# What is aerodynamic damping?

Could someone explain what aerodynamic damping exactly is? I'm not able to understand the whole concept. Pls try to keep the explanation simple.

I tried to understand the concept from the link below. Is aerodynamic damping the same as the dihedral effect, or is that a whole different story?

https://encyclopedia2.thefreedictionary.com/aerodynamic+damping

• You may add your current state of research. What ressources have you read so far? What is unclear for you in this ressources ? Nov 28 '19 at 10:05
• Ok, I have edited. Nov 28 '19 at 10:24
• I suggest you read how it flies Nov 28 '19 at 10:34
• I think I missed seeing this question. An interesting side note is that in the special case where rate of curvature of flight path, yaw rate, pitch rate, are all constant, the "aerodynamic damping" of pitch rotation and yaw rotation can be also viewed as a change in local angle-of-attack (e.g. of horizontal stabilizer, vertical stabilizer) due to the free-stream relative wind curving to conform to the curvature of the flight path. Sep 29 at 13:39
• There are some other cases where this concept also applies, but if the aircraft is pitching or yawing in a way that is not synchronized to the curvature in the flight path, (for an extreme case consider the famous "Cobra" maneuver, or a flat spin) then it does not apply. Sep 29 at 13:41

The link you provided has a poor choice of words: "restoring moment".

Damping forces are not restorative, i.e. they do not attempt to return the body to equilibrium, but rather oppose its movement. That is an important nuance.

Imagine a classic spring and dashpot vehicle suspension: the spring tries to restore the vehicle to its regular position, while the dashpot damps the velocity. By itself, the dampener will not restore equilibrium, it will stay at whatever position you extend it to, despite fighting the movement itself.

How does this apply to your question: aerodynamic damping is exactly that, the opposition of the aircraft to rotation. You can observe it without flying: just imagine an aircraft hanging by its nose and tail, in such a manner that its CG is right between the supports. You can roll it by hand, but the drag on the wing will eventually stop this roll, but it will not level out the wings.

In flight, there are other forces at play that do provide a restoring moment, but aerodynamic damping does just what it says on the tin, it damps.

• Technically, damping applies to translation too (for airplanes, mostly to up/down motion), not only to rotation.
– Zeus
Nov 29 '19 at 6:50

The free dictionary is correct: Damping results from rotation.

Since all rigid-body rotations of a flying aircraft will occur around its center of gravity (this is a consequence of the conservation of momentum), that rotation will cause a vertical movement of parts which have a distance to the axis of rotation. This vertical movement changes the local angle of attack in a way that a moment is created which opposes that rotation.

Let's use a roll movement for example. The sketch below should indicate how the local angle of attack changes: The aircraft rotates around its lengthwise axis and one wingtip moves up while the other moves down (red arc segment arrows). The rolling speed $$\omega_y$$ caused by the aileron deflection $$\xi$$ causes a vertical movement $$\omega_y\cdot y$$ that grows with the distance y from the rolling axis. This vertical speed (green arrows) adds to the speed of the aircraft v$$_\infty$$ (cyan arrows) and results in an inclination of the local flow speed (red arrows). Since the ailerons are deflected, the local lift (blue arrows) should be different between left and right. But the change in local speed adds a lift increment which is of opposite strength and equalizes the lift change from the ailerons. This stops the aircraft from accelerating the roll movement.

If the aileron deflection is set to neutral, the rotation will now result in a lift difference between left and right, and since that lift difference acts on a lever arm y to the center of gravity, it causes a rolling moment. This rolling moment acts against the rolling motion, so the roll speed will quickly drop to zero. This is aerodynamic damping.

The lever arm y occurs twice: The local speed change grows linearly with y and the opposing moment, being the product of the lift change and y, also grows linearly with y. The result is a damping moment which is proportional to y squared.

The free dictionary article also mentions that damping depends on density. With lower density, the flight speed v$$_\infty$$ needs to grow so the dynamic pressure stays constant. With a greater v$$_\infty$$, the local speed change from rotation will proportionally be smaller, and so will be the damping moment. Since dynamic pressure is proportional to density and speed squared, damping goes down with the square root of density.

The sketch also illustrates another effect: Adverse yaw. Since the local lift in attached flow is approximately perpendicular to the local flow speed, the local lift points forward on the down moving wing and vice versa. This causes a yawing moment which will rotate the aircraft around its vertical axis unless opposed by a rudder deflection.

Pitch damping works the same: Just exchange the subscripts!

• Nice explanation @Peter Kampf. Do you have similar drawings/rationales for pitch and yaw as well? Nov 29 '19 at 8:10
• @Kolom: No, but they are quickly made. Nov 29 '19 at 11:24
• One question - I read somewhere, that during a turn we should even give opposite aileron, beacuse during a turn an upper wing moves faster than lower wing and thus upper wing generates greater lift force, and the result is overbanking tendency. And here, you write (correct me if I don't understand you properly) that at some roll angle without change in aileron deflection the roll rate becomes zero and if we move ailerons to neutral position the airplane will start rolling to level flight. What am I missing? Feb 1 at 11:50
• @Konrad What you know is correct. Most airplanes will fall into the roll when banked steeply enough - that is called roll instability. With moderate bank angles the aerodynamic and inertial uprighting tendency might be greater and bring the airplane back to level. But there are some which will enter a spiral dive when left to their own devices, even when flying level initially. There are several effects which influence the rolling tendency in parallel and the outcome depends on the individual design. But in general this happens slowly thanks to roll damping. Feb 1 at 12:38

Damping is a force that opposes motion, and is a function of velocity. It is an important factor in responses of equilibrium distortions - the classical way to explain this is to consider a spring/damper combination, as described here. Damping provides energy loss, so that the oscillation stops.

If an aeroplane is trimmed and stable, it can be flown hands-off in this equilibrium state. When now a wind gust blows the aeroplane nose up, the change in attitude will want to return the nose back to trimmed position. but like the spring system it will overshoot the trimmed position to the other side, return to trim etc.

Aerodynamic damping prevents oscillations from occurring indefinitely. It is damping provided by the aerodynamic resistance acting upon the oscillation movement of the aeroplane.