# What does it mean for a plane to be aerodynamically stable?

I've heard that most planes (excepting fighter jets) are "aerodynamically stable." What does that mean?

Let's say you're cursing around in a Cessna 172 without autopilot, and you take your hands off the controls. What happens?

• Will the plane stay at the same pitch and avoid stalls and dives?
• Will it stay at the same altitude?
• Will it say at the same heading?
• Will it correct each of these as the plane is buffeted by turbulence?
• Didn't your parents tell you not to curse in a 172? – copper.hat Feb 7 '15 at 19:21
• @copper.hat wow!! I think I might leave that typo in there cuz I find it so funny... – raptortech97 Feb 7 '15 at 19:22
• Do! It creates a wonderful visual :-). – copper.hat Feb 7 '15 at 19:24
• Haha, I absolutely love that image, definitely leave it – Jon Story Feb 7 '15 at 20:17
• "Let's say you're cursing around in a Cessna 172" Sounds like some of the guys I hear on the CTAF around here. – reirab Feb 8 '15 at 5:45

## Static stability

is the tendency of a system to return to its initial state after a disturbance. Typical disturbances in case of airplanes are:

• Flying into a vertical or horizontal gust
• A jerk on the stick

The classic explanation is with a ball sitting in a pit. Whenever its position is changed by a disturbance, it will roll back towards the center. This does not mean that it will stop there - in an ideal world free of friction it will keep moving back and forth like a pendulum.

This is static stability. Broadly speaking, static stability is achieved by placing the center of gravity ahead of the neutral point, the point in which all additional forces due to a change in angle of attack can be summarized. There are two neutral points, one for longitudinal stability and one for directional stability. In both cases the change in angle of attack or sideslip will create a correcting moment around the center of gravity, pulling the aircraft back on its old path.

Even altitude stability can be achieved, but here we take advantage of the fact that air becomes less dense the higher you climb. If the aircraft is trimmed for horizontal flight at a certain altitude, an altitude change will mean that the power setting does no longer match drag at this new altitude. The aircraft will either climb or sink, depending on the altitude change, until the old altitude has been reached again.

In all cases you will experience overshoots and oscillations around the trim point. It can even happen that these overshoots become worse the longer the oscillation lasts (the phugoid motion in a glider is a good example). To stop the oscillations, you need to add

## Dynamic stability

which describes the behavior of the aircraft over time. In most cases, friction will ensure that motions die down, and sometimes aircraft need little helpers like yaw dampers to get those under control.

You mention stalls and dives: They can indeed occur in a statically stable airplane. Low drag means low damping, therefore many high performance gliders have a dynamically unstable phugoid motion. I know, Wikipedia spells this wrongly, but the explanation is OK, so I linked it nonetheless. If you wait long enough after an initial upset, the oscillations will become so severe that the aircraft stalls at the upmost point of the cycle.

If you keep enough altitude and have no traffic nearby, this is fun to try.

## Spiral dive

Note that I omitted to say something about roll stability so far. The glider (and your Cessna 172) will also start to roll, and in many cases the roll motion will increase more quickly than the phugoid, so you might need to try several times before you get a phugoid-induced stall. Most aircraft have a weak tendency to increase roll angle and to eventually fall into a spiral dive.

There is no aerodynamic mechanism to right the aircraft up after a roll disturbance. Sorry, @kevin, but dihedral won't help - it only works in case of sideslip.

• I'm not quite clear why there would be no possible aerodynamic mechanism to right an aircraft after a roll disturbance. If one were to drop a plane with a "V"-shaped wing, then (once the plane started falling) whichever side was lower would experience more lift, would it not, establishing an equilibrium where both wings were equally high? What would prevent such a principle from establishing roll stability in flight? – supercat Feb 7 '15 at 22:03
• @supercat: There is an inertial mechanism, but no aerodynamic mechanism. Your plane will be helped by dihedral to fly coordinated turns, that's all. If you want to know more, post another question. – Peter Kämpf Feb 7 '15 at 22:29
• @supercat: The upwards component of lift, which is the one we want for keeping the plane in the air, is indeed largest for the lower wing, but the component perpendicular to the line between that wing's center of lift and the roll axis, which is the one that makes the plane roll, is the same for both wings. – Marcks Thomas Feb 8 '15 at 11:27
• I edited this and replaced all instances of "phygoid" with "phugoid", which I think are the respective German and English terms for what I was always taught to just call "Long Period Mode". I hope you don't mind. – AEhere supports Monica Aug 6 '19 at 11:54
• @AEhere I do mind indeed. "Phugoid" is wrong - the word comes from ancient greek and the correct spelling should be "Phygoid". That the English literature is using the - in my eyes - wrong spelling should not mean that I repeat the same mistake blindly. German, by the way, uses the correct spelling. – Peter Kämpf Aug 6 '19 at 20:47

Your guesses are pretty correct - an "aerodynamically stable" aircraft tends to stay (relatively) straight and level if the controls are let go.

