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airfoil. In other words, an airfoil is a two-dimensional wing with a constant airfoil
section.
      The objective of analytical, computational, or experimental investigations is to
design an efficient airfo:l section that has a low drag coefficient, a high lift-to-drag
ratio, a high value of maximum lift coefficient, a small  value of pitching-moment
coefficient, and a sraooth gradual stall.
    Since the early days of aviation, several efforts-ljave been made to design and
develop series of efficient airfoil sections. Notable among these are the works at
Goettingen, Germany; Royal Aircraft Establishment in the United Kingdom; and
National Advisory Committee for Aeronautics (NACA) in the United States. The
NACA airfoils hayve gained wide acceptance throughout the world and have influ-
enced the airfoil design of others. The NACA airfoils have been used on several
commercial and military airplanes that have been built over the years. The follow-
 ing is a brief description of NACA airfoil sections. For more information, refer to
Ref. 2.
       The typical geometry of an airfoilis shown in Fig.  1.14. The line drawn midway
between the upper and lower surfaces is called the meanline. The leading and
trailing edges are defined as the forward and rearward extremities, respectively,
REVIEW OF BASIC AERODYNAMIC PRINCIPLES                 13
A\
Fig.1.13    Wing section geometry.
of the meanline. The straight line joining the leading and trailing edges is called
the chordline, and the length of the chordline is usually known as the chord of
the airfoil. The distance between the meanline and the chordline measured normal
to the chordline is denoted by yc  The variation of yc along the chord defines the
camber of the airfoil.ln view of this, the meanline is also known as the camberline.
The distance between the upper and lower surfaces measured perpendicular to the
meanline is called the thickness of the airfoil. The abscissas, ordinates, and slopes
of the meanline are designated as xc, Yc, and tan0, respectively. If xu and Yu
represent, respectively, the abscissa and ordinates of a point on the upper and
lower surfaces of the airfoil and Yr is the ordinate of the symmetrical thickness
distribution at chordwise position x, then the upper and lower surface coordinates
y
Leading Edge /lr
=:y
Fig. 1.14    Airfoil geometry.
PERFORMANCE, STABfU-fY, DYNAMtCS, AND CONTROL
are given by the following relations:
                                              xu - xc - yr sin O
Yu - Yc + Yt cos0
xt = xc + Yt sin0
yL = Yc -- Yr coS0
(1.15)
(1.16)
(1.17)
(1.18)
To find the center of the leading-edge radius, we draw a line through the end of
the chordline at the leading edge with a slope equal to the slope of the meanline at
that point and mark a distance equal_ to the leading-edge rach~ along that line.
     Thus, the geometrical shape of the airfoilis specified by three parameters, the
leading-edge radius p, the variation of Yc along the chordline, and~:e variation of
yr along the chordline for the symmetric thickness distribution.
  Basically there are two types of airfoil sectio.ns, symmetrical and cambered
sections. A symmetrical airfoil is one whose lower surface is a mirror image of
the upper surface about the chordline. In other words, a symmetrical airfoil has
zero camber, or the meanLine coincides with the chordline as shown in Fig. 1.15a.
If the meanline is convex up, there is a positively cambered airfoil as shown in
Fig. 1.15b. If the meanline is concave up, then it is a negatively cambered airfoil
as shown in Fig. 1.15c.
     For a symmetrical airfoil, Ci: Cm - O at a - 0. Here, C, and Cm  are the sec-
tional lift and pitching-moment coefficients of the airfoil.lf UOL denotes the angle
of attack when q -.0 then, for a symmetrical zrkfoil, CtOL -0. For a positively
cambered airfoil, at ct - 0, q > 0 and, therefore, c:rOL < O.If Cmo iS denoted as thi
value of the pitching-moment coefficient at a  - aOL then, for a positively cambered
airfoil, q     < 0. Similarly, for a negatively cambered airfoil,aOL > 0 and Cmo > 0.
a) Symmetric airf'oil
c) Negatively cambered airfoil
Fig.1.15 Typic.alairfoilshapes.
　
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