Overview of Stability
Many of the tools in Ferram Aerospace Research (FAR) deal with the concept of stability. In order to understand these tools, one must first understand the concept of stability in the context of airplanes and rockets.
There are two primary concepts of stability: static stability and dynamic stability. Static stability is the tendency for a system to, when disturbed from equilibrium, return to equilibrium. Dynamic stability is what happens to the system after it has been disturbed from equilibrium. Each of these types of stability is important to consider when designing airplanes and rockets with FAR installed.
Equilibrium is a state that, if undisturbed, will not change. In other words, if nothing touches something that is in equilibrium it will not move.
As mentioned above, static stability is the tendency of a system to return to equilibrium when disturbed. For example, consider a ball inside of a bowl, pictured below. This ball is in equilibrium.
If the ball is displaced in either direction, the ball will want to return to its initial position at the bottom of the bowl. This is an example of a system that is statically stable.
Now consider a ball that, instead of being placed inside of a bowl, is placed on top of a mound. This ball is also in equilibrium, but it is not stable.
If the ball is displaced in either direction, it will not return to its initial state. It will gain speed and roll off of the mound. This is an example of a system that is statically unstable.
Finally, consider a ball that is placed on top of a flat table. This ball is also in equilibrium.
If the ball is displaced in either direction, it will not return to its initial state, so it is not statically stable. It will also not roll any further away from the initial state, so it is not statically unstable. This is referred to as neutral stability or marginal stability.
Under construction
An aircraft must have its center of lift behind the center of mass to be statically stable. Statically unstable aircraft are almost always unflyable in KSP; in the real world, computer control and quick acting control surfaces can actively stabilize such designs, but they remain rare.
With stock aerodynamics, the ASAS is actually sometimes capable to make unstable aircraft (barely) flyable: unfortunately, ASAS doesn't work correctly under FAR, since it doesn't account for realistic deflection times of the control surfaces. High speed operation of ASAS in FAR will cause oscillations. (This paragraph might become outdated in the future, if ASAS becomes moddable and Ferram can adapt it to FAR).
Aerodynamic forces will tend to rotate an aircraft around its center of mass. If an aircraft has its c. of lift aft of the c. of mass, the overall lift from its surfaces causes a nose-down moment: an increase in lift will act to dive the airplane.
In level flight, this nose-down tendency is exactly counteracted by the elevators: when pilot input, or an external disturbance, increases the pitch angle and thus lift, the downward moment will increase, and vice versa: the aircraft resists changes to its pitch attitude. This is negative feedback, the basis of stability.
Were the CoL to be forwards of the CoM, a slight pitch-up generating higher lift would tend to raise the nose higher, generating still higher lift, and the positive feedback if unchecked would very rapidly flip the aircraft on its back. Similar considerations can be made for the yaw axis.
A high stability margin (i.e. a very aft center of lift) is not without drawbacks, though: a very stable aircraft will have, by definition, sluggish controls. Also, the strong nose-down tendency might actually overpower the pitch controls, making it impossible to raise the nose over some angle and, in extreme cases, sending the aircraft into an unrecoverable dive.
Special care should be taken for aircraft that have a large percentage of weight in fuel, or that drop cargo during flight: if the center of mass moves significantly, stability characteristics could be altered drastically.
The "conventional" tailplanes, placed behind the wing, have a stabilizing effect. To mantain level flight, they will produce downforce to counteract the nose-down moment due to the wing; so, they create a small aerodynamic penalty.
The "canard" configuration, with elevators in front of the wing (often right at the nose) has the control surfaces producing positive lift in level flight, which is desirable. It also often has a longer moment arm (longitudinal distance between surfaces and the CoM) than could be possible with a conventional tails, making controls more effective. Canards are destabilizing, though: when the aircraft pitches up, the canard lift will increase and tend to pitch up even more. The wing must be configured to ensure static stability, which could partly counteract the aerodynamic advantages.
A very efficient configuration is the "three lifting surfaces" concept, with both canards and rear mounted surfaces, all oriented to produce positive lift in level flight: if the rear surfaces have a larger pitching moment (product of lift and moment arm) than the forward ones, the combined effect is stabilizing.
Pitch and yaw static stability are the most immediately important, and are primarily affected by the center of lift position. Roll stability, while often a secondary concern, is a more complex phenomenon. A number of factors influence it, of which the most important is the dihedral angle of the wings.
Wings have a (positive) dihedral if they are angled upwards, with the tips higher than the root: the dihedral effect will tend to restore the airplane to level flight after it banks to one side. Negative dihedral has the opposite effect, and is often called "anhedral"; contrarily to an unstable center of lift position, anhedral might be beneficial in some cases.
Another factor that influences roll stability is the wing vertical position: a high wing (with the fuselage slung under it) is stabilizing in roll, while low wings are destabilizing. Low-wing aircraft are common, though, and often counteract this effect with dihedral angle.