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T
 CL
_L
  b  <_
   - 2-
Fig.1.17   Wing planform parameters.
REVIEW OF BASIC AERODYNAMIC PRINCIPLES                17
Positive
Negar;ivc Twist
a) Wash-in
             l,) Wash-out
Fig.1.18   Concept ofwing twist.
where A,is the taper ratio given by
}., = ct                                         (1.27)
   Cr
Here, ct is the tip chord and Cr iS the root chord.
     To have the desired variation ofaerodynamic loading and stall pattem along the
span, wing sections are sometimes given what is called the twist.lf a wing is so
twisted that the angle of attack increases from root to the tip, such a twist is called
wash-in. If it is the other way, i.e.,  the angle of attack decreases from the root to
the tip, then that type of twist is called wash-out. The concepts of wash-in and
wash-out are illustrated in Fig. 1.18.
1.5   Aerodynamic Characteristics of Wing Sections
       Typical pressure distribution over an airfoil at an angle of attack is schematically
shown in Fig. 1.19. Arrows toward the surface indicate positive pressures, and
those that point away from the surface represent negative pressures or suction.
An integration of the pressure distribution over the body gives a net or resultant
force that can be resolved into two components called lift and drag. The component
of the force perpendicular to the freestream directionis called the lift,and that along
the freestream direction is called the &ag. The point along the chordline where
the resultant force acts is known as the center of pressure. Thus, if the moment
reference point coincides with the center ofpressure, the pitching momentis zero.
For any other moment reference point along the chord, the pitching moment is
in general nonzero. Therefore, to specify forces acting on the airfoil, one has to
specify the lift, drag, and pitching moments and the location of moment reference
pomt on the chord. Because values of the lift, drag, and pitching moments vary
with the speed, it is usual to specify the aerodynamic characteristics of an airfoil
18
pERFORMANCE, STAB/LITt, DybIAMtcs, AND CONTROL
                                                                                                                                    Rcsultant Forcc
                                   19
REV/EW OF BAS\C AERODYNAMIC PRINCIPLES
Fig.1.20 Schematici/lustrationofairfoilcharacteristics'
20                 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
the moment reference point. The sign of g depends on the location ofthe moment
reference point.  If this point is located close to the leading edge, the incrementallift
caused by angle ofattack acts aft of the moment reference point, and the associated
incrementin pitclung moment will be negative, making g  < 0. On the other hand,if
 the moment reference pointislocated close to the trailing edge, then theincremental
lift acts ahead of the moment reference point, and the corresponding incremental
pitching moment is positive; hence g > 0. Therefore, there must be some point
on the chordline where g = 0 so that the incremental pitcfung moment caused
by angle of attack is zero and the pitching-moment coefficient remains constant
with respect to angle of attack and equal to Cmo. This point is called aerodynamic
center. In other words, all the incremental lift caused by angle of attack acts at the
aerodynamic center. The pitching-moment coefficient with aerodynamic center as
　
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