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before it encounters the disturbance. In principle, the angles of sideslip and yaw
are independent of each other. However, in the special case when the direction
~
. -.: r.
;t:j
260 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
n
h_Reference
r Line
b)
D
U
Fig.3.68 Definitions of angles ofyaw and sideslip.
-p
3.5.1 Criterion of DirectionaIStabilffl]
An airplane is said to be directionally stable if it has an inherent capability to
realign itself into the resultant wind whenever disturbed from steady level flight.
Mathematically, this requirement for directional stability can be expressed as fol-
lows:
or, in coefficient form,
Here, N is the yawing moment and
Np >O
Cnp > 0
Cn -
(3.23 8)
(3.239)
(3.240)
(3.241)
The concept of directional stabilit3r is schematically illustrated in Fig. 3.69.
STATIC STABILITY AND CONTROL
+
┏━━━━━━━━┳━━━━━━━┓
┃ ┃ ┃
┣━━━━━━━━╋━━━━━━━┫
┃\ ┃~~~r/ X N~t' ┃
┃ ┃ ┃
┃ / ┃ ┃
┗━━━━━━━━┻━━━━━━━┛
Fig. 3.69 Concept of static directional stability.
261
(Cnp)w = (C,,p)r.w + (cn~h.W
We will discuss these effects in the following sections.
(3.242)
VN = Vo(siricr -J: p siri:f')
(3.243)
As done before for the longitudinal static stability, we assume that the Cn~ of
the airplane is the sum ofindividual contributions caused by fuselage, wing, and
tail surfaces. A brief discussion on the qualitative effects of power is presented but
ignored in the analysis.
N
qSb
acn
ap
262 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
L
a)
X
┏━━━━┳━━━━━━┓
┃-rj._-_ ┃- ~lr--{v,l ┃
┣━━━━╋━━━━━━┫
┃ ┃ ┃
┗━━━━┻━━━━━━┛
cTa
vop
VoP
y
sin r
Fig. 3.70 Strip theory analysis of wing dihedral effect.
or, assuming a, p, and F to be small,
VN - Vo(ct +_ pr)
(3.244)
Note that "+" and "-" signs apply respectively to the right (starboard) and left
(port side) wings when sideslip is positive. The chordwise component of velocity
is given by
Vc - Vo cosct
- VO
The local angle of attack and local dynamic pressure are given by
VN
LYI = TVc
- CL +_ pr
(3.245)
(3.246)
(3.247)
(3.248)
STATIC STABILITY AND CONTROL
qi - 2lp(VA~ + Vc2)
~ 2J p Vo2
263
(3.249)
(3.250)
In the above equations, higher order terms like a2 and ct,B are ignored. Thus, we
observe that for a positive sideslip, the local dynamic pressure on both wings is
approximately equal to the freestream dynamic pressure. Furthermore, the leading
(starboard) wing experiences an increase in angle of attack and, therefore, an in-
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