PDA

View Full Version : Aircraft C of G and wing pitching moment


hawk37
12th May 2004, 20:32
I believe Airbus aircraft plan to balance fuel to keep the CG as far aft as possible, requiring the tail to produce very little down force. But isn't there a significant pitching moment from the wings, in which case the tail is still required to produce a down force?
Thoughts?
Hawk37

Milt
13th May 2004, 08:53
Longitudinal Stability and Fly by Wire

Huge benfit of FBW is that you can get away with artificial stability and end up with an up load on the tail instead of the 30 odd tonnes of down load that the wings of a 747 have to overcome at/near AUW.

Result is a large reduction in induced drag and enhanced manoeuvrability. In flight the elevators with FBW are continually on the move to prevent pitch up or pitch down unless the designer leaves in some residual natural stability.

The US terminology for such design is Controlled Configured Vehicle!!

F16 was one of the first. It is close to neutral naturally stable subsonic and becomes negatively stable naturally when supersonic.

Has this explanation been too complicated?

john_tullamarine
13th May 2004, 11:37
The benefits can be dollar material.

One 744 operator, payload limited on long range operations, examined a modified fuel usage to better control CG and achieved a several hundred pound decrease in burn (ie increase in payload). Annualised, this amounted to enough money for me to retire in luxury ..... oh, well, a chap can always dream ...

hawk37
14th May 2004, 15:06
Milt, do Airbusses use this “upload on the tail” and the equivalent of “controlled configured vehicle”
I’m assuming not, but someone correct me please.
In any case, for a conventionally controlled aircraft, reference my first post on pitching moment, I’ll guess that the weight of the tail, or perhaps better said as the aft component of the aircraft’s weight can be used to offset the wing pitching moment. By wing pitching moment I mean of course that since the center of pressure of the underside of the wing is ahead of the center of pressure of the top side of the wing, there is a force couple, or moment trying to rotate the nose of the aircraft down. But surely then the net contribution of the tail, ie weight and aerodynamic forces, must still give a resultant down force, in order to assure stability.

Hawk37

Keith.Williams.
14th May 2004, 19:30
Hello Hawk,

I think you are getting a bit confused about wing pitching moments. It is true that a camered aerofoil produces a nose-down pitching moment when at its zero-lift angle of attack. But at normal (more positive lift-producing) angles of attack it will produce a nose up pitching moment. The greater the angle of attack (up to the stall), the greater will be the nose-up pitching moment.

But when considering the trim of an aircraft we must consider not just the wings, but the whole aircraft. The most inportant factor here is the lift-weight couple. With a forward C of G this will generate a nose-down piching moment. This must be balanced by trimming the tailplane to give a nose-up (or tail down if you prefer) moment.

The magnitude of the nose-down moment caused by the lift-weight couple depends upon the mass of the aircraft and the distance from the C of G to the C of P. So moving the C of G aft towards the C of P will reduce the nose-down pitching moment.

This will reduce the amount of tailplane down-force that is needed to trim the aircraft. This reduction in tailplane down-force reduces the total amount of lift required from the wings (which must equal weight plus tailplane down-force). This in turn reduces the total drag and hence reduces the thrust and fuel consumption required.

A canard on the other hand trims the aircarft by producing an upward force. This reduces the amount of wing lift required, which in turn reduces drag and fuel consumption rate. But canards (as with everything else in this world) introduce their own little problems.

The best solution is to keep the C of G as close to its rear limit as possible. More and more aircraft types are now being designed with things like fuel tanks in the fin to enable this to be done automatically in flight.

hawk37
15th May 2004, 18:22
Keith, your quote
“a camered aerofoil produces a nose-down pitching moment when at its zero-lift angle of attack. But at normal (more positive lift-producing) angles of attack it will produce a nose up pitching moment. The greater the angle of attack (up to the stall), the greater will be the nose-up pitching moment.”

