limit is set by the minimum permissible con- 
trollability while the aft c.g. limit is set by 
the minimum permissible stability. 
LONGITUDINAL DYNAMIC STABILITY. 
All previous considerations of longitudinal 
stability have been concerned with the initial 
tendency of the airplane to return to equilib- 
rium when subjected to a disturbance. The 
considerations of longitudinal dynamic sta- 
bility ate concerned with time history response 
of the airplane to these disturbances, i.e., the 
variation of displacement amplitude with time 
following a disturbance. From previous deli- 
nition, dynamic stability will exist when the 
amplitude of motion decreases with time and 
dynamic instability will exist if the amplitude 
increases with time. 
Of course, the airplane must demonstrate 
positive dynamic stability for the major longi- 
tudinal motions. In addition, the airplane 
must demonstrate a certain degree of longitu- 
dinal stability by reducing the amplitude of 
motion at a certain rate. The requited degree 
of dynamic stability is usually specified by 
the time necessary for the amplitude to reduce 
to one-half the original value-the time to 
damp to half-amplitude. 
The airplane in free flight has six degrees of 
freedom: rotation in roll, pitch, and yaw and 
translation in the horizontal, vertical, and 
lateral directions. In the case of longitudinal 
dynamic stability, the degrees of freedom can 
be limited to pitch rotation, vertical and 
horizontal translation. Since the airplane is 
usually symmetrical from port to starboard, 
there will be no necessity for consideration of 
coupling between longitudinal and lateral- 
directional motions. Thus, the principal vari- 
ables in the longitudinal motion of an airplane 
will be: 
(1) The pitch attitude of the airplane. 
(2) The angle of attack (which will differ 
from the pitch attitude by the inclination of 
the flight- path). 
(3) The flight velocity. 
NAVWEPS DD-801-80 
STABILITY AND CONTROL 
(4) The displacement or deflection of the 
elevator when the stick-free condition is 
considered. 
The longitudinal dynamic stability of an 
airplane generally consists of three basic modes 
(or manners) of oscillation. While the longi- 
tudinal motion of the airplane may consist of a 
combination of these modes, the characteristics 
of each mode are sufficiently distinct that each 
oscillatory tendency may be studied separately. 
The first mode of dynamic longitudinal sta- 
bility consists of a very long period oscillation 
referred to as the phagoid. The phugoid or long 
period oscillation involves noticeable vatia- 
tions in pitch attitude, altitude, and airspeed 
but nearly constant angle of attack. Such an 
oscillation of the airplane could be considered 
as a gradual interchange of potential and 
kinetic energy about some equilibrium airspeed 
and altitude. Figure 4.20 illustrates the char- 
acteristic motion of the phugoid. 
The period of oscillation in the phugoid is 
quite large, typical values being from 20 to 100 
seconds. Since the pitching rate is quite low 
and only negligible changes in angle of attack 
take place, damping of the phugoid is weak and 
possibly negative. However, such weak or 
negative damping does not necessarily have any 
great consequence. Since the period of oscilla- 
tion is so great, the pilot is easily able to 
counteract the oscillatory tendency by very 
slight and unnoticed control movements. In 
most cases, the necessary corrections ate so 
slight that the pilot may be completely un- 
aware of the oscillatory tendency. 
Due to the nature of the phugoid, it is not 
necessary to make any specific aerodynamic 
provisions to contend with the oscillation. 
The inherent long period of the oscillation al- 
lows study to be directed to more important 
oscillatory tendencies. Similarly, the diffet- 
ences between the stick-fixed and stick-free 
phugoid are not of great importance. 
The second mode of longitudinal dynamic sta-