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┃i-, ,. ┃ ┃
┣━━━━━━━━━━━╋━━━━━━━━━━━━━━━━━┫
┃~ -\ 6 ┃ ┃
┃~-y ┃ ┃
┃i-y ┃ ┃
┗━━━━━━━━━━━┻━━━━━━━━━━━━━━━━━┛
Fig. 3.94 Concept of static lateral stabiLity.
295
Here, L is the rolling moment, (Remember that Lhe symbol L is also used to de-
note the lift,) Thus, an airplane with Ctp < O is said to be laterally stable and that
with Cip > 0 is laterally unstable. An airplane with Ctp = 0 is said to be neutrally
stable. An airplane that is neutrally stable or unstable in roll can still be fiown
but needs constant intervention from the pilot to counter roll disturbances, which
can be quite annoying. Usually, such airplanes are made closed-loop stable using
feedback control systems, which we will study in Chapters 5 and 6.
3.6.2 Evaluation of Lateral Startn7itjr
As before, we assume that the lateral stability of an airplane, as measured by the
parameter Cip, is equal to the sum ofindividual contributions from the fuselage,
wing, and tail surfaces. The effects ofpower on lateral stability are generally small
and ignored.
Fuse/age contribution. The direct contribution ofthe fuselage to lateral sta-
bility is neYgligible. However, because of its significant interference effect on the
wing, it makes an indirect contribution as discussed in the following section under
wing contribution.
Wing contribution. The wing contribution to lateral stability mainly depends
on 1) wing-fuselage interference, 2) wing dihedral angle, and 3) wing leading-edge
sweep. A brief discussion of these effects is given in the following section.
Wing-fuse/age interference. This interference effect depends on the loca-
tion of the wing~A high wing produces a stable contribution, and a low wing
produces an unstable or destabilizing contribution.
~p = ~~
Cl = q~-b
296 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
a) High-wing configuration
b) Low-wing configuration
Fig. 3.95 Schematicillustration of wing-fuselage interfeRnce in sideslip.
Ctl = ct i:pr
qi = ;p\/o2
(3.341)
(3.342)
The wing contribution to lateral stability at low subsonic speeds can be estimated
using the strip theory as follows.
Let c(y) be the local chord and ao(Y) be the local sectional lift-curve slope. The
lift force developed by the elemental strip RT of width dy on the'right wing is
given by
STA11C STABILITY AND CONTROL
dL = qtc(y)dy Cu
= 2ip Vo2c(y)ao(Y)(a + f3r)dy
The rolling moment due to the e,lemental strip RT is given by
dL = -~p Vo2c(y)ao(Y)(cy + f/r)y dy
The rolling moment due to the right wing is given by
297
(3.343)
(3.344)
(3.345)
~R = - ~p \/o2 ['/2 c(y)ao(y)(a, + pr)y dy (3.346)
Similarly, the rolling moment due to the left wing is given by
L, = ~p\jo2 "1~c(y)ao(y)(ce - pI')ydy (3.347)
The total rolling moment
- ~ = -p I/o2f/~ [b/2c(y)ao(Y)Y dy
or, in coefficient form,
P b/2
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