise power.

[barit1]

some aircraft save fuel by keeping the CG back in cruise

People keep "discovering" this technique. In the 60s one UAL F/E got a nice bonus check for his "invention" of loading the hold as far aft as C/G would allow.

[john_tullamarine]

Indeed - I recall an RAeS lecture by a QF chap which detailed a study for the 744 on max range sectors.

By some judicious variation to the OEM standard fuel schedule, the airline was able to vary the range-payload characteristic and pick up, as I recall, an additional several bodies in the paying section for the sector ....