## Pitch

Let's say the aircraft's elevator is trimmed to fly level (maintaining the same altitude). You push on the yoke to lower the nose, then release the pressure on the control. The nose-down altitude allows the aircraft to pick up more speed. As speed increases, the wing generates more lift, and the aircraft slowly pitches up. If you pull on the yoke then let go, the nose-up altitude will slow the plane down, which reduces lift. When lift is reduced, the nose drops, picking up speed. A similar argument applies if the plane's pitch is altered by a gust.

This stability is called Longitudinal Stability. It is closely related to the forward/aft position of the Center of Gravity (CG). An aircraft with an aft CG has less longitudinal stability.

## Roll

Similarly, the ability of the plane to level its wings when banked is called Lateral Stability. If you roll the plane right 10 degrees then let go, it has a tendency to slowly roll left, going 7 degrees right, 5 degrees right, eventually to almost level.

A Wing Dihedral is a design which adds lateral stability.

## Yaw

This is called Directional Stability. Similar to pitch and roll, it is the tendency for an airplane to recover from a disturbance in the yawing plane.

# Stability vs maneuverability

The more stable an aircraft is, the less maneuverable. This is a natural trade-off following the laws of physics. Cessna 172s are very stable, suitable for student pilots. But you can't make a Cessna 172 do very rapid changes. Aerobatic aircrafts and fighter jets can respond to pilot inputs very rapidly, but controlling one requires much more skill.

*On single engine propeller planes like the Cessna 172, the torque spinning the propeller (usually clockwise) tends to roll the aircraft counterclockwise (i.e. left) if the controls are fully released. This is due to the "action and reaction" physics principle.

• Thanks! And for altitude, the pitch is the relatively constant so vertical speed should stay around 0, right? But if there's turbulence or something and the plane drops 200ft, is there anything that makes a plane "want" to return to it's cruise altitude or will it stay at the new altitude? – raptortech97 Feb 7 '15 at 18:54
• Planes fly "iso-pressure". What that means is, flying at a specific "altitude" is really flying at along a constant atmospheric pressure. It's very seldom a plane drops literally 200 feet in space. Rather, it travels horizontally level, but due to a rapid change in the atmospheric pressure, the altimeter reading jumps 200 feet. A dropped altimeter reading means the planes enters a higher pressure region, but flying at the same speed it was moments before. There's excess lift, so it'll climb. – kevin Feb 7 '15 at 19:03
• You are very optimistic when it comes to roll stability. Most aircraft will slowly diverge into a spiral dive. Try it! – Peter Kämpf Feb 7 '15 at 19:21
• @PeterKampf edited the roll angle to 10. Yea at 30 you may need counter aileron to keep it from rolling too far. – kevin Feb 7 '15 at 19:25
• Normally you don't need roll input, just patience, to experience a spiral dive. Dihedral will not help, btw. – Peter Kämpf Feb 7 '15 at 19:56

Stability has a number of definitions from a control system perspective, but most boil down to a system not doing anything 'unexpected'.

Just to be clear in the following, pitch, roll, yaw refer to angles not rate of change of angles.

Roll tends to be stable because there is a feedback mechanism (dihedral, or low COG) as Kevin's answer points out.

Pitch & yaw tend to be stable because the rudder/elevator are at the rear (or high wing loading for a canard) which provides a feedback mechanism.

Without feedback (such as from the pilot or autopilot) no matter how well you have trimmed the aircraft, external noise (pressure, air density, changing wind, fuel burnoff, loud cursing, etc.) will result in some slight climb/descent and turn. This is because it is (i) difficult to get the pitch, yaw, roll to be exactly what you want and (ii) things change.

However, if you are checking your map during a flight, things will remain mostly the same for a while. Of course, this depends on the aircraft, and what options you have to trim.

• It is not nonsense and I don't understand why you say that. Obviously it won't right an inverted aircraft, but it does move the associated mode into the left half plane (\$\mathbb{C}\$, here). It works for aircraft, model planes and the same principle works to improve a boat's metacentric stability. Can you provide some background as to why you say that it is not stable? – copper.hat Feb 7 '15 at 20:30
• Just wait long enough ... if you think that roll stabilizes you simply did not let the aircraft fly without control inputs long enough. Regarding links: ($\mathbb{C}$, here) looks like a link gone bad. Regarding dihedral: It will roll the aircraft back, but not to level. Roll angle will build up not in one go, but in steps. But build up it will. – Peter Kämpf Feb 7 '15 at 20:46