Leaves me puzzled. Aerodynamics for Naval aviators pg 50 shows that “section moment coefficient, Cmac to be negative for all examples of cambered airfoils, namely naca 23012, 631-412, 4412, and 23012 with various flap types. And specifically, it is a constant negative value from 0 section lift coefficient Cl up to just before the stall. The sign convention applied to moment coefficients is that the nose-up moment is positive.

Any idea what gives?

Hawk

Keith.Williams.
15th May 2004, 19:16
What they are talking about is the pitching moment about the aerodynamic centre of the aerofoil. By definition the aerodynamic centre is the point on the chord line about which the pitching moment does not vary with changes in angle of attack.

But this constant pitching moment is true only when measured about the aerodynamic centre. If you make a small model of a cambered wing (or even a flat one - a small sheet of card or balsa wood does nicely) ) you will find the when released at a slight nose down pitch attitude it (usually) tumbles in a nose up direction. This indicates a nose up pitching moment about its C of G. But when attached to an aircraft with a forward C of G the moment about the C of G of the aircraft will be nose down.

To visualise what is happening to the C of P you need to look at those diagrams that illustrate the pressure envelopes above and below the aerofoil at various angles of attack. As angle of attack increases the C of P of the upper surface envelope moves forward, while that of the lower surface moves aft. Until you get very close to the stall both the uper and lower envelopes are decreased pressure (we might call it suction). So the
movements of the upper and lower C of Ps causes an increasing nose up pitch.

Milt
16th May 2004, 06:03
Tail Loads and Stability

Natural longitudinal stability for an aircraft is achieved by having the Centre of Pressure behind the CG which has to be between forward and aft limits.. The nose down pitching moment is balanced by a down load from the tail.

If the CG gets to be too far forward there will be inadequate elevator to flare on landing. The stick will be against the rear stops and you will be wanting more. It's a very off putting feeling.

If the CG gets to be too far aft the A/C will start to run away in pitch, either up or down, at any small disturbance. The P51 Mustang is like this with a full aft fuselage tank or an F86 Sabre with 4 big jugs or any of those wrongly loaded aircraft that pitch up on take off and full forward stick is inadequate at the slow speed.. May they RIP and may others please learn from their mistakes.

So a 747 at/near AUW will have a down force from the tail of about 30 tonnes. What a waste. Yes, the wings have to overcome that load and there is significant.induced drag penalty as a result.

Along comes artificial stability with Fly By Wire and computers.

F16 Falcon was one of the first to benefit with its side stick control. Now the centre of pressure and the CG can be closely aligned resulting in the need for very little down or up force from the tail during cruising flight. The now inherent tendency to run away in pitch, up or down, has to be countered by the elevators which under command of the flight computers work hard to stop any pitching unless demanded by the pilot with stick force input. Result is an extremely manoeuvreable A/C in pitch with the elevators working in reverse to back off the tendency to over pitch. And a significant contribution to lesser induced drag. The US describes this type of aircraft as a Control Configured Vehicle. CCV. Wonder who dreamed up that one?

Don't know how far Airbus have gone in reducing tail down loads using artificial stability but they would just love to have zero tail load on the cruise.

Boeing will be trying to do the same. Big $$$$s at stake.

You can expect that auto balance will relieve the crew of any need for them to keep the CG near the C of P by proportional fuel feed from tanks.

First saw this auto balance in the RAF Vulcan and Victor. The Valiant required interminable crew attention managing fuel use from wing tanks which took the CG one way and fuselage tanks the other way. Must be a big problem with tankers off loading.

hawk37
26th May 2004, 15:13
Keith,
The whole idea of pitching moments, why they should be a constant about the AC, but that they can be either negative or positive for a cambered airfoil about the C of P makes me realize I’m out of my league in fully understanding this subject.
I can’t seem to find any of these diagrams you mention that illustrate the pressure envelopes above and below the aerofoil at various angles of attack. I have those that show the magnitude of the upper and lower C of P versus distance along the chord from the LE. And I’ve come across many graphs the past week showing the pitch moment about the AC as a constant.
Any available on the internet you know of?
Such a diagram would make it easy to understand the contribution of the tail to stability, once one adds in the moment from the aircraft C of G. And consider then, the C of G range of the whole aircraft and the limitation/capabilities of the tail can be further understood.
And provide some clear reading to the M crit, M buffet, thread still ongoing
Thanks for your informative post

