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A high wing airplane will correct itself (lateral stability) when disturbed because its c.g. is below the c.p. (looking at the plane from it's side), according to this forum post and the book below.

So my question is, how does this "pendulum effect" affect a biplane with two centres of pressure?enter image description hereenter image description here

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  • $\begingroup$ ....Fixed...... $\endgroup$
    – Jessica Ham
    Jul 6, 2019 at 19:47
  • $\begingroup$ I must note that at the end of that forum discussion somebody (totally not Peter in an alternate timeline) also makes the point Peter explains in his answer: there is no such thing as pendulum stability, its a misconception $\endgroup$
    – AEhere supports Monica
    Jul 6, 2019 at 20:16
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    $\begingroup$ See Rocket pendulum fallacy. And here’s a good demonstration using a drone: youtube.com/watch?v=OYHCP3-mpxk $\endgroup$
    – TomMcW
    Jul 6, 2019 at 20:34

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Disturbed - but how? A fixed wing aeroplane in a stationary, zero sideslip turn is roll neutral. There is no tendency from gravity to upright the roll. Not for a monoplane. Not for a biplane. Not for any number of fixed wings.

enter image description here

The last picture in the OP with the vertical lift vector for the rolled aircraft is wrong: the lift vector deflects with the wing and is always perpendicular to it, therefore always points though the CoG. The picture only considers the stabilising moment of the vertical component $L_v$. and conveniently disregards opposite moment of the horizontal lift component $L_h$, which magically counteracts the rolling effect of the vertical component.

Disturbed in sideslip caused by $L_h$: yes, this causes an aerodynamic rolling moment, from several mechanisms.

  1. Wing/fuselage interference The high wing aeroplane tends to upright itself due to the usual sideslip direction in a turn, a low wing wants to increase the bank angle.

old uni book

  1. Wing dihedral or V-shape. Velocity w in the aeroplane Z-axis when the wing is not perfectly aligned with the airflow.

Same old uni book

  1. Wing sweep. The sideways velocity of the sideslip causes different relative velocities over the two wing halves.

Gotta love old uni books

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    $\begingroup$ Please explain how a hang glider turns. Displacement of lift and center of gravity will create a rolling motion. A side slip must have significant velocity for purely aerodynamic effects to "right" the aircraft. What you propose essentially is an aircraft that must constantly "Dutch Roll" to remain upright. Obviously, this is not a practical mechanism for passenger transportation (although it is theoretically possible). Please review aircraft design. $\endgroup$
    – Robert DiGiovanni
    Jul 7, 2019 at 11:25
  • $\begingroup$ @RobertDiGiovanni a hang glider turns by pointing the lift vector sideways, like all aircraft do when they do a banked turn. $\endgroup$
    – AEhere supports Monica
    Jul 7, 2019 at 11:36
  • $\begingroup$ Bingo! And how is that wing rolled sideways??? "Pendulum" is a bit more palatable considering the case of weight ABOVE the wing (destabilizes roll). Dihedral and lower CG are roll stabilizers, sweep and high CG create "Dutch Roll". Shifting CG away from Lift Center (hang glider), or shifting Lift Center away from CG (ailerons), will create roll. $\endgroup$
    – Robert DiGiovanni
    Jul 7, 2019 at 15:10
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    $\begingroup$ @quietflyer. Oops, lost in translation, thx. $\endgroup$
    – Koyovis
    Jul 8, 2019 at 2:52
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    $\begingroup$ @RobertDiGiovanni: A hang glider does not shift the weight, it shifts the wing. Weight shifting is impossible due to the conservation of momentum. $\endgroup$
    – Peter Kämpf
    Jul 8, 2019 at 5:07
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It will affect a biplane just as much as a monoplane.

Not at all.

The pendulum effect does not exist in airplanes. It does in airships, but not in heavier than air craft.

For a proper discussion, we should first define what a pendulum is. Only then can be established if such an effect can exist in airplanes.

Let's base the definition on Wikipedia. It says that

A pendulum is a weight suspended from a pivot so that it can swing freely.

Maybe it is also worth to look closer what a pivot is: A thing on which something turns.

