CG on high & low wing

[shumway76]

I was reading up regarding lateral stability, and when it comes to high & low wing, I found some discrepency:- High wing - has pendulum effect due to low CG which will tend to "swing" the aircraft back to a wings level attitude.But another book (not related to lateral stability topic) states that a high wing aircraft has a high CG, which sounds logical as there is greater mass at the upper side of the aircraft due to the wings.And low wing aircraft has a low CG.Which is right then? Does a high wing aircraft have a low or high CG?

[Mark1234]

Both

All other things being equal, a high wing a/c will have a CoG nearer the top of the fuselage than if it had low wings; however, the CoG will still be below the wing, hence having 'pendulum' stability.

For a low wing configuration, the CoG will be nearer the bottom, but unlikely to be below the wing. That's one reason why low wing a/c usually have some dihedral, but high wings typically have far less / none.

[Pilot DAR]

Though your observations are correct, you'll find that certified aircraft are designed so as to minimize these affects. As Mark mentions, dihedral plays a role in this. There is nor requirement for determination or control of the vertical position of the C of G. Even, a Lake Amphibian, with the engine way up there, does not really show much affect in this regard.

You can see the affect of vertical C of G when amphibious floats are installed on a wheel plane. There is a noticeable pendulum affect in some float planes, as the C of G is much lower. While a passenger once in a C 185 amphib, I asked my friend the owner/pilot, if the pendulum affect was so great, as to prevent the aircraft from being rolled. A minute later, we had the answer - a 185 amphib can be rolled!

The installation of a STOL kit leading edge cuff on a Cessna wing can have the affect of very slightly reducing the lateral stability, but because of the effective dihedral as seen at the leading edge, not the weight of the kit.

[IO540]

It is also the case that every certified plane I know of, low wing or high wing, will perfectly happily go into a spiral dive if you take your hands off the controls. I don't think any of the high wing ones have long term stability in roll. Maybe some floatplanes are different?

All certified planes have short term (small signal) stability in roll, and all have long term stability in pitch (phugoid should decay within X cycles). Otherwise, they would not be practically flyable by a human, for any length of time.

[24Carrot]

I've always had a problem understanding this "pendulum" effect, or even finding it in text books.
(I just checked "Aerodynamics for Naval Aviators".)

A low CG can increase the leverage of a high vertical tail, (and I suppose the leverage of the fuselage in the float plane case), but for anything to do with lift differences between wings, (eg classic dihedral), the forces act out along the wing-span, so the vertical CG position is second order.

High wing aircraft get their extra lateral stability because the fuselage forces the sideslip to move around it: the into-wind wing sees a higher AoA, the out-of-wind wing sees a lower AoA. This can easily be equivalent to 3 degrees of true dihedral.

For low-wing aircraft the effect is reversed, and designers tend to give them more real dihedral to compensate.

I am assuming a rigid aircraft. For hang-gliders I imagine the pendulum effect is very real!

[vihai]

The explanation for which a CG lower than the pressure center should provide roll stability has never convinced me.

Suppose an external force makes you depart from level flight into a 30° roll. You're now in a turn but the forces will still be parallel to the vertical axis, so there is no momentum against the roll.

However, in the extreme case of a parachute/paraglider where the CG is much lower than the center of pressure there is a strong stability.

How is it, then?

[AussieAirman]

There is no such thing as "pendulum stability" or a "pendulum effect" for airplanes

The whole notion of airplanes having "pendulum stability" or the existence of a "pendulum effect" seems to me to be a misconception that one frequently reads about here and there on various sites and even in pilot handbooks. It leaves several contributors to this forum unconvinced, and it leaves me unconvinced, too, for the simple reason that the notion just doesn't compute.

Here are a few sample statements on "pendulum stability" or "pendulum effect" that I found on sites that supposedly offer professional content.

"Most high wing airplanes are laterally stable simply because the wings are attached in a high position on the fuselage and because the weight is therefore low. When the airplane is disturbed and one wing dips, the weight acts as a pendulum returning the airplane to its original attitude."

"Mounting the wings above the center of gravity aids lateral stability because the weight of the aircraft will act as a pendulum to restore level flight."

"The location of the wing will also determine the stability of the aircraft. The most stable type is the high wing configuration on a typical monoplane. The pendulum stability of its wing gives it the natural stability because the weight is under the wing."

The simple truth, if I may be so blunt, is that statements such as these are misleading and incorrect in terms of both the physics of flight involved as well as in terms of Newton's equations of motion. In what follows, I therefore propose to offer a cool explanation that to the best of my knowledge is correct and does respect the relevant fundamental principles of flight mechanics, aerodynamics and Newton's equations of motion.

Here then are a few comments and ideas that may clear the skies. In formulating these comments, I draw upon my own background in aerodynamics and applied physics.

1. Let me start with a general remark about the so-called pendulum effect or pendulum stability. I think it is a confusing analogy to begin with to use for airplanes or other aerial vehicles such as para-gliders, powered parachutes, hang-gliders, airships, or whatever.

A pendulum is severely constrained to move around its suspension point. For a simple pendulum, it is easy to formulate its equations of motion.

