# Aircraft Stability - Theory of Flight

When an airplane is in straight-and-level flight at a constant velocity, all the forces acting on the airplane are in equilibrium. If that straight-and-level flight is disrupted by a disturbance in the air, such as wake turbulence, the airplane might pitch up or down, yaw left or right, or go into a roll. If the airplane has what is characterized as stability, once the disturbance goes away, the airplane will return to a state of equilibrium.

## Static Stability

The initial response that an airplane displays after its equilibrium is disrupted is referred to as its static stability. If the static stability is positive, the airplane will tend to return to its original position after the disruptive force is removed. If the static stability is negative, the airplane will continue to move away from its original position after the disruptive force is removed. If an airplane with negative static stability has the nose pitch up because of wake turbulence, the tendency will be for the nose to continue to pitch up even after the turbulence goes away. If an airplane tends to remain in a displaced position after the force is removed, but does not continue to move toward even greater displacement, its static stability is described as being neutral.

## Dynamic Stability

The dynamic stability of an airplane involves the amount of time it takes for it to react to its static stability after it has been displaced from a condition of equilibrium. Dynamic stability involves the oscillations that typically occur as the airplane tries to return to its original position or attitude. Even though an airplane may have positive static stability, it may have dynamic stability which is positive, neutral, or negative.

Imagine that an airplane in straight-and-level flight is disturbed and pitches nose up. If the airplane has positive static stability, the nose will pitch back down after the disturbance is removed. If it immediately returns to straight­and-level flight, it is also said to have positive dynamic stability. The airplane, however, may pass through level flight and remain pitched down, and then continue the recovery process by pitching back up. This pitching up and then down is known as an oscillation. If the oscillations lessen over time, the airplane is still classified as having positive dynamic stability. If the oscillations increase over time, the airplane is classified as having negative dynamic stability. If the oscillations remain the same over time, the airplane is classified as having neutral dynamic stability.

Figure 1 shows the concept of dynamic stability. In view A, the displacement from equilibrium goes through three oscillations and then returns to equilibrium. In view B, the displacement from equilibrium is increasing after two oscillations, and will not return to equilibrium. In view C, the displacement from equilibrium is staying the same with each oscillation.

 Figure 1. Dynamic stability

## Longitudinal Stability

Longitudinal stability for an airplane involves the tendency for the nose to pitch up or pitch down, rotating around the lateral axis, which is measured from wingtip to wingtip. If an airplane is longitudinally stable, it will return to a properly trimmed angle of attack after the force that upset its flight path is removed.

The weight and balance of an airplane, which is based on both the design characteristics of the airplane and the way it is loaded, is a major factor in determining longitudinal stability. There is a point on the wing of an airplane, called the center of pressure or center of lift, where all the lifting forces concentrate. In flight, the airplane acts like it is being lifted from or supported by this point. This center of lift runs from wingtip to wingtip. There is also a point on the airplane, called the center of gravity, where the mass or weight of the airplane is concentrated. For an airplane to have good longitudinal stability, the center of gravity is typically located forward of the center of lift. This gives the airplane a nose-down pitching tendency, which is balanced out by the force generated at the horizontal stabilizer and elevator. The center of gravity has limits within which it must fall. If it is too far forward, the forces at the tail might not be able to compensate and it may not be possible to keep the nose of the airplane from pitching down.

In Figure 2, the center of lift, center of gravity, and center of gravity limits are shown. It can be seen that the center of gravity is not only forward of the center of lift, it is also forward of the center of gravity limit. At the back of the airplane, the elevator trailing edge is deflected upward to create a downward force on the tail, to try and keep the nose of the airplane up. This airplane would be highly unstable longitudinally, especially at low speed when trying to land. It is especially dangerous if the center of gravity is behind the aft limit. The airplane will now have a tendency to pitch nose up, which can lead to the wing stalling and possible loss of control of the airplane.

 Figure 2. Longitudinal stability and balance

## Lateral Stability

Lateral stability of an airplane takes place around the longitudinal axis, which is from the airplane’s nose to its tail. If one wing is lower than the other, good lateral stability will tend to bring the wings back to a level flight attitude. One design characteristic that tends to give an airplane good lateral stability is called dihedral. Dihedral is an upward wing angle, with respect to the horizontal, and it is usually just a few degrees.

Imagine a low wing airplane with a few degrees of dihedral experiencing a disruption of its flight path such that the left wing drops. When the left wing drops, this will cause the airplane to experience a sideslip toward the low wing. The sideslip causes the low wing to experience a higher angle of attack, which increases its lift and raises it back to a level flight attitude. The dihedral on a wing is shown in Figure 3.

 Figure 3. The dihedral of a wing

## Directional Stability

Movement of the airplane around its vertical axis, and the airplane’s ability to not be adversely affected by a force creating a yaw type of motion, is called directional stability. The vertical fin gives the airplane this stability, causing the airplane to align with the relative wind. In flight, the airplane acts like the weather vane we use around our home to show the direction the wind is blowing. The distance from the pivot point on a weather vane to its tail is greater than the distance from its pivot point to the nose. So, when the wind blows, it creates a greater torque force on the tail and forces it to align with the wind. On an airplane, the same is true. With the CG being the pivot point, it is a greater distance from the CG to the vertical stabilizer than it is from the CG to the nose. [Figure 4]

 Figure 4. Directional stability caused by distance to vertical stabilizer

## Dutch Roll

The dihedral of the wing tries to roll the airplane in the opposite direction of how it is slipping, and the vertical fin will try to yaw the airplane in the direction of the slip. These two events combine in a way that affects lateral and directional stability. If the wing dihedral has the greatest effect, the airplane will have a tendency to experience a Dutch roll. A Dutch roll is a small amount of oscillation around both the longitudinal and vertical axes. Although this condition is not considered dangerous, it can produce an uncomfortable feeling for passengers. Commercial airliners typically have yaw dampers that sense a Dutch roll condition and cancel it out.

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