So the pendulum is fixed to a fulcrum which keeps it suspended and allows it to swing freely. The ideal pendulum has all its mass in its massive bob and, therefore, pivot and center of gravity are not in the same place. If the center of gravity and the pivot would fall together, a pendulum could only rotate but not swing. And that swinging motion is what the pendulum is all about.

Now for airplanes: Here we have no pivot. All rotation can only happen around the center of gravity. This is equivalent to the pendulum with no length which is no pendulum any more.

Lift is the sum of all pressure acting perpendicular to the direction of movement. Lift on a banked wing will also bank with it. The lift vector will still be in the plane of symmetry of the banked aircraft and will have no lever arm with the center of gravity, thus causing no uprighting rolling moment. The Figure 34 of your copied book page is simply wrong. The author did not know what he was talking about.

Edit especially for @JohnK:

I added an answer here about the rolling maneuver of paragliders. The description should make obvious that no pendulum effect is involved. Rather, the whole is quite similar to roll control in hang gliders where the lift is shifted sideways in order to create an imbalance, but then again different in wonderful ways. The discussion below would not allow me to explain my thoughts in such detail.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – Federico
    Jul 8, 2019 at 5:07
  • $\begingroup$ But, as long as we are consulting Wikipedia, see this page. This is what I mean when I talk about "pendulum effect". Note the importance of sideslip. Yes, it is a bit of misnomer, but it's come to be a widely-used term. To me the term "keel effect" is just as problematic as "pendulum effect" or more so, because it gives the impression that there is a parallel to the way that buoyancy exerts an upward force at the center of buoyancy, high above the CG (which is low due to the heavy keel weight), creating a righting force even without sideslip. en.wikipedia.org/wiki/Keel_effect $\endgroup$
    – quiet flyer
    Jul 8, 2019 at 12:00
  • $\begingroup$ An important point is that even if true sideforce is minimal, drag can still create a roll torque during sideslip, if it acts well above or well below the CG. $\endgroup$
    – quiet flyer
    Jul 8, 2019 at 12:03
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Pendulum effect is a bit of a misnomer. What is thought of as "pendulum effect" is actually just a favourable rolling moment that can be generated during sideslip if the center of mass is a large distance from the lateral aerodynamic center, which doesn't really exist on normal aircraft.

Paragliders however, which operate in a kind of topsy turvy alternate world of control, exploit this effect to achieve lateral stability and to turn. A paraglider turns by skidding, the skid being created by increasing the lift and drag on the into-turn side when you pull the trailing edge down with brake application (you are only interested in the drag increase, not the lift increase, which is working against you - you are only interested in the lift increase when using both brakes together to slow down and flare).

Doing this (applying brake on one side to turn that way) actually creates a small aerodynamic rolling moment in the opposite direction of the turn (like trying to turn an airplane to the right by lowering the right flap and aileron only - doesn't work so well in that case), but because the center of mass is more or less down where the pilot is, and the lateral aerodynamic center is up by the wing someplace, the lateral force on the pilot to the outside of the skid massively overpowers the differential lift created by the brake application and rolls the glider to the right. And you can say that it's sort of acting like a pendulum, kind of.

You could say that paragliders exploit this effect to use adverse yaw to turn the wrong way, allowing control with inputs that are seemingly opposite to the normal world (turning right by lowering right aileron as it were).

As well, the mass way below the wing creates a strong centering effect (you're basically hanging from a parachute that is able to glide forward) and if spontaneous sideslip occurs the restorative rolling moment is immediate. It's also how paragliders are to somehow magically be able to achieve very strong yaw stability without any weathervaning element like a fin or sweep. Yaw and roll are strongly interconnected due to the mass 15 feet below.

So you could say that there is a pendulum effect but it only works for paragliders, or maybe some crazy airplane with most of its mass in a concentrated bob weight at the bottom of a long rigid pole extending below it, with most of its surface area at the top. In any normal airplane, the lateral aerodynamic center and the center of mass are too close together for this effect to overpower the other forces and are insignificant if they exist at all.