Milt,
I’m not trying to split hairs here, but based on what I’ve interpreted from Keith, I’d add to your fine post that perhaps longitudinal stability in some aircraft could still be achieved by having the C of G just slightly aft of the C of P (yes, I do mean C of G aft of C of P), for cases where there is a nose down pitching moment from the C of P. In such case, the tail could still provide a slight tail down force. And of course, the full aoa would need to be considered.

Hawk

Keith.Williams.
27th May 2004, 20:47
Hello again Hawk,

I'm afraid I cannot give any internet references. Sadly I am not a great user of the internet search facility.

The pressure envelope diagrams are in almost every book on aerodynamics and may well be the CP diagrams you mention. They are simply profiles of aerofoils with an eliptical line above and below to indicate the degreee of pressure change at each point along the curve.

For a cambered aerofoil at zero-lift angle of attack (usualy quoted to be about -4 degrees) the stagnation point is above the leading edge. This causes rapid acceleration around the underside of the leading edge, so the greatest pressure drop below the aerofoil is just behind the leading edge. The pressure drop then gradually reduces to zero at the trailing edge.

This entire lower envelope represents reduced pressure so the resulting force is downwards. If we guestimated the lower surface CP is it would be fairly close to, but under the leading edge. So we have a force tending to pull the leading edge downwards.

At this same zero-lift angle the lowest pressure above the wing would be at about 30% chord. So the upward force acting on the upper surface would be behind the downward force acting on the lower surface. These two forces would therefore produce a nose-down pitching moment. So at zero-lift angle of attack a cambered aerofoil produces a negative pitching moment.

As angle of attack increases the stagnation point moves down and aft, so there is less acceleration under the leading edge and more acceleration above it. This causes the lower CP to move aft and the upper CP to move forward. At some angle of attack the two CPs are directly one above the other, so there is zero pitching moment.

At still greater angles of attack the upper CP moves further forward while that below moves further aft. This creates an increasing nose up pitching moment.

At very high angles of attack the stagnation bubble (which is an increased pressure) enevelopes the entire lower surface, with its CP close to the 50% chord point. We now have both the upper and lower surfaces producing positive lift, so the overall CP starts to move aft again.

The problem with using the CP as our reference is that it moves about as angle of attack changes. It is far easier to do the maths if we can find a fixed point to use as our datum, particularly if the pitching moment about this point is constant. This point is the Aerodynamic Centre or AC.

To understand this we need to carry out a little mental (or physical experiment) Imagine that we have made a small aerofoil section out of thin card and pinned it to a board using a drawing pin through the trailing edge. Any lift force acting upward will cause the aerofoil to pitch nose up. The magnitude of the nose up pitching moment is equal to the lift force multiplied by the distance between the CP and the drawing pin at the trailing edge.

Now if we imagine what happens as angle of attack increases, the lift force increases and the CP moves forward. This cause the nose up pitching moment to increase. So if we measure pitching moments about the trailing edge they are nose up and increase as angle of attack increases.

Now if we pull out the drawing pin and push it through the leading edge we will find the opposite effects. The pitching moment is nose down and increases as angle of attack increases.
So piching moment about the leading edge is always nose down and increases as angle of attack increases.

We must now pull out the pin and try again, first with the pin one inch in front of the trailing edge then with it one inch behind the leading edge. We will find that the pitching moment are as described in our first tests but that the rate of change with angle of attack are less. If we keep repeating the process gradually brining the two pin holes closer together we will eventually find a point at which the rates of change of nose up and nose down moments exactly balance, giving a constant nose-down moment. This point is the AC of the aerofoil.

