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Let 'VN be the fiight velocity of the straight-wing aircraft. Then for equal normal
dynamic pressure, the flight velocity of the swept-wing aircraft will be equal to
V/cos A.
For the straight-wing aircraft,
L -. 21p VA~SCt (1.61)
and for the swept-wing aircraft,
s.= -,p( / )2SCls
(1.62)
50 . PERFORMANCE, STABIUTY, DYNAMICS, AND CONTROL
Z
HI
Fig.1.51 Effect of wing sweep on drag coefficient at high speeds.
Equating the two,
Similarly, we can show that
Cts = Ct COS2 A
= Cd CoS2 A
(1.63)
(1.64)
Thus, for equal lift aDd drag forces (which means equal engine power), an
aircraft with swept wings can fly at a higher Mach number by a factor of l/cos A
compared to an aircraft with straight unswept wings, and the use of wing sweep
considerably softens the amount of drag-coefficient rise in the transonic range.
It may be noted these observations are mainly based on considering two-
dimensional wings. However, for finite or thrce-dimensional wings, the benefits
appear to be smaller and closer to the factor of 1/\ instead of l/cos A as
assumed here. A schematic variation ofdrag coefficient for various values of wing
sweep is shown in Fig. 1.51.
While the application of wing sweep offered significant benefits for high-speed
fiight, it is accompanied by poor subsonic capabilities because ofits high induced
drag and low lift-curve slope. Because of the low value of lift-curve slope, the
angle of attack needs to be considerably high during takeoff and landing, which
may create problems oftail scraping and pilot visibility. Funhermore, conventional
high-lift devices like the trailing-edge fiaps perform poorly on swept wings. For
those aircraft missions requiring very high levels of both subsonic and supersonic
performance,itis advantageous to use variable sweep. Examples of variabl~:sweep
designs are the F-lll, F-14, and B- 1 aircraft. Variable-sweep aircraft position the
wings at zero or small sweep angle for low-speed operations such as landing and
takeoff and then sweep the wings as required for high-speed operation.
by
REVIEW OF BASIC AERODYNAMIC PRINCIPLES
l, .-
┏━━━┓
┃A ┃
┣━┳━┫
┃ ┃ ┃
┣━┻━┫
┃A ┃
┗━━━┛
Section AA
a) Straight wing
b) Swept-oack wing
ko sin a
Section AA
Fig. 1.52 Straight and swept wings at angle of attack.
V sina
taricteff - Voo osA~osa
CXe:rf ~ a sec A
Let a be the lift-curve slope of the wing. Then,
L -. (;:p Vo% COS2 A) Sa(a sec A)
1
-. - 2
s'ir) cl'
51
(1.65)
(1.66)
(1.67)
(1.68)
To understand why the lift-curve slope of a swept wing is smaller compared to
a straight wing, consider straight and swept wings, both operating at an angle of
attack ce (Fig. 1.52). Then the effective angle of attack of the swept wing is given
'jq
;s
.a
't
.:/
' .,
:t-.
. .:;
:.t
:--
' :!
- ::
./+:;
.,
.i
Jt
;;
.":
;
.' 7
:-:
. ":
. '-
:: f:
;
:-;
':!
;:
:s:
';::'
,t
:.r
o
. .:
;/
}l :
! -'
:}
i.
52 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
According to the conventional definition oflift, we have
Equating the two, we get
or
where
L = ~p Vo%SCr.s
Cu. = aa cos A
ay - a cos A
a, = (aac. ),.
(1.69)
(1.70)
(1.71)
(1.72)
From the consideration of delaying the adverse effects ofcompressibility to higher
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