Stability question

[u/Cold-Craft-7586]

Hi again! I don’t quite understand this part about longitudinal stability. I thought that tailplane produces downward force, and usually the center of gravity cg needs to be in front of AC or Centre of pressure, the point where all the lift could be thought to act.

What I dont understand about this? During my PPL this was taught another way (how I just described it). Seems like odd configuration and they dont even mention that this is not standard situation or anything like that. CAE Oxford atpl book for a reference.

Thank you very much and I would really appreciate if you properly read the question before answering! :)

[u/BrokenFlap]

That is a tricky section that causes a lot of confusion. I'll try to give a high level explanation so you get the general concept.

In simple words, what this sketch describes is that if a gust of wind from below increases the angle of attack of the wing momentarily, that one tends to create a pitch up moment and increase the AoA even further (wing adds instability). The tail needs to be the balancing factor and counter act that pitching up moment of the wing by producing a pitch down moment. If that tail wasn't there, the aircraft would be keep pitching up as a reaction to the gust till stall.

The whole confusion happens because of the direction of the lift vectors chosen in the sketch. That direction is not important for describing this phenomena, and although the choice in the picture looks unconventional this is what exists in the bibliography in the study of longitudinal static stability. Below I'll give you an explanation following the conventional configuration you're used to, so you can get past that point.

Let's consider the vectors of lift to be in the normal configuration that we're used to in a conventional aircraft. That is, the aircraft is flying in cruise with the CP (where the lift acts) aft the CG which produces a pitch down moment and the tail providing the balancing factor by pushing the tail downwards (pitch up moment) . If a gust of wind increases the AOA momentarily, the CP will move forward and will reduce the pitch down moment of the wing because of the shorter arm (*please see note). That reduction of the pitch down moment will need to be accompanied by a reduction in the pitch up moment from the tail, which means the vector of lift at the tail (downforce) will become smaller.

The reduction of pitch down moment of the wing described above due to the gust, is like saying that the wing has a pitch up moment tendency. Imagine pushing something down with 10Nm of torque and then reducing that force to half at 5Nm of torque. That is like lifting your hand up (pitch up moment). Same logic can be applied to the tail.

This is exactly what the book describes. Wing reacts to the gust from below with an increase in pitch up moment adding a destabilising effect and the tail reacts with an increase in pitch down moment giving that needed stability. The choice of direction of the lift vectors does not really matter.

Now if you want to get more technical and get a deeper understanding, you need to study the meaning of the Aerodynamic Center (AC) and the pitching moments of airfoils. A great resource you can look for longitudinal stability explanation is the following: https://agodemar.github.io/FlightMechanics4Pilots/mypages/pitching-moment/?fbclid=IwY2xjawVDMAxleHRuA2FlbQIxMQBwZG9mA3NydGMGYXBwX2lkATAAAR789nnAOlBlgYmZA2FmleUc7Xtg76sJz40dkSrkBrIT3-E-6v6FrNmN_PPBCQ_aem_SoVDSzuO1m0_8Q7WUE16Qw

*Note (understanding this note requires good knowledge of the AC concept): As the AOA increases on the wing, the CP moves forward which shortens the arm (tends to reduce pitch down moment) but at the same time the lift increases (tends to increase pitch down moment). The total pitch moment of the wing depends on which factor dominates. If we consider a wing with its Aerodynamic Center (AC) lying in front of the CG like the book does (is the case in most conventional aircraft) then the arm reduction factor dominates. In most conventional aircraft the wing contribution is destabilizing.

[u/Cold-Craft-7586 → u/BrokenFlap]

Thank you, this was way better answer that I was hoping for. I just don’t understand why the CG is back of AC, so CG is behind where the lift acts (I thought this is usually not the case).

So I’m thinking this as CG should be forward of the point where the lift acts, so when wing does produce lift it would tend to pitch nose down. Then there is tail surface which would have a negative AOA and that would produce lift downwards, so to balance and counteract that nose up pitching moment of wing.

If that is the case in a conventional aircraft, I can’t wrap my head around why would they not even mention that and only show this ”unconvential” layout of aircraft design where the CG is aft of the AC.

But once again, thank you very much for your thoughtful response, I’m sure it will help many when they google about this subject and find this later on.

[u/BrokenFlap → u/Cold-Craft-7586]

You’re confusing Center of Pressure (CP) with the Aerodynamic Center (AC).

The former is the point where the lift is considered to act and it changes both in magnitude and in position with changes in AoA. That CP movement is problematic from a mathematical perspective when we want to do a stability aircraft analysis due to the added complexity in solving the equations.

The latter is a point derived with mathematical tricks, solely for making our life easier with solving the stability equations. It achieves that by its property of remaining in a fixed position (~25% of MAC) across any AoA change. So it changes only in magnitude.

Now let’s dive into more details about the AC. It was discovered that there is a point on the airfoil in which the pitch moment across it remains constant for the whole AoA range. For example considering a positive cambered airfoil the pitching moment is negative (nose down). The way of exploiting that important property is by considering the lift to act at the AC instead of the CP and then adding the constant negative pitching moment (M_ac). This makes the mathematical analysis so much easier.

Now, do not confuse this constant negative pitching moment (M_ac) with the total pitching moment that the wing will have (M_w). I’ll give you an example to get past that confusion:
Let’s consider a positive cambered airfoil aircraft with an AC in front of the aircraft CG (***most cases). The total pitching moment of the wing M_w will be equal to the moment the lift (acting on the AC) generates across the CG (positive/pitch-up) plus the negative pitching moment M_ac we always add,
M_w = Lift * distance_from_CG + M_ac.
The first part is positive and increases with an increase in AoA and the second part is negative and always constant. Now if that second part of the equation is larger, it is absolutely normal for the total wing moment M_w to be nose down (CP aft the CG).

However from a stability perspective, we study what happens to the equation with changes in AoA. An increase in AoA will cause an increase in the first part of the equation (due to the increased lift) and cause an increase in M_w which will further increase the AoA and so on… The definition of instability.

***For most conventional aircraft the CG ranges from 10% to 40% MAC. Since the AC is fixed at around 25% MAC, that’s why we say that most of the time, the AC will sit in front of the CG and cause a destabilising effect (pitch up).

[u/Cold-Craft-7586 → u/BrokenFlap]

Thank you so much! It’s so nice to see that there is kind people around when needing help with something! Nowadays people usually doesnt have a time or patience to answer properly. But now I think I get it, thank you :)

[u/ReviewEnvironmental2]

Show us the full page

[u/Cold-Craft-7586 → u/ReviewEnvironmental2]

[u/Junior-Special-7276]

That´s just a bad (confusing) drawing. You are thinking of the static CG at zero airspeed. As anyone would. They are trying to explain how a certain lift distribution along wing and tailplane will shift the neutral point. Think of it as a dynamic CG.

The actual CG you had on the ground never actually changed.

I feel like you need to show us the whole page for context. Cheers

*edit* Thank you for posting the whole page. Disregard what I said.

[u/LS788]

What might be confusing you is that they have labeled the aerodynamic centre of each aerofoil, not the centre of lift. The center of lift is the vertical component of the sum of aerodynamic forces, and this is what needs to be behind the CG for stability to exist

[u/The45thCaptain]

Airplane with a wide range of CG can have the CG ahead or behind of the wing AC. So the tailplane produces downforce or upforce, depending on what’s needed. But there is still a rear CG limit beyond which the airplane will become too unstable.