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f21t
= V- (3.179)
(n - l)l,g
= ~2 (3.180)
e_ _ _/...__
250 PERFORMANCE, STABILtTY, DYNAMfCS, AND CONTROL
\
\
-
V
n
/
-<Flight Path
Fig. 3.63 Induced angle of attack at horizontal tail during a pull-out maneuver.
With An :n - 1,
Actt.r lr9
A~ = \/2
Because both Aau and An are assumed to be small, we can write
(3.181)
dry/.r lr 9
d z7 - V2 (3.182)
At D, L' = n W and at A, L - W.. The airplane at Dis disturbedin angle of attack
and load factor compared to the steady lcveJ flight at A. These two disturbances
together lead to a net increase in lift AL so that
or
n-l= AC~
CL
An 1
dn 1
dCL = CL
(3.183)
(3.184)
(3.185)
(3.186)
(3.187)
Then we have
STATIC STABtLITY AND CONTROL
dcy,., dor/.r dn
dCL = dzdCL
lt9
- 2CL
lr pgS
N-
2W
1
251
(3.188)
(3.189)
(3.190)
= 2p,i (3.191)
where /ri - W]pgSI,. The parameter p.i is often called the longitudinal relative
density parameter.
The total angle of attack of the horizontal tail is given by
at - (aw - iw + /r - €) + Acr/.r (3.192)
d~Yt ]
d~ =' (1-:1 )+2;_
Stick-fixed maneuverpoint. We have
Cm - CLXa + Cmac*rn + Cmf - a,a;Vi 77t
(3.193)
(3.194)
= CLXa + Cmac.rn + Cm f - at[aw - iw + it - € + Aat.t] Vi r7, (3.195)
Differentiating with respect to CL, we get
ar fVi r/,
~C~),=a+(tlC~_)f--..V,,7,(1-:1: : 7/ (3.196)
2)ul
The stick-fixed maneuver point Nm is that position of the center of gravity where
(dCm]dCL)m - O and is given by
Nm = a.- (:C/ ),+V 7 [(1- ~) + 2p~,] (3.197)
Hm = Nm - Xc8
For a stable airplane, Hm is positive.
(3.198)
L' -. L + AL
n=1+ \CC,
252 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
Elevator required per g. Because ofincreased stability level during the ma-
neu'ver, the magnitude of the elevator deflection required for trim also increases.
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