An airplane, on the other hand, just isn't at all like a pendulum. It enjoys six degrees of freedom in its motions and is completely free and unconstrained. When we look at the familiar frontal diagram of a high-winged airplane in a turn, it might look like a situation analogous to the pendulum, but that doesn't therefore imply that it is. It just isn't.

There is, however, one scenario that comes to mind in which it is legitimate to interpret the motions involved as being similar to that of a pendulum, and that is when a rescue helicopter picks up a survivor who finds himself suspended on a wire from the winch. As the helicopter starts to climb, the survivor may find himself at a lateral offset from directly below the winch as he is lifted off the ground. He will then indeed start to swing like a pendulum. The period of oscillation is easily estimated.

2. Next, let's turn to the airship I mentioned above, for its illustrative value. The airship has the kind of roll (and pitch for that matter) stability we're talking about. Classic texts on airship aerodynamics explain it in detail. In a stable airship in equilibrium, the CM (center of mass) is located vertically below its CB (center of buoyancy). Now suppose for some reason the airship suffers an unexpected roll angle displacement, say 30 degrees.

What happens is that the "lift vector" (buoyancy vector from its helium-filled fuselage or tanks, or whatever) remains vertical and points upward. It must, because we're talking about aerostatics here. The weight vector obviously continues to act vertically downward. We now have a horizontal separation between the lines of action of buoyancy and weight vectors, which equals h x sine (roll angle), where h = vertical separation between CM and CB. The restoring roll-moment we now get = W x h x sine (roll angle), which acts to reduce the roll angle and restore the airship to an upright position. This stability mechanism (simple for roll, more involved for pitch due to aerodynamic moments which then complicate the picture when airship has forward motion) constitutes a "natural stability" of the kind that airplanes simply do not possess.

Note that we aren't talking about roll-slip coupling, where we must turn to explain the dihedral and related effects. We're talking about a pure roll or bank angle.

3. So far, so good, for an airship, which obeys the principles of aerostatics. Its "lift" always remains vertical, as it must. Now what about an airplane, say, a high-wing floatplane? Let's give it a 30 degree roll angle, and look at what happens before any sideslip develops.

Is there a "pendulum effect"? Does the floatplane (or indeed, any other banked airplane, whether low or high-wing) have some sort of automatic self-righting capacity as does the airship? No, it does not.

There is a fundamental difference between airships and airplanes (and paragliders, hang-gliders, powered parachutes, and so on). Airships (in the present context) as we know obey the principles of aerostatics and airplanes obey the principles of aerodynamics.

Now we left our floatplane in a banked position. If its lift vector (like that of the airship) remained vertical, then, yes, it would generate the same kind of restoring roll-moment as did the airship, and as a consequence all airplane-handling texts would have to be revised and all turning airplanes would start to behave differently. Obviously, they don't. Why not? Because as we all know the lift vector on a banked airplane does not remain vertical but continues to act perpendicular to the wing.

Right there is the fundamental difference. The same holds true in principle for hang-gliders, paragliders, powered parachutes, and so on. As long as the lift forces on the aerial vehicle in question are aerodynamic in nature rather than aerostatic, well, then the lift vector remains perpendicular to the "wing" and no restoring moment arises because the line of action of the lift vector continues to act through the CM of the banked airplane (or other aerial vehicle, including the paraglider with very low-slung pilot). No horizontal separation of the lift vector and weight vector occurs, as was the case for the airship.

Conclusion: no roll moment is generated and there is no such thing as a "pendulum effect" or "pendulum stability" for an airplane (or similar aerial vehicle).

Bob Hoover, for example, in his famous aerobatics display with an Aero Commander, would surely have noticed any "self-righting" tendency in roll if it existed. No such thing. Heck, he's so clever that he can pour himself a cup of iced tea during a barrel roll and not spill a drop -- and the generals in the back didn't spill a drop of their coffee, either!

Please note carefully what the real pendulum is doing that Bob has suspended under the cup holder during the barrel roll. Slight disturbances apart, the pendulum remains happily suspended as it was during level flight as seen from the pilot's perspective. Furthermore, the iced tea pours straight down into the glass. Bob Hoover is obviously having a great time, but the pendulum effect is nowhere to be seen!

4. Misconceptions nevertheless continue to abound all over the place, even on websites for paragliders, powered parachutes, and so on. One might read that the powered parachute "exhibits strong pendulum stability." If it does, where would it come from?

Here's an expert author's explanation for hang-gliders (emphasis added): "Most hang-gliders are controlled by shifting the pilot body weight either to the side, front or back. This gives very good control, and because a hang glider is very pitch stable (it returns to normal speed by itself) and neutrally roll stable (if you turn, it will tend to stay turning until you straighten things out) they are easy to both fly and land." No mention is made of any "pendulum stability". For good reason.

5. It is good to remember that when formulating the equations of motion for a rigid body such as an airplane, one always formulates them relative to the center of mass. Forces act along three axes and one computes the moments (torques) to act about the CM or CG if you prefer.

