STABILITY AND CONTROL

An aircraft must have satisfactory handling qualities in addition to adequate performance. The aircraft must have adequate stability to maintain a uniform flight condition and recover from the various disturbing influences. It is necessary to provide sufficient stability to minimize the workload of the pilot. Also, the aircraft must have proper response to the controls so that it may achieve the inherent performance. There are certain conditions of
flight which provide the most critical require­ments of stability and control and these condi­tions must be understood and respected to accomplish safe and efficient operation of the aircraft.

DEFINITIONS

STATIC STABILITY

An aircraft is in a state of equilibrium when the sum of all forces and all moments is equal

POSITIVE STATIC STABILITY

to zero. When an aircraft is in equilibrium, there are no accelerations and the aircraft continues in a steady condition of flight. If the equilibrium is disturbed by a gust or deflec­tion of the controls, the aircraft will experi­ence acceleration due to unbalance of moment or force.

The static stability of a system is defined by the initial tendency to return to equilibrium conditions following some disturbance from equilibrium. If an object is disturbed from equilibrium and has the tendency to return to equilibrium, positive static stability exists. If the object has a tendency to continue in the direction of disturbance, negative static stability or static instability exists. An intermediate condition could occur where an object dis­placed from equilibrium remains in equilibrium in the displaced position. If the object subject to a disturbance has neither the tendency to return nor the tendency to continue in the dis­placement direction, neutral static stability ex­ists. These three categories of static stability are illustrated in figure 4.1. The bail in a trough illustrates the condition of positive static stability. If the ball is displaced from equilibrium at the bottom of the trough, the initial tendency of the ball is to return to the equilibrium condition. The ball may roll back and forth through the point of equilib­rium but displacement to either side creates the initial tendency to return. The ball on a hill illustrates the condition of static insta­bility. Displacement from equilibrium at the hilltop brings about the tendency for greater displacement. The ball on a flat, level surface illustrates the condition of neutral static sta­bility. The ball encounters a new equilibrium at any point of displacement and has neither stable nor unstable tendencies.

The term "static” is applied to this form of stability since the resulting motion is not considered. Only the tendency to return to equilibrium conditions is considered in static stability. The static longitudinal stability of an aircraft is appreciated by displacing the aircraft from some trimmed angle of attack. If the aerodynamic pitching moments created by this displacement tend to return the air­craft to the equilibrium angle of attack the aircraft has positive static longitudinal stability.

DYNAMIC STABILITY

While static stability is concerned with the tendency of a displaced body to return to equilibrium, dynamic stability is defined by the resulting motion with time. If an object is disturbed from equilibrium, the time history of the resulting motion indicates the dynamic stability of the system. In general, the system will demonstrate positive dynamic stability if the amplitude of motion decreases with time. The various conditions of possible dynamic behavior are illustrated by the time history diagrams of figure 4.2.

The nonoscillatory modes shown in figure

4.2 depict the time histories possible without cyclic motion. If the system is given an initial disturbance and the motion simply subsides without oscillation, the mode is termed "sub­sidence" or "deadbeat return.” Such a motion indicates positive static stability by the tend­ency to return to equilibrium and positive dy­namic stability since the amplitude decreases with time. Chart В illustrates the mode of "divergence" by a noncyclic increase of ampli­tude with time. The initial tendency to con­tinue in the displacement direction is evidence of static instability and the increasing ampli­tude is proof of dynamic instability. Chart C illustrates the mode of pure neutral stability. If the original disturbance creates a displace­ment which remains constant thereafter, the lack of tendency for motion and the constant amplitude indicate neutral static and neutral dynamic stability.

The oscillatory modes of figure 4.2 depict the time histories possible with cyclic motion. One feature common to each of these modes is that positive static stability is demonstrated in the cyclic motion by tendency to return to

DISPLACEMENT

NON-OSCILLATORY MODES

equilibrium conditions. However, the dy­namic behavior may be stable, neutral, or un­stable. Chart D illustrates the mode of a damped oscillation where the amplitude de­creases with time. The reduction of amplitude with time indicates there is resistance to mo­tion and that energy is being dissipated. The dissipation of energy—or “damping”—is nec­essary to provide positive dynamic stability. If there is no damping in the system, the mode of chart E is the result, an undamped oscilla­tion. Without damping, the oscillation con­tinues with no reduction of amplitude with time. While such an oscillation indicates posi­tive static stability, neutral dynamic stability exists. Positive damping is necessary to elimi­nate the continued oscillation. As an example, an automobile with worn shock absorbers (or “dampers”) lacks sufficient dynamic stability and the continued oscillatory motion is neither pleasant nor conducive to safe operation. In the same sense, the aircraft must have sufficient damping to, rapidly dissipate any oscillatory motion which would affect the operation of the aircraft. When natural aerodynamic damp­ing cannot be obtained, a synthetic damping must be furnished to provide the necessary positive dynamic stability.

Chart F of figure 4.2 illustrates the mode of a divergent oscillation. This motion is stat­ically stable since it tends to return to the equilibrium position. However, each subse­quent return to equilibrium is with increasing, velocity such that amplitude continues to increase with time. Thus, dynamic insta­bility exists. The divergent oscillation occurs when energy is supplied to the motion rather than dissipated by positive damping. The most outstanding illustration of the divergent oscillation occurs with the short period pitch­ing oscillation of an aircraft. If a pilot un­knowingly supplies control functions which arc near the natural frequency of the airplane in pitch, energy is added to the system, nega­tive damping exists, and the “pilot induced oscillation” results.

In any system, the existence of static sta­bility does not necessarily guarantee the existence of dynamic stability. However, the existence of dynamic stability implies the existence of static stability.

Any aircraft must demonstrate the required degrees of static and dynamic stability. If the aircraft were allowed to have static in­stability with a rapid rate of divergence, the aircraft would be very difficult—if not impos­sible—to fly. The degree of difficulty would compare closely with learning to ride a uni­cycle. In addition, positive dynamic stability is mandatory in certain areas to preclude objectionable continued oscillations of the aircraft.