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  • $\begingroup$ Please rethink the last paragraph. The paraglider first creates a lift and drag difference between both wingtips which pulls the wing sideways and starts a yawing rotation. This rotation in combination with the now offset pilot mass will increase the bank angle. The question, however, is about how a bank angle can create a counteracting rolling motion without pilot input. This is quite different from how a paraglider turns. $\endgroup$
    – Peter Kämpf
    Jul 7, 2019 at 17:38
  • $\begingroup$ Peter and John, I will not insist on butting in on your conversation too much, but please consider the paraglider - it turns by wing warping! This works because the Pendulum prevents it from rolling into the other direction! The wing (and pilot) will yaw in the direction of the increased drag. Now a bird will have another trick up its sleeve, it will fold up its inside wing to roll into the turn (instead of ailerons), then use its tail to yaw (a slip turn). This is more like air craft do. $\endgroup$
    – Robert DiGiovanni
    Jul 7, 2019 at 19:31
  • $\begingroup$ If you are turning a paraglider and remove the brake input, adverse yaw created by the brake application stops and the glider starts to fly straight. Being banked with the yaw removed, it starts to sideslip toward the low side. The mass below the side slipping wing rolls the glider level, or at least level after several overshoot oscillations if you just let it go, depending on the glider. Some gliders are very well damped in roll and immediately return to wings level, some oscillate and get get into rolling PIOs if counteracting brake inputs are ill timed and end up feeding the oscillation. $\endgroup$
    – John K
    Jul 8, 2019 at 1:07
  • $\begingroup$ John, that is exactly what shows a stabilizing force. Pendulum is much smaller in aircraft, but it does exist and can contribute to roll damping. What is very interesting is what happens when a pendulum is YAWED. It rolls the aircraft! $\endgroup$
    – Robert DiGiovanni
    Jul 8, 2019 at 11:03
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The issue here is "disturbed" as opposed to being rolled and yawed intentionally into a turn.

The "pendulum" concept, amazingly, is still being debated more than 120 years after the dawn of heavier than air flight.

The key is the mass of the object relative to its surface area.

Let us take 3 high wing aircraft, a simple paper airplane, a Cessna 172, and the mighty Antonov 225. After being disturbed, the paper airplane will immediately slip and correct due to its light weight. Dihedral helps paper airplanes. Putting a paper clip on the bottom does not work nearly as well. Now the Cessna 172. It has a combination of dihedral and pendulum. Because of its greater mass, it will take appreciably longer to reach a significant side slip velocity and uses the offset of CG and center of vertical lift to a greater degree. Now the Antonov 225. Picture a see-saw with 700 tons on one side and someone pushing UP on the other. A very powerful torque indeed.

So the exact mechanism of roll stability will vary from aircraft to aircraft.

Now for a biplane, you simply compare the NET center of pressure to the CG location, but remember aerodynamic, as well as gravitational forces will determine stability.

Here is a picture of one that handily trounced a mono plane in a crosswind free flight.

enter image description here

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    $\begingroup$ "The "pendulum" concept, amazingly, is still being debated more than 120 years after the dawn of heavier than air flight." A flat earth is also still being debated. $\endgroup$
    – Koyovis
    Jul 7, 2019 at 6:36
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    $\begingroup$ Your answer argues that there is a pendulum effect as shown in the OPs "figure 34", I believe. That is simply wrong, unless I am misunderstanding your fourth paragraph, which is a tad messy. $\endgroup$
    – AEhere supports Monica
    Jul 7, 2019 at 11:33
  • $\begingroup$ The OP's "figure 34" shows a displacement of VERTICAL lift center and CG from a line perpendicular to earth. The center of this roll displacement is debatable, and worthy of further study. $\endgroup$
    – Robert DiGiovanni
    Jul 7, 2019 at 15:14
  • $\begingroup$ The figure uses L for lift, the vertical qualifier is only present in your discourse. $\endgroup$
    – AEhere supports Monica
    Jul 7, 2019 at 20:37
  • $\begingroup$ @AEhere the figure actually uses L for vertical lift, which is displaced from CG (straight up and down line), producing roll torque. The horizontal and Perpendicular to Wing Lift component (as we know it) are not diagrams, which is incomplete. The interest in the mechanism is: will this roll torque "right" the aircraft BEFORE it can accelerate horizontally enough for aerodynamic side slip forces to become significant. I believe lower set CG and dihedral will, there for I prefer high wing designs as safe and stable. Many ideas here, and many good points of view to consider. $\endgroup$
    – Robert DiGiovanni
    Jul 8, 2019 at 0:42

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