Let's go back to the familiar frontal diagram of our banked floatplane. Let's make it a C-172. Its CM would presumably be lower than its sister that doesn't have floats. Some would then claim that the floatplane ergo must have larger "pendulum stability". Not true, as I think I have demonstrated, as far as pure roll is concerned before any sideslip develops. (But see below for the discussion on roll-slip coupling.) The lift vector of the banked airplane continues to act perpendicular to the wing (as it must, because aerodynamic pressures per definition act perpendicular to the surface upon which they act). The line of action continues to pass through the airplane's CM, whether that CM be located higher or lower in the airplane.

The equations of motion demand that we take torques or moments around the CM and in so doing we once again realize that there just is no roll moment from the wing of a banked airplane.

The wing as we know doesn't care where the horizon is. It only cares about relative wind. Not so for the airship, whose lift vector must remain vertical in an absolute sense.

6. In respecting how equations of motion of a rigid body are formulated and solved, it is therefore incorrect to conceive of e.g. a powered-parachute (or the tandem skydivers we see executing beautiful turns as they descend toward the beach out here on the Gold Coast), which has a very low-placed CM relative to the position of its "wing", as somehow moving or rotating around that wing, in the same way that a pendulum swings around its suspension point.

When we sketch the forces on a banked powered parachute (PPC), as long as it behaves as a rigid body, and the lift vector remains perpendicular to the wing, its line of action will continue to pass through the low-slung CM and no roll-restoring moment arises. It isn't there for the hang-glider either, whose pilot is quite low-slung as well.

Formulate Newton's laws of motion for a rigid body in the correct way, investigate what torques act around the CM, and reason from there.

7. The question now arises as to why high-wing aircraft such as the C-172 often have little or no dihedral, while low-wing airplane such as the Piper Cherokee often has considerable dihedral.

Surely, it's because the high-wing aircraft has "pendulum stability". Just kidding. On the other hand, maybe I'm not kidding, for it is possible for an airplane to behave like a pendulum, and that is when it has been donated to a museum and finds itself suspended from the ceiling!

Museum displays aside, to understand what's really going on we have to leave pure roll (i.e. roll before side-slip develops) and investigate roll-slip coupling. Enter dihedral and other effects that compose roll-wise stability via roll-slip coupling. Note in passing that a pendulum never develops sideslip and so provides an unsuitable analogy in that respect, too.

The best explanation I have found to date of the dihedral effect and other roll-wise stabilising effects comes from a section of John Denker's brilliant online book.

John describes four different effects, all additive, and concludes that: "All four effects just mentioned are in the same direction, and can be combined: You can have a high-wing, swept-wing airplane with lots of dihedral and a really high tail — in which case you would probably have more slip-roll coupling than you need."

This probably explains why an aircraft such as the massive Antonov An-124 has anhedral. It also explains the difference we noted above between a C-172 and a Cherokee.

As far as I understand the game, in order of importance the stabilising roll-slip coupling rolling moments tend to be: dihedral, sweepback, wing position relative to CG and in relation to fuselage, fin area (and fuselage area where relevant) above CG.

The wing position is normally chosen for practical considerations (no coincidence that tough military transport airplanes such as the Hercules are high-wing), the sweepback in relation to cruising at a certain Mach number, and the amount of dihedral or anhedral to achieve a desired level of lateral (roll-wise) stability in relation to other important stability and design considerations.

8. This right stuff still leaves open the question as to what the popular notion of "pendulum effect" may actually refer to.

Here's my answer.

There is one component of the stabilising roll moment that stands out from the others as a high-wing floatplane, a parasol airplane such as the Supermarine Seagull or the Catalina, a powered parachute or a paraglider starts to develop a sideslip velocity toward the low wing as a consequence of a roll disturbance.

The sideslip sets up an oblique flow over the entire airplane. This in turn leads to the production of sideways forces on the fuselage, wing and its support structure, floats, tail and any other relevant parts. The sideways forces on those parts of the airplane in particular that stick up high above the low-placed CG (the roll axis) now produce a larger stabilising rolling moment than would occur for similar configurations with a higher CG placement.

This I think is the “pendulum effect” that one reads about from time to time.

Now here comes the crucial point: this roll-wise stabilising effect is a function of the sideslip that develops as a consequence of a roll disturbance, but is not a function of the roll angle itself. Its is therefore clear once again that the analogy of the simple pendulum is an unsuitable one to apply to the much more complex and dare I say dignified motions of an airplane.

Contrast the previous sequence of events with one wherein the pilot of the Catalina executes a coordinated steady and level turn. Now we have bank but no sideslip.

Does the Catalina during the turn exhibit any form of "pendulum stability" whatsoever in that it wants to level its wings? The answer is, no, it doesn't. On the contrary, assuming the Catalina behaves like most airplanes do, it will want to steepen the turn due to its overbanking tendency not level it.

Meanwhile, as long as the pilot maintains coordinated flight, the Catalina will happily keep on turning. The pilot, sending a silent wink to Bob Hoover, can pour himself a cup of tea and drink it, too.

To conclude this ramble, I therefore suggest that we leave the pendulum suspended from Bob Hoover's instrument panel, old airplanes displayed in museums and functional airplanes free to roam the skies in six degrees of freedom!

Thank you for your attention.