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n - -.
W
TEm
z= W
V
li -. -
VR
VR -
(2.12)
(2.13)
(2.14)
(2.15)
Here, E is known as the lift-to-drag ratio and the maximum value of E is denoted
by Em. The parameter n, which is the ratio of lift to weight, is called the load
factor. The parameter z is the nondimensional thrust, and u is the nondimcnsional
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72 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
Then,
which gives
CD CDO+kCZ
C~ -- - CL
d CD -CDO+kC2
d~ C)=~
-. 0
CL -
(g )-..= 2~
Inverting Eq. (2.19) we obtain
Em = (g ),ax
1
= 2~
Let C2 denote the value oflift coefficient when E = Em. Then,
Cz =
(2.16)
(2.17)
(2.1 8)
(2.19)
(2.20)
(2.21)
Schematic variations of CL, CD, and E with angle of attack are shown in Fig. 2.3.
The drag of the aircraft is given by .
D = ;:p V2S(CDO + kCZ) (2.22)
With L - n W, we have
, 2n W
CL = p~2S (2.23)
Then,
D = ~p V2S[CDO + (%kV T2.)]
1
= 2pS[CDOV2+ (%kV V; )] (2.24)
T
coo
L
AIRCRAFT PERFORMANCE
cc
Fig. 23 Variation ofaerodynamic parameters with angle of attack.
Substituting V = u VR, where VR iS given by Eq. (2.15), we obtain
D = 2V~ (.2+ -,,)
Equations (2.7) and (2.8) for static performance can now be expressed as
or
and
73
(2.25)
z W VI
Em 2g(.2+.,)_Wsiny.0 (2.26)
2zt12 _ ll4 _ t12 _ 2Em U2 sin y = O (2.27)
n -cosy =O
(2.28)
Equations (2.27) and (2.28) describe the static performance of the airplane for such
flight conditions as steady level fiight, steady climb, range, and endurance. Before
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