Longitudinal Stability
 

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.

Longitudinal Stability
 

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.

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 yourselfNo doubt there will be lots of complicated answers coming, but this one should do.:)

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 :)

Too right they do.

The tailplane generates a downforce.

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

Disturbances of Short Duration
 

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.

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.

Thanks
 

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.

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

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.

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

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.

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.

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.

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.

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

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.

@ 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.

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.

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