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aerodynamic characteristics.
7.2.3 Prevention of Inertia Coupfing
For an aircraft prone to divergencein yaw, we can improveits resistance toinertia
coupLing by increasing the level of static directional stability Cnp or by increasing
the inertia in roll Ir relative to the inertia in pitch Iy. These methods call for major
oh-4
638 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
modifications and have to be considered early in the design cycle. As we know, the
vertical tailis the major contributor to the static directional stability parameter Cnp.
Therefore, to increase C ip, we have to incrcase the vertical tail area and vertical tail
arm. However, this may cause some problems in spiral stability. Thus, a tradeoff
is involved in deciding how much directional stability can be pernutted on a given
aircraft. The second option calls for distributing more mass into the wings such as
placing fuel tanks in the wings. Also, we can have a larger wing span or a higher
aspect ratio. This explains why the earlier aircraft that had a short bulky fuselage
and high aspect ratio wings did not experience inertia coupling problems.
Similarly, for an aircraft prone to pitch divergence, we can increase its resis-
tance to inertia coupling by increasing the static longitudinal stabilit)r level Cma
or increasing the inertia in roll Ix relative to the inertia in yaw Iz. The main fac-
tors affecting the longitudinal stability parameter C are the horizontal tail area,
horizontal tail moment arm, and the location of the center of gravity. The designer
has to make a proper selection of these variables. However, the second option is of
very limited valuein this case because we cannotincrease Ix withoutincreasing Iz.
Another option is to use a feedback control system, which wiU increase both the
damping in pitch and damping in yaw. Referring to Fig. 7.3, we observe that.this
will result in widerung the area, which connects regions I and III. However, we
will not be going into the design of such a feedback control system. The interested
reader may refer elsewhereJ for additionalinformation on this subjecL .
Example 7.1
To illustrate the above theory, we consider the following aircraft.6 The data given
in Ref. 6 is an FPS (foot-pound-second) system, whicl , convertel
as given in the following: mass - ,0872 x , _-~w}x~~~:5:;4881:3edltj04jkg,m"j:
Iy = 7J417 x l04 k~Dr2,1z = 8.7850 x l04 kg/,m~:: Sar5ar7 mSC.j
mean aerodynamic chord c = 3.442 m,wing span b = :nr - ~0.095,
Cmq = -3.5, Cmct - -0.36, Cip - 0.057, Cyp = -0.28, CLa : 3.85, and
CIP = -0.255. All the derivatives are per radian.
For fiight at a velocity of 210.6168 m/s and a dynamic pressure of 9432.4 N/m2,
examine the stability o9this aircraft in steady rolling maneuvers.
I I)=87 x850 l04_l.4881xl04
Iy ) 7.7417x~0~
-. 0.9425
(I I,' = 7.7417 x l04 -1.4881x l04
8~850 x~0~
- 0.7118
The pitch divergence and yaw divergence boundaries are shown in Fig. 7.4.
INERTIA COUPLING AND SPIN
We have
(#)2
Fig. 7.4 Stability diagram for Example 7.1.
/y, = ql.cS-
7,7417 x l04
= 9432.4 x 35 0233 x 3.442
- 0.06808
(-oo -
I~I = qjSb
= 2.299 rad/s
8.7850 x l04
= 9432 4 x 35.0233 x 11.1557
- 0.0238
639
Texts Published in the AIAA Education Series (continued)
Optinuzation of Observation and
Control Processes
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