NAVWEPS OO-ROT-80  STABILITY AND CONTROL  In any system, the existence of static sta-  bility  does not necessarily guarantee the  existence of dynamic stability.  However,  the existence of dynamic stability  implies  the existence  of static stability.  quilibrium  conditions.  However, the dy-  namic behavior may be stable, neutral, or un-  stable. Chart D illustrates the mode of a  damped oscillation where the amplitude de-  creases  with time. The reduction of amplitude  with time indicates there is resistance to mo-  tion and that energy is being dissipated.  The  dissipation of energy-or “damping ’‘ -is  nec-  essary to provide positive dynamic stability.  If there is no damping in the system, the mode  of chart E is the result, an undamped oscilla-  tion.  Without damping, the oscillation con-  tinues with no reduction of amplitude with  time. While such an oscillation indicates posi-  tive static stability, neutral dynamic stability  exists. Positive damping is necessary  to elimi-  nate 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 damp-  ing cannot be obtained, a synthetic damping  must be furnished to provide the necessary  positive dynamic stability.  Any aircraft must demonstrate the required  degrees of static and dynamic stability.  If  the aircraft were allowed to have static in-  stability with a rapid rate of divergence, the  aircraft would be very difficult-if  not impos-  sible-to  fly. The degree of difficulty would  compare closely with learning to ride a uni-  cycle. In addition, positive dynamic stability  is mandatory in certain areas to preclude  objectionable continued oscillations of the  aircraft.  An aircraft is said to be trimmed if all  moments in pitch, roll, and yaw are equal to  zero.  The establishment of equilibrium at  various conditions of flight is the function of  the controls and may be accomplished by  pilot effort, trim tabs, or bias of a surface  actuator.  The term “controllability”  refers to the  ability of the aircraft to respond to control  surface displacement and achieve the desired  condition of flight.  Adequate controllability  must be available to perform takeoff and  landing and accomplish the various maneuvers  in flight.  An important contradiction exists  between stability  and controllability  since  adequate controllability does not necessarily  exist with adequate stability.  In fact, a high  degree  of stability tends to reduce the controlla-  bility of the aircraft. The general relation-  ship between static stability and controlla-  bility is illustrated by figure 4.3.  Chart F of figure 4.2 illustrates the mode of  a divergent oscillation.  This motion is stat-  ically stable since it tends to return to the  equilibrium position.  However, each subse-  quent return to equilibrium is with increasing.  velocity such that amplitude continues to  increase with  time.  Thus, dynamic insta-  bility 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 pitch-  ing oscillation of an aircraft. If a pilot un-  knowingly supplies control functions which  are near the natural frequency of the airplane  in pitch, energy is added to the system, nega-  tive damping exists, and the “pilot  induced  oscillation” results.  Figure 4.3 illustrates various degrees of  static stability by a ball placed on various  surfaces. Positive static stability is shown by  the ball in a trough; if the ball is displaced  from equilibrium at the bottom of the trough,  there is an initial tendency to return to equilib-  rium.  If it is desired to “control”  the ball  TRIM AND CONTROLLABILITY  247 