of oscillation which coincide with the pilot- 
control system response lag. Also, the high 4 
flight condition provides the aerodynamic 
capability for failing flight loads during the 
oscillation. 
If a pilot induced oscillation is encountered 
the pilot must rely on the inherent dynamic 
stability of the airplane and immediately 
release the controls. If the unstable excitation 
is continued, dangerous oscillation amplitudes 
will develop in a very short time. 
ROLL COUPLING 
The appearance of “inertia coupling” prob- 
lems in modern airplanes was the natural result 
of the progressive change in aerodynamic and 
inertia characteristics to meet the demands of 
high speed flight. Inertia coupling problems 
were unexpected only when dynamic stability 
analyses did not adequately account for the 
rapid changes in aerodynamic and inertia 
characteristics of airplane configurations. The 
The term of “intertia coupling” is somewhat 
misleading because the complete problem is 
one of aerodynamic as well as inertia coupling. 
“Coupling” results when some disturbance 
about one airplane axis causes a disturbance 
about another axis. An example of uncoupled 
motion is the disturbance provided an airplane 
when subjected to an elevator deflection. The 
resulting motion is restricted to pitching 
motion without disturbance in yaw or roll. 
An example of, coupled motion could be the 
disturbance provided an airplane when sub- 
jected to rudder deflection. The ensuing mo- 
tion can be some combination of yawing and 
rolling motion. Hence, the rolling motion is 
coupled with the yawing motion to define the 
resulting motion. This sort of interaction 
results from aerodynamic characteristics and is 
termed “aerodynamic coupling.” 
A separate type of coupling results from the 
inertia characteristics of the airplane conligura- 
tion. The inertia characteristics of the com- 
plete airplane can be divided into the roll, yaw, 
NAVWEPS OO-SOT-80 
STABILITY AND CONTROL 
and pitch inertia and each inertia is a measure 
of the resistance to rolling, yawing, or pitching 
acceleration of the airplane. The long,slender, 
high-density fuselage with short, thin wings 
produces a roll inertia which is quite small in 
comparison to the pitch and yaw inertia. 
These characteristics are typical of the modern 
airplane configuration. The more conventional 
low speed airplane may have a wingspan 
greater than the fuselage length. This type of 
configuration produces a relatively large roll 
inertia. A comparison of these configurations 
is shown in figure 4.34. 
Inertia coupling can be illustrated by con- 
sidering the mass of the airplane to be con- 
centrated in two elements, one representing the 
mass ahead of the c.g. and one representing the 
mass behind the c.g. There are two principal 
axis systems to consider: (1) the aerodynamic, 
or wind axis is through the c.g. in the relative 
wind direction, and (2) the inertia axis is 
through the c.g. in the direction of the two 
element masses. This axis system is illus- 
trated in figure 4.34. 
If the airplane shown in figure 4.34 were in 
some flight condition where the inertia axis 
and the aerodynamic axis are alined, no inertia 
coupling would result from rolling motion. 
However, if the inertia axis is inclined to the 
aerodynamic axis, rotation about the aero- 
dynamic axis will create centrifugal forces and 
cause a pitching moment. In this case, a 
rolling motion of the aircraft induces a pitch- 
ing moment through the action of inertia 
forces. This is “inertia coupling” and is 
illustrated by part B of figure 4.34. 
When the airplane is rotated about the 
inertia axis no inertia coupling will exist but 
aerodynamic coupling will be present. Part 
C of figure 4.34 shows the airplane after rolling 
90” about the inertia axis. The inclination 
which was initially the angle of attack (a) is 
now the angle of sideslip (-6). Also the 
original zero sideslip has now become zero