fluid_mechanics

9.4 Lift 515
U
α
Symmetrical
U
α
c
Nonsymmetrical
F I G U R E 9.32
nonsymmetrical airfoils.
Symmetrical and
Not stalled
Stalled
At large angles of
attack the boundary
layer separates and
the wing stalls.
1903 Wright Flyer aircraft was 1.5 lbft 2 , while for the present-day Boeing 747 aircraft it is
150 lbft 2 . The wing loading for a bumble bee is approximately 1 lbft 2 1Ref. 152.
Typical lift and drag coefficient data as a function of angle of attack, a, and aspect ratio, a,
are indicated in Figs. 9.33a and 9.33b. The aspect ratio is defined as the ratio of the square of the
wing length to the planform area, a b 2 A. If the chord length, c, is constant along the length of
the wing 1a rectangular planform wing2, this reduces to a bc.
In general, the lift coefficient increases and the drag coefficient decreases with an increase
in aspect ratio. Long wings are more efficient because their wing tip losses are relatively more minor
than for short wings. The increase in drag due to the finite length 1a 6 2 of the wing is often
termed induced drag. It is due to the interaction of the complex swirling flow structure near
the wing tips 1see Fig. 9.372 and the free stream 1Ref. 132. High-performance soaring airplanes and
highly efficient soaring birds 1i.e., the albatross and sea gull2 have long, narrow wings. Such wings,
however, have considerable inertia that inhibits rapid maneuvers. Thus, highly maneuverable fighter
or acrobatic airplanes and birds 1i.e., the falcon2 have small-aspect-ratio wings.
Although viscous effects and the wall shear stress contribute little to the direct generation of
lift, they play an extremely important role in the design and use of lifting devices. This is because of
the viscosity-induced boundary layer separation that can occur on nonstreamlined bodies such as
airfoils that have too large an angle of attack 1see Fig. 9.182. As is indicated in Fig. 9.33, up to a certain
point, the lift coefficient increases rather steadily with the angle of attack. If a is too large, the
boundary layer on the upper surface separates, the flow over the wing develops a wide, turbulent
wake region, the lift decreases, and the drag increases. This condition, as indicated by the figures in
the margin, is termed stall. Such conditions are extremely dangerous if they occur while the airplane
is flying at a low altitude where there is not sufficient time and altitude to recover from the stall.
1.4
1.2
1.0
= 7
= 3
0.8
0.6
C L
0.4
0.03
= 1 = 1 = 3
0.02
0.2
C D
= 7
0
0.01
–0.2
–0.4
0
–10 0 10
20
–10 0 10 20
α , degrees
α , degrees
(a)
(b)
F I G U R E 9.33 Typical lift and drag coefficient data as a function of angle of attack and the
aspect ratio of the airfoil: (a) lift coefficient, (b) drag coefficient.