Any numbers used in this description are of course generalisations but hopefully it all makes sense. I wouldn't be too concened if some of this subject appears to be a bit mind boggling. I have been reading it on and off for years and still don't understand it.

Oktas8
2nd Jun 2004, 12:13
hawk37,

You mentioned internet resources for AC and pressure distributions, and the contribution of the tail surface to stability.

Perhaps you could look at this site (http://www.av8n.com/how/htm/aoastab.html#sec-teeter) which describes the function of a tailplane with respect to longitudinal dihedral.

I have found longitudinal dihedral (or decalage) to be much more helpful than the concept of an AC of an aerofoil, in understanding longitudinal dihedral in a practical (as opposed to theoretical or design-orientated) sense. What I mean is, knowing the AC of a wing does not help me to visualise different loading / AoA scenarios - but understanding longitudinal stability does.

Two references that may help you, both of which are more readable and less mathematical than the Aerodynamics for Naval Aviators text, are:

Aircraft Flight 2nd Ed 1995, Barnard & Philpott, and
Principles of Flight 10th Ed 1998?, AC Kermode.

Milt
Natural longitudinal stability for an aircraft is achieved by having the Centre of Pressure behind the CG which has to be between forward and aft limits..
I think this may not always be true. In some circumstances the CG may be at or slightly behind the CP, the aircraft as a whole still having slightly positive static longitudinal stability. Most civil aircraft are quite strongly longitudinally stable, so the condition you have described is certainly the most common.

Hope this is at least slight helpful hawk37.
O8

alatriste
4th Jun 2004, 19:49
A 320.

It is not unusual to fly this a/c with a really aft CG like 36% MAC, when taking off it calls for a AND triming ( e.g. 1.2 DN).

I would like that someone could explain me if are we really flying with the CG rear of the CP ( cause of the nose down trim).
As far as I ´ve learnt this is not an stable scenario. Even though A 320 is FBW it might be imposible to control in mech back-up if the CG were really behind the CP.
During walk around the a/c, it seems that the THS is inverted chambered, so that it will develop down load forces at the tail even if the triming is for positive angle ( AND).

THANKS.

NigelOnDraft
4th Jun 2004, 20:10
From my limited experience...

A320 - no CG management, other than trying to get loaders to get CG towards aft end of envelope. In that BA are also trying to sell "premium" seats, that are towards the front, slightly contrary motives.

A340 (from a previous life). At 25K' on the climb, fuel is pumped rearwards into tailplane tank. The moment you hint towards aircraft you are going to land soon (Dest, or Divert), it empties said tank (I think at ~2hrs to landing?)

Also, noisy red flashing awkening warning "Aft CG Limit" that we don't get on A32x. Normally went off towards end of cruise, and maybe when there was a "congregation" in rear galley. At this point, aircraft started furiously pumping the fuel back forward again.

So - yes, Airbus do try to get aft CG since it is more efficient. Sounds like safety and regulation allow a greater extent of this in cruise, than for TO/Ldg. However, I dount it gets anywhere near the "unstable" regime of modern fighters - just "less stability" than permitted without these protections.

NoD

hawk37
8th Jun 2004, 23:51
Keith, nice explanation re moving a pin from the LE to the TE of an example airfoil in order to explain AC. And of releasing a card at a slight down pitch attitude and seeing it tumble nose up (but isn't a card basically symmetrical airfoil, so no pitch moment?).
However the more I read from you and other sources, the more I realize I'll need to study even further to fully understand. Frankly, it seems to me it must be simply freaks of nature that (1) a cambered airfoil has a point along it's chord that the pitching moments are (almost nearly) constant as aoa in increased, and (2) that this point works out to be (almost exactly) at the quarter point, and (3) that a symmetrical airfoil will have upper and lower C of P's at the same point on the chord (ie, no pitch moment about the AC)
Thanks for your contributions
Hawk

Keith.Williams.
9th Jun 2004, 14:28
HAWK 37

You are correct that the flat card is effectively a symmetrical aerofoil, so its pitching moment about its AC is zero. But when dropped into the air it is not at its zero lift angle of attack (or at least is unlikely to remain at that angle) and it pitches about its C of G (not its AC). These two factors generate a leading edge up moment.

