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. 
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. 
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. 
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. 
TRIM AND CONTROLLABILITY 
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. 
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,