can be assumed to take place with negligible 
changes in velocity. The second mode consists 
of a pitching oscillation during which the air- 
plane is being restored to equilibrium by the 
static stability and the amplitude of oscillation 
decreased by pitch damping. The typical mo- 
tion is of relatively high frequency with a 
period of oscillation on the order of 6.5 to 5 
seconds. 
For the conventional subsonic airplane, the 
second mode stick-fixed is characterized by 
heavy damping with a time to damp to half 
amplitude of approximately 0.5 seconds. IJsu- 
ally, if the airplane has static stability stick- 
fixed, the pitch damping contributed by the 
horizontal tail will assume sufficient dynamic 
stability for the short period oscillation. How- 
ever, the second mode stick-free has the possi- 
bility of weak damping or unstable oscilla- 
tions. This is the case where static stability 
does not automatically imply adequate dy- 
namic stability. The second mode stick-free is 
essentially a coupling of motion between the 
airplane short period pitching motion and ele- 
vator in rotation about the hinge line. Ex- 
treme care must be taken in the design of the 
control surfaces to ensure dynamic stability for 
this mode. The elevators must be statically 
balanced about the hinge line and aerodynamic 
balance must be within certain limits. Control 
system friction must be minimized as it con- 
tributes to the oscillatory tendency. If insta- 
bility were to exist in the second mode, “por- 
poising” of the airplane would result with 
possibility of structural damage. An oscilla- 
tion at high dynamic pressures with large 
changes in angle of attack could produce severe 
flight loads. 
The second mode has relatively short periods 
that correspond closely with the normal pilot 
response lag time, e.g., 1 or 2 seconds or less. 
There is the possibility that an attempt to 
forceably damp an oscillation may actually re- 
inforce the oscillation and produce instability. 
This is particularly true in the case of powered 
controls where a small input energy into the 
NAVWEPS 00-BOT-80 
STABILITY AND CONTROL 
control system is greatly magnified. In addi- 
tion, response lag of the controls may add to 
the problem of attempting to forceably damp 
the oscillation. In this case, should an oscilla- 
tion appear, the best rule is to release the con- 
trols as the airplane stick-free will demonstrate 
the necessary damping, Even an attempt to 
fix the controls when the airplane is oscillating 
may result in a small unstable input into the 
control system which can reinforce the oscilla- 
tion to produce failing flight loads. Because 
of the very short period of the oscillation, the 
amplitude of an unstable oscillation can reach 
dangerous proportions in an extremely short 
period of time. 
The third mode occurs in the elevator free case 
and is usually a very short period oscillation. 
The motion is essentially one of the elevator 
flapping about the hinge line and, in most 
cases, the oscillation has very heavy damping. 
A typical flapping mode may have a period of 
0.3 to 1.5 seconds and a time to damp to half- 
amplitude of approximately 0.1 second. 
Of all the modes of longitudinal dynamic 
stability, the second mode or porpoising oscil- 
lation is of greatest importance. The por- 
poising oscillation has the possibility of 
damaging flight loads and can be adversely 
affected by pilot response lag. It should be 
remembered that when stick-free the airplane 
will demonstrate the necessary damping. 
The problems of dynamic stability are acute 
under certain conditions of flight. Low static 
stability generally increases the period (de- 
creases frequency) of the short period oscil- 
lations and increases the time to damp to half- 
amplitude. High altitude-and consequently 
low density-reduces the aerodynamic damp- 
ing. Also, high Mach numbers of supersonic 
flight produce a decay of aerodynamic damping. 
MODERN CONTROL SYSTEMS