So it will usually tumble leading edge upwards (but occasionally screws up the classroom demo by doing the opposite).

Oktas8
10th Jun 2004, 00:06
alatriste,

I don't know much about the A320, nor am I an aeronautical engineer. However, with that in mind, I may be able to help with your question.

An aircraft may still be longitudinally stable as long as the horizontal stabiliser is operating at a lower coefficient of lift than the wing. Thus, some aircraft may use nose down trim and still be stable - as long as the trim is only slightly nose down!

I'm cautious with my answer because it does depend very much on the CL characteristics of both the wing and the stabiliser.

For example:
=> of the wing and the stabiliser, which has the steeper CL / AoA curve, and which has the greater critical AoA?
=> as you've commented, the stabiliser may be cambered or not, affecting lift and therefore stability at a given pitch setting.
=> the shape of the fuselage affects aircraft stability - usually fuselages of circular cross section are unstable in pitch.

Awaiting experts' corrections,
cheers,
O8

Alex Whittingham
10th Jun 2004, 18:38
What does zero or neutral trim imply? Does it imply a body angle of zero, an angle attack of zero, CG at the CP or is it just an arbitrary manufacturer's datum? Not a trick question, I have just never seen it defined.

hawk37
7th Jul 2004, 12:52
Keith,
I think there is an explanation of why a flat card will sometimes tumble LE down. If the card initially stays at a low CL, and is not completely symmetrical, then the CP could be aft of the CG. The CP should continue to stay aft of the CG as long as the CL says low. Ergo, the card can pitch down.
But this should never happen it the card can stay completely symmertrical, and at a positive aoa, since the upper and lower surfaces CP's would be directly above/below each other, and at the AC, approx 25% chord. Thus any positive aoa would produce a nose up pitch moment about the CG.
Do I make any sense at all?

Octas8,
I could find nothing on longitudinal dihedral (or decalage). I'm hesitant to use the internet since often erroneous data present. It these are other terms for longitudinal stability, OK

Octas8 & Milt
Octas, I don't see how "in some circumstances" the CG can be aft of the CP but still having positive static stabilty. You included "the aircraft as a whole" which makes sense since all factors affecting CG and CP need to be included. If the CG was aft of the CP, then for even a short time, a slight upgust (increase in aoa) would rotate the aircraft about its CG, further increase aoa etc. So I'm with Milt.


Alatriste,
I'm not familiar with your terms, or any bus, however I suggest that "1.2 DN" trim does not mean that the tail is producing a nose down force, ie the tail is not producing an up force.

Octas8,
Your quote "An aircraft may still be longitudinally stable as long as the horizontal stabiliser is operating at a lower coefficient of lift than the wing. Thus, some aircraft may use nose down trim and still be stable - as long as the trim is only slightly nose down!"

I'm assuming you're suggesting that both tail and wing produce an up force. The CL producing an up force from the tail will have a moment that depends on the arm (distance to tail CP to aircraft DB). So that will factor in as well as the the arm from the wing CP to the aircraft CG.
Based on your scenario, I'd suggest just the opposite, the tail needs a higher lift/arm moment than the wing. Thay way, an upgust (increased aoa), will cause the main wing to increaes lift AND the tail to increase lift. However if the tail produces more moment, the aircraft re aligns into the airflow, hence stable.
HOWEVER, I don't think conventionally controlled/configured aircraft, including air busses, use this positive lift from the tail scenario

Comments/corrections?

Hawk

spleener
8th Jul 2004, 09:25
A330/A340 - FBW = artificial stability = CG control = reduced downforce requirement on the tail = reduced trim drag. Tailplane is an inverted aerofoil. Other than perhaps during some dynamic manoeuvering, there is a downforce on the tailplane - all flight control laws [ie normal, altn, direct].

hawk37
9th Jul 2004, 12:00
Spleener, your quote

"A330/A340 - FBW = artificial stability = CG control"

is not clear to me. Are you saying that since the 330/340 has FBW that it also means that it has artificial stability?

yet you also later say there is downforce on the tail for all control laws.

and artificial stability somehow give CG control?

Are there no mechanical back up modes anymore, should the computers fail? After all, without this artificial stability, it would be up to the pilots to sense the instability, judge the flight conditions such as attitude, speed, and pitch rate, and continually adjust the control surfaces. Orville and Wilbur did it, after all.

Hawk

Oktas8
12th Jul 2004, 06:39
I could find nothing on longitudinal dihedral (or decalage).

My text is AC Kermode's Mechanics of Flight if you have access to it. Briefly (vaguely, non-technically), longitudinal dihedral is the tailplane AoA subtracted from the wing AoA. As you point out, the vast majority of aircraft have a tailplane at some minor negative AoA, so are said to have positive longitudinal dihedral.

Regarding tailplanes generating upwards force - yes, I know it's almost unheard of in cruising flight. But since someone brought up the possibility of very precise locating of CP close to the CG, I thought I'd bring it up.

Consider a wing at +6° AoA and a tailplane at +2° AoA (both generating upforce on this mythical aircraft).
A gust giving an effective increase of AoA of 2° will:
add approximately 33% to wing lift (new AoA 8°), and
add 100% to tailplane lift (new AoA 4°).

Regardless of the absolute size of each lift force, the pitch-down tailplane moment will overcome the pitch-up wing moment in this case, and the aircraft will pitch down, giving us a form of positive longitudinal stability.

This is an example of longitudinal dihedral. Canard equipped aircraft are good examples of this kind of arrangement - front "wing" is at greater angle of attack than main wing, giving longitudinal stability (and unfortunately, quite a lot of trim drag :( ).

The original post referred to the possibility of a tailplane generating zero lift, and whether this was possible. Yes, it is possible from the point of view of longitudinal stability, although you may need electronic stability controls to ensure stability is maintained as CG moves in flight, or at extreme angles of attack.

O8

spleener
14th Jul 2004, 12:03
Hawk 37,
sorry my quote ref Airbus 330/340 should not have been so simplistic but I didn't wish to stray too far from the main thread.
Suffice to say that in the most basic FBW Direct Law [stick position= control surface position] the aircraft is stable [download on tailplane]and flyable. This Direct Law is overlaid by artificial means both in Alternate Law and [the usual case] Normal Law. In these cases [in pitch] stick position is usually a G command with Normal Law providing enhanced response and flight envelope protection. This provides enhanced stability to certification requirements. Therefore, CG can be controlled further aft [fuel trim tank transfer] with ensuing lower drag.
This is a short explanation only! please accept that there is more to this...
spleener

hawk37
15th Jul 2004, 12:20
Octas, thanks for your explanation on "longitudinal dihedral". I never had heard of it, but your explanation makes sense. I can only surmise there must be further stability problems with this method, since it has clear advantages over the conventional tail down force type of stability.
I'd summarize by saying the posters seem to be of the opinion that conventional airliners (all airbus and boeing) have a tail down force throughout their operating envelope, ie the CG must be forward of the CP, at all times. I'd add that when we hear of aft CG up to about 35% mac, this can only mean the CP can never get as far forward as 35%.
Of further note, this can only mean that these airfoils are NOT symmetrical, since if they were, the CP would be at the 25% mac, reqardless of Cl, and thus limit the CG range to 25% aft of the leading edge.
Make sense?
Hawk

PleinGazSec
15th Jul 2004, 17:01
Positive longitudinal static stability required for certification in direct law. The authorities won't yet allow fully unstable pax aircraft understandably in case of failure and flight control law reversion. However relaxing the stability requirements is OK within limits.