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blowing methods. In the boundary-layer suction method, low energy fluid from
the upper surface is removed by the application of suction. This process helps to
delay the fiow separation to higher angles of attack. Significant increases in max-
imum lift coefficients have been obtained by this method. Another advantage of
this method is that the application of suction also stabilizes the laminar boundary
layer by delaying the fiow transition. This results in a significant reduction in the
skin-friction drag. An example of application of this method is the C-140 JetStar
aircraft.
     In boundary-layer control using the blowing methods, high-energy air is blown
tangentially on the upper surface of the wing and the flap as shown in Fig.  1.24g.
This addition of energy helps to delay boundary-layer fiow separat.ion on the
upper surface. As a result, the maximum lift coefficientincreases. This method of
boundary layer controlis sometimes called "circulation control:'In this method,
the main emphasis is to enhance the lift coefficient without worrying too much
about the drag coefficient. Therefore, the drag coefficient of an airfoil with blown
fiap may be lugher than that of the basic airfoil.
     However, the main disadvantage of boundary-layer control based on suction or
blowing is the mechanical complexity and additional weight.
1.6   Aerodynamic Characteristics ot Finite Wings
      Theories for calculating thelift and moment characteristics of finite wings at sub-
sonic speeds fall mainly into two categories:  1) the lifting line theory and 2) lifhng
surface theories. In lifting line theorjl only the spanwise lift distribution is con-
sidered. The chordwise variation is not considered. Hence, the lifting line theory
is more suitable for application to high-aspect ratio wings. Lifting surface theo-
ries also consider the chordwise variation oflift distribution and hence give more
accurate results for lift and pitching-moment curve slopes of finite wings. In gen-
eral, lifting surface theoriestl-l0 are more difficult to apply than lifting line the-
ories and hence are typically used for low-aspect ratio wings. It is beyond the
scope of this text to go into the details of these two types of wing theories. In the
REVIEW OF BASIC AERODYNAMIC PRINCIPLES
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 .
Wing
Fig. 1.27    Horseshoe vortex model of a finite wing,
27
 following, the lifting line theory will be used to obtain expressions for the lift-curve
 slope and induced-drag coefficient of finite wings.
          In liffingline theory, the lifting wingis modeled as ahorseshoe vortex as depicted
in Fig. 1.27. The part of the vortex sheet attached to the wing surface is called the
 bound vortex. The bound vortex continues beyond the wing tips in the downstream
direction, and these parts of the horseshoe vortex are called the trailing vortices or
tip vortices. According to Helmholtz theorem, a'vortex system cannot end abruptly
 in a fiuid medium. Therefore, the system ofbound vortex and trailing vortices must
be closed in some manner. This closure is provided by the so-called starting vortex
as shown in Fig. 1.27.
    To understand how the starting vortex is a physical reality, let us consider the
motion of a finite wing, which starts to move forward impulsively, i.e., it is im-
parted a forward velocity instantaneously. As explained e~rlier, the first batch of
fiuid particles goes around the wing sections smoothly, forming the front and rear
stagnation points as shown in Fig. 1.28a. Once this flow pattern is formed, pres-
sure gradients come into existence. Of particular interest is the adverse pressure
gradient on the upper surface. As a result, the flow separates on the upper surface
upstream of the trailing edge, and the fiow coming from the lower surface cannot
go around the sharp trailing edge as it did at t - O_ Thus, the curved or vortex fiow
formed at t =O (Fig. 1.28a) is no more formed for t > 0 (Fig. 1.28b), and that
formed at t = O is swept away in the downstream direction.

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28                 PERFORMANCE, STABILJTY, DYNAMICS, AND CONTROL
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