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Here, we assume that the load factor n given by Eq. (2.256) is smaller than or equal
to nUm, and the lift coefficient given by the Eq. (2.259) is smaller than or equal to
CL.rn,x. If these two conditions are not satisfied, the aircraft will not be capable
of producing the maximum turn rate predicted by Eq. (2.257), and the analysis of
this section is not valid.
With u - 1, the dimensional flight velocity and radius of turn are given by
V -.
R = (jSrg)
(2.260)
(2.261)
b 2
2 (Vg 2~=_2u+.
-. O
132 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
R = gj Y~-f
(2.262)
Substituting for load factor from Eq. (2.249) and using V - ulVR, we have
:~
R=g Lj_]
For Rnun,
dR
-, = (-,) (
-0
Solving, we get
Then,
The rate of tum is
2u "2(4zr1_4r13)
2 --uz)-l
J
~2~22~2~ 1
R n = -V~
g-f/2--f
c-o g
VR
The corresponding load factor and lift coefficient are given by
, 7
n-
CL -
z
(2.263)
(2.264)
(2.265)
(2.266)
(2.267.)
(2.268)
(2.269)
(2.270)
Here, it is presumed that n < nUm and CL < CL,max. If not, the aircraft cannot
achieve the Rmin predicted by Eq. (2.267), and the analysis presented in this section
is not valid.
AIRCRAFT PERFORMANCE
Turn for maximum /oad factor. We have
Ft2 = 2ZrL2 _ U4
For the maximum load factor nmax,
u =,~
rimax - z
133
(2.271)
(2.272)
(2.273)
(2.274)
Once again, it is presumed that nmax S nmn. Furthermore, Eq. (2.274) implies that
T < rilim W
- v (2.275)
m
In other words, the thrust should be limited as above. If not, the load factor will
exceed the structural limit factor, causing a structural failure during such a turn.
The flight velocity is given by
V = A~VR
With Em - I/2Jk~, Eq. (2.276) simplifies to
The lifi coefficient is given by
V:
(2.276)
(2-277)
2nmax W
CL - pS /-2 (2.278)
Substituting nmax ~ z and V = ~VR, Eq. (2.278) reduces to
CL -.
= CZ (2.279)
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