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henceimprove the value of Ci.   x.
       For the blown fiap, high  pressure air is blown over the upper surface of the flap
as shown in Fig.  1.24g. In this way, considerable energy is added to stabilize the
upper surface boundary layer that delays flow separation. The magnitude of Cl,max
depends on the mass of the added air and the blowing velocity (momentum of the
blown air). A jet fiap (Fig. 1.24h) also functions in a similar way.
      The flap effectiveness depends on many factors. The mostimportant ones are the
fiap-chord-to-wing-chord ratio,shape of the fiap leading edge, and width ofthe gap.
For a finite wing, value of the increment in maximum lift coefficient also depends
 on the ratio of flap span to the main wing span, sweep angle ofthe flap hingeline, etc.
    Boundary-/ayer controL    Another method of increasing the maximum lift
coefficient of the wing is the application of boundary-layer control methods. The
slotted fiap and the Fowler-fiap are some forms of boundary-layer control although
this term"7s usually used for"9ctual flow control using boundary-layer suction or
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
<
 .
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-
　
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