CG and stability
 

Anyone know why forward CG improves longitudinal stability? Or why aft CG worsens it?
I can visualize that an arrow shot from a bow would be unstable if the CG were at the tail end (if that's an appropriate analogy), I just can't figure out why that would be...

Think of it as the weight pulling versus the weight pushing.
Think of forward CG pulling the aircraft along versus pushing it along which means when a small deviation occurs it will push it further out or worsen it. That’s instability.

Thanks for the response. Could you elaborate? I'm unsure how CG would push or pull anything

When an aircraft is moving, it has mometum that tries to keep it going. Think that the cg has all that momentum and it will try to pull forward if anything tries to slow down the aircraft. Then think the center of lift as a point where the air resistance tries to slow or pull back the aircraft. Now you shoud see that if you apply those pulls, the aircraft will always end up cg beeing forward of center of lift.

There are also aerodynamic forces in play that try to keep the pointy end going first and that's why stability is slowly getting worse with cg moving aft instead of momentarily flip when cg moves behind center of lift.

There are 2 concepts to think about, controllability (how easy is it for pilot to change the aircrafts pitch) and stability (how the aircraft resists/reacts to changes in pitch).

An aircraft that is more stable (ie one that tends to maintain its pitch attitude) is less controllable (ie it is less responsive to pilot inputs) and vice-a-versa.

The tail surfaces of the aircraft provide a balancing force to make the aircraft more stable in pitch - if the nose pitches down, the tailsurfaces, rise up and the airflow over them will act to produce a downward force on the tail, this will tend to raise the nose.

If the nose pitches up, the tail goes down and the airflow now produces an upward force on the tailplane, acting to lower the nose.

The aircraft pitches around the CofG position.

Like lifting a long armed lever, if the CofG is more forward, it doesn't need much force on the tail to get it to pitch (making it more stable) however it requires a large up/down movement of the tail to make it pitch by a certain angle (making it less controllable).

With that forward CofG, if the aircraft's pitch is changed, eg by turbulence, the tail will only need to change its angle of attack by a small amount to get it to give enough force to correct for the pitch deviation - so it is more stable. However if the pilot wants to pull up into a loop, they may not have enough control deflection to get it to pitch up as desired.

Conversely a rearward CofG gives you the opposite effect - more controllability - it is easy to pitch the nose up into a loop but you also get less stability - the tail will need to generate more force to correct for unwanted pitch.

Not exactly an aerodynamicists explanation but that is how I would explain it.

From 'Handling Light Aircraft' by Julien Evans:

https://cimg6.ibsrv.net/gimg/pprune....62f26671f7.jpg


3.8.1 Longitudinal stability

Remember that the tailplane generates the tail down-force, and that this force, because of the manner in which it is generated, responds to the same factors which affect the lift force generated by the wings.

Suppose that while an aircraft is in level flight, a gust of air disturbs it, causing the nose to pitch upwards. The aircraft will now start to climb, decelerating as it does so (in the same manner as a car tends to slow down as it runs up a hill).

The reduced speed will decrease the tail down-force. From consultation of Figure 2, we can see that in this situation the lift force, acting behind the CG as it does, will now raise the tail, so restoring the aircraft to level flight. Thus although the gust upsets the aircraft, the stability conferred by the tailplane will soon restore it to its original flight path.

If a gust pitches the nose downwards, the aircraft will start to descend, accelerating as it does so. The faster speed will increase the tail down-force and the tailplane will be pulled down, again bringing the aircraft back to level flight.

3.8.5.1 Effect of position of centre of gravity on longitudinal stability

The tail down-force has the stabilising effect of bringing the nose of the aircraft back to its original position after disturbance. Refer back to Figure 2, which showed the usual disposition of the weight force, the lift force and the tail down-force during flight. It is possible for the pilot to vary the magnitude of the tail down-force, using the aircraft's controls.

Now, suppose that the aircraft is loaded so that its CG is further rearward, coinciding with the point from which the lift force acts, as in Figure 121. In this case, the original tail down-force would now pull the tail down, thus pitching the nose up.

To prevent this, the pilot would have to use his controls to reduce the tail down-force to zero, thus restoring the equilibrium. But now, if a gust upsets the aircraft, the tailplane will have no stabilising effect, because, regardless of the aircraft's speed, the tail down-force would remain zero.

Taking the argument a stage further, suppose now that the CG was so far to the rear that it was behind the point from which the lift force acts, as in the top image in Figure 122.

It can be seen that the lift force, because it is now acting ahead of the CG, will have the effect of pitching the nose up, and to prevent this from happening, the pilot would have to adjust his controls so that the tail force acted upwards, as in the lower image in Figure 122.

Well, the equilibrium has been restored again, but imagine that a gust now pitches the nose down. The aircraft will, of course, start to accelerate––the tail force will increase, pulling the tail further up, and the situation would quickly develop into a steep dive. In other words, the aircraft is longitudinally unstable. (The reader is left to prove that this instability would aggravate any pitch up of the nose caused by a gust.)

The conclusion can be drawn that, as the CG of an aircraft is positioned further rearwards, so its longitudinal stability decreases, and, at extreme rear CG positions, the aircraft may become longitudinally unstable. Conversely, forward CG positions enhance longitudinal stability. (However, extreme forward positions of CG have a detrimental effect on aircraft controllability, for reasons which will be explained later.)

Now it can be understood why the manufacturer specifies limits for the CG positions in his aircraft. A CG position outside these limits renders the machine unsafe for flight. The importance of correct loading can be appreciated, and one of the pilot's responsibilities is to ensure that this requirement is complied with.

Further to the above:

3.3 TAIL DOWN-FORCE

As previously mentioned, the tailplane generates the tail down-force. To understand how this force is generated, it is merely necessary to visualise the airflow past the aircraft (Figure 105).

https://cimg0.ibsrv.net/gimg/pprune....9562deea60.jpg

Notice that the downwash strikes the tailplane at an angle. If the diagram is now turned upside-down, it will be appreciated that the tailplane will generate a force in the same manner as do the wings. Figure 105 shows the force resolved into a downward-acting component, which is the tail down-force, and a backward-acting component, which is obviously drag.

Hoping I am not causing confusion: is there a parallel with taildraggers risking groundlooping, because their CG is behind the main wheels?

Would I be correct in saying that whatever force is required by the tailplane for level trimmed flight is just exaggerated depending on whether airspeed increases or decreases?

The following bit I find a bit confusing though:
If an aircraft with a tailplane applying zero TDF is displaced by a gust into, say, a pitch up attitude, wouldn't the AOA increase on the tailplane causing the tail to rise? Or is the airflow the tail experiences purely from the wings downwash?

Avoid considering a horizontal tail with zero downforce, it is so incredibly rare in certified airplanes, it is not worth consideration, and really fusses up the logic path. The tail always exerts some downforce - more downforce for forward C of G, less for aft C of G. The difference is trimmed out by the pilot to bring the pitch control force to zero (but there is still tail downforce, it's just trimmed to no control force for pilot comfort). For economy cruise flight, and aft C of G is preferred, because less tail downforce is required, so less drag.

If there were no tail downforce, the airplane would not behave as expected (and required for certification) in stall recovery. This is a prime element of determining the aft C of G limit - there still must be enough tail downforce, that the nose wants to drop when down elevator is applied. During spin testing, I have flown a few types, where spin recovery at the aft C of G limit requires that full nose down elevator be applied and held during the recovery - you know that you're at that plane's aft C of G limit then!

Certification requires that a pull always be required when airspeed is slowing toward the stall. This pull could be trimmed out if the pilot desires, but is the stability indicator to the pilot that they are approaching the stall. I have flown two types where under certain configurations a pull was not required to slow, but rather at a certain [slowing] airspeed, the pitch control force went to zero, and then a restrained push was required to slow more. This is a pitch unstable airplane. The two examples I have flown which had this characteristic were the turbine DC-3 and the Siai Marchetti 1019. It is very un nerving! Modern certified airplanes either do not have this characteristic, or have artificial stall barriers to simply keep you away from this regime of flight.

I was initially thinking to say no to this, but upon further reflection, it's not a full no. In the yaw axis, a taildragger is stable during ground roll until the fin stops being effective, then a groundloop is possible if the pilot is inattentive to maintaining heading with rudder. This does have similarities to the pitch scenario, when the horizontal tail stops being effective, and the nose drops. So yes, kinda like a groundloop in flight in the pitch axis, other than it is an intended design characteristic for safety, and automaticcally corrects itself when airspeed returns (which a groundlooping taildragger generally would too, if the pilot increased speed during the groundloop, to make the fin effective again. Any stalled tail surface ceases to be effective in maintaining stability in that axis.

Thanks everyone. So far my understanding is this (...hopefully I'm in the right ballpark):

• Forward CG = more TDF required
• Aft CG = less TDF required
• If the aircraft is disturbed and it...
  • pitches up, airspeed decreases = TDF decrease = nose goes back down
  • pitches down, airspeed increases = TDF increases = nose goes back up

And if I'm not mistaken that describes static stability. But I'm unsure what factor determines whether the oscillations would then increase, or decrease from this point onwards.

i.e. what could cause dynamic instability?

You're about right for static stability.

There are two different dynamic modes, the long period - commonly called the phugoid or sometimes "porpoising" typically with a period around half a minute in light aeroplanes, and the short period. They are driven by static stability, but the dynamic stability is down to damping terms. At first approximation I would tend to expect the phugoid to be stabilised at aft CG but the SPO to be destabilised, and vice-versa, but those are not universal rules.

G

The vertical component of any gusts will affect the angle of attack of both the wings and the tailplane, and also the positions of their respective centres of pressure, which in turn will generate variable pitching moments experienced by the aircraft - a complex situation. Overall the behaviour of the aircraft will be as described above.

The main reason single-engined propeller-driven aircraft tend to pitch up when thrust is increased is the more powerful propwash generating greater TDF as it flows past the tailplane.

This was the problem Boeing faced with the 737 Max. The geometry of the new (further forward) engine nacelles generated an extra pitch up moment which reduced the control wheel pull as the stall was approached. The solution was to arrange that the stabilizer (= tailplane) reduced the TDF by adjusting its angle of incidence. If they had designed a fail-safe system (using both angle of attack sensors rather than just one and a comparator to prevent false readings triggering the stab input) the Max debacle would have been avoided.

Proper failsafe wants three AoA sensors, then if any one is out of alignment, you disregard it and take the mean of the other two.

Two sensors is not really any better than one in a safety critical system like that, as if they're reading differently, you don't automatically know which one is wrong.

G

Two sensors indicating high A of A --> stab trim (MCAS) input

Discrepancy between sensors --> no stab trim input (but possibly reduced stall protection).

Fair point, although the AoA sensor wasn't just used for MCAS, it was also used to feed the AFCS.

There's actually also a bunch of logic Boeing employed to tell you if you think you have a problem with a single sensor - but as we've clearly seen, those tools can sometimes be flawed. The cost of three sensors, versus one or two, on an aeroplane as big and complex as a B737 is trivial and should have been done.

G

A bit off-topic, but I'd like to reference my own trade (when I had one): high availability IT. This is usually accomplished by having all critical components duplicated, with one active and the other standby*; and the two in permanent communication to determine the status. If the one says "temperature is 15 degrees" and the other says" temperature is 25 degrees" then there is a problem, called a "split brain" situation, which is normally solved by adding a third component, called the quorum device. Funny how totally different technologies apply the same tactics.

And indeed the cost and complexity of adding a third AoA sensor to a plane as complex and expensive as an airliner must be more than bearable - Boeing certainly spent a lot more money now.

* this is called an active/passive setup; there are other configurations, load sharing and what not, but let us not diverge too far

3rd Component.
 

Quote from Jan... which is normally solved by adding a third component,
So maybe all commercial aircraft should have 3 pilots.. Just in case one pushes whilst the other pulls..?

If you consider crew members to be "components"...

Re the original subject, a gentleman by name John S. Denker has written a fascinating lot about almost every aspect of how aircraft fly here: Welcome to Av8n.com. There is a long section on Angle of Attack Stability, Trim, and Spiral Dives here: 6 Angle of Attack Stability, Trim, and Spiral Dives (av8n.com). He discusses something called decalage which I think is about ensuring that the tailplane normally has a smaller angle of attack than the wings. Would be interesting to hear some of you experts comment on this, and how relates to earlier explanations here!

To take us back to the beginning. The arrow is a simple and effective way to explain the problem. How the four forces are applied in a modern aircraft has been explained but force x distance hasn't;

A Newton = 1 Kg over 1 metre.

So a body in motion can only be maintained resisting deviation (wobble) by an external body that is equal but that isn't always enough: Unstable air adds complex additional forces. It was then discovered, from no doubt the observation of nature, air resistance could be used as an additional and variable force to neutralise the erratic wobbling forces. Three feathers provided the required force effect in pitch, roll and yaw.

The aeroplane trimmed stability has to be varied to change vectors using pitch, roll and yaw. This is achieved by adding a flap to the three planes (feathers) in order to vary the force of each by the pilot at will. If the CG is in the middle then to raise the nose weighing 1 kilo 1 metre then the force from the horizontal tailplane downward must also be effective to an additional 1 kilo for 1 metre. Move the CG forward to 25% then to raise the nose 1 metre the tail plane must be lowered 2 metres. If the tailplane force available cannot do that then it will be impossible to raise the nose sufficiently. This will also be the case if restricted by the runway on landing and the nose lands first. So by moving the CG aft the balance will be eventually be found and this will be the most forward limit but on the edge. Keep moving the CG further aft and reach a safe forward limit published by the manufacturer. Moving further aft again to the point the aircraft becomes unstable and now an advanced level of skill is required not to overcontrol. Then bring the CG forwards again to a point where only the average pilot skill is required; this is the published aft CG.

Yes, but your ignoring the outcome. A set of traditional scales can demonstrate: Put 1 Kg weight in one dish and the dish will continue downward until it is forced to stop. Add a 1 Kg weight into the other dish and this dish will fall forcing the first dish to rise until both stabilise level. Add another small weight to the second dish and it will fall again and the first dish will continue to rise but only by a predictable distance until a new balance between the two dishes is achieved.

Traditional scales are designed to change the leverage as the pans go from even. Also, it's a 1 kg mass, not a weight; weight is a force proportional to acceleration.

In any case holding the item against the fall from gravity is accelerating the item.

There are several demos on YouTube of accelerometers being wired to speakers to make a noise proportional to the acceleration. They all go silent when dropped, indicating they are not accelerating in their own frame of reference when in free fall.

Sdwings really answered his own question in his first post by mentioning the arrow shot backwards.

Theoretically, if a normal arrow was fired backwards very accurately it would continue in a straight line. But if there was the tiniest displacement at the tail, the aerodynamic force at the tail feathers (now at the front) would become greater with a greater displacement until the arrow “flipped” over the C of G. From then onwards, the aerodynamic forces would reduce until the arrow flew straight as it was really designed to do.

An aircraft needs to be stable in all axes to some extent but unlike an arrow it needs to fly at various all up masses, in other than a straight line, ie have manoeuvrability. The centre of lift and the C of G are therefore placed relatively close together to find a safe compromise between outright stability and reasonable manoeuvrability. To prevent it “flipping” like the arrow fired backwards (a theoretical extreme only mentioned to illustrate the point) the designer works out the safe C of G envelope, which must be adhered to if the aircraft is to stay in full control.

Talking about "mass" is a little esoteric, every flight manual I've seen talks about "weight", Concorde and SR-71 both, the speeds of those two aircraft and the direction in which they flew influenced the "weight" to an extent that was measurable by the boffins.

Conversely, the manufacturers’ flight manuals for aircraft I’ve flown for a living since 1985 have used the term “Mass” rather than “Weight”.

I remember there being an amendment to the RAF Gazelle Flight Reference Cards at that time which caused some discussion.

But argument over that point has little to do with this question.

For a whole bunch of reasons, "weight" and "mass" can be treated as interchangeable when you do everything at 1g. That includes doing your shopping, or calculating an aeroplane's weight/mass and balance from a weighing on the ground. This is how the incorrect market metric unit of kilogrammes-force comes into such widespread use, and in imperial units so many people get confused between the pound-mass (lb) and pound-weight (lbf).

In flight however, we are regularly NOT at 1g, thus it's important for e.g. doing aircraft stability or performance calculations, we differentiate between the two. It's also where SI becomes suddenly massively superior to Imperial, since SI only has one unit for weight/force, the Newton, and one for mass, the kilogramme, whilst Imperial has two mass units (the slug and the pound) and two force units (the pound and the poundal).

G

Nobody seems to have answered you.
Yes, groundlooping arises due to instability because the centre of mass is behind the lateral forces when the plane veers every so slightly off line.
It's a bit like balancing a pencil on it's tip, or a cricket bat on it's handle on your outstretched palm. (Do Americans do that with a baseball bat?)
As long as everything is perfectly in line, it's stable, but nothing in the real world is ever perfect, and as soon as it deviates, even slightly, it is unstable and gets worse.

It's also the reason trailers need their centre of mass forward of the axle(s) for stability, resulting in downforce at the coupling.

There was an elaborate and to me quite satisfactory response from @DAR. Just as per usual, of course :) March 6th, 23:33, second paragraph.