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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.
REVIEW OF BASIC AERODYNAMIC PRINCIPLES 15
Most of the NACA airfoils are classified among three types of airfoils: the four
digit the five digit, and the series 6 sections. The nomenclature and meaning of
various digits are explained with the help of following examples:
1) Four digit series, example NACA 2412
2: The maximum camber of the meanline is 0.02c
4: The position of the maximum camber is at 0.4c.
12: The maximum thickness is 0.12c.
2) Five digit series, example NACA 23012
2: The maximum camber of the meanline is approximately equal to 0.02c.
The design lift coefficient is 0.15 times the first digit of the series, which in
this case is 2.
30: The position of maximum camber is 0.30l2 = 0.15c.
12: The maximum thickness is 0.12c.
3) Series 6 sections, example NACA 653-418
6: Series designation.
5: The minimum pressure is at 0.5c.
3: The drag coefficientis near mirtimum value over a range oflift coefficients
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