1.4 Aeronautical Definitions
about 25% of the chord, whereas for some more extreme sections it is more than
60% of the chord behind the leading edge.
Any airfoil section may be regarded as a thickness distribution plotted around
a camber line. American and British conventions differ in the exact derivation of
an airfoil section from a given camber line and thickness distribution. The British
convention is to plot the camber line and then plot the thickness ordinates from this,
perpendicular to the chord line. Thus the thickness distribution is in effect sheared
until its median line, initially straight, has been distorted to coincide with the given
camber line. The American convention is to plot the thickness ordinates perpendicular to the curved camber line, so the thickness distribution is regarded as bent until
its median line coincides with the given camber line.
Since the camber-line curvature is generally very small, the difference in airfoil
section shape given by these two conventions is also very small.
1.4.2 Wing Geometry
The planform of a wing is its shape seen on a plan (top) view of the aircraft.
Fig. 1.5 illustrates this and defines the symbols for the various planform-geometry
parameters. Note that the root ends of the leading and trailing edges have been connected across the fuselage by straight lines. An alternative to this is to produce the
leading and trailing edges, if straight, to the