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48 PERFORMANCE, STABILITY, DYNAMICS: AND CONTROL
a) Swept-back wing
b) Swept-forward wing
Fig. 1.49 Schematic illustration of effect of wing sweep.
--
REVIEW OF BASIC AERODYNAMIC PRINCIPLES 49
/
/
t
/
a) Subsonic leading edge
--
b) Supersonic leading edge
Fig.1.50 Subsoruc and supersorucleading edges.
A > Lr
A < Li
To demonstrate the advantage of sweep, consider two aircraft, one straight wing
and the other swept-back wing. We assume that the gross weight, wing area, and
airfoil section ofboth aircraft are identical. Furthermore, assume that both aircraft
are required to operate at the same values of normal dynamic pressure, lift, and
drag forces.
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
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