NAVWEPS DGROT-50 
STABBITY AND CONTROL 
spiral motion is so gradual that the pilot can 
control the tendency without difficulty. 
Dutch roll is a coupled lateral-directional 
oscillation which is usually dynamically stable 
but is objectionable because of the oscillatory 
nature. The damping of this oscillatory mode 
may be weak or strong depending on the prop- 
erties of the airplane. The response of the air- 
plane to a disturbance from equilibrium is a 
combined rolling-yawing oscillation in which 
the rolling motion is phased to precede the 
yawing motion. Such a motion is quite unde- 
sirable because of the great havoc it would 
create with a bomb, rocket, or gun platform. 
Generally, Dutch roll will occur when the 
dihedral effect is large when compared to static 
directional stability. Unfortunately, Dutch 
roll will exist for relative magnitudes of dihe- 
dral effect and static directional stability be- 
tween the limiting conditions for directional 
divergence and spiral divergence. When the 
dihedral effect is large in comparison with 
static directional stability, the Dutch roll 
motion has weak damping and is objectionable. 
When the static directional stability is strong 
in comparison with the dihedral effect, the 
Dutch roll motion has such heavy damping 
that it is not objectionable. However, these 
qualities tend toward spiral divergence. 
The choice is then the least of three evils. 
Directional divergence cannot be tolerated, 
Dutch roll is objectionable, and spiral diver- 
gence is tolerable if the rate of divergence is 
low. For this reason the dihedral effect should 
be no more than that required for satisfactory 
lateral stability. If the static directional sta- 
bility is made adequate to prevent objection- 
able Dutch roll, this will automatically be 
sufficient to prevent directional divergence, 
Since the more important handling qualities 
are a result of high static directional stability 
and minimum necessary dihedral effect, most 
airplanes demonstrate a mild spiral tendency. 
As previously mentioned, a weak spiral tend- 
ency is of little concern to the pilot and cer- 
tainly preferable to Dutch roll. 
The contribution of sweepback to the lateral 
dynamics of an airplane is significant. Since 
the dihedral effect from sweepback is a function 
of lift coefficient, the dynamic characteristics 
may vary throughout the flight speed range. 
When the swept wing airplane is at low C,, the 
dihedral effect is small and the spiral tendency 
may be apparent. When the swept wing air- 
plane is at high C,, the dihedral effect is in- 
creased and the Dutch Roll oscillatory tendency 
is increased. 
An additional oscillatory mode is possible 
in the lateral dynamic effects with the rudder 
free and the mode is termed a “snaking” oscil- 
lation. This yawing oscillation is greatly 
affected by the aerodynamic balance of the 
rudder and requires careful consideration in 
design to prevent light or unstable damping 
of the oscillation. 
CONTROL IN ROLL 
The lateral control of an airplane is ac- 
complished by producing differential lift on 
the wings. The rolling, moment created by 
the differential lift can be used to accelerate 
the airplane to some rolling motion or control 
the airplane in a sideslip by opposing dihedral 
effect. The differential lift for control in 
roll is usually obtained by some type of ailerons 
or spoilers. 
ROLLING MOTION OF AN AIRPLANE. 
/ When an airplane is given a rolling motion in 
flight, the wing tips move in a helical path 
through the air. As shown in figure 4.29, a 
rolling velocity to the right gives the right 
wing tip a downward velocity component and 
the left wing tip an upward velocity com- 
ponent. By inspection of the motion of the 
left wing tip, the velocity of the tip due to 
roll combines with the airplane flight path 
velocity to define the resultants motion. The 
resulting angle between the flight path vector 
and the resultant path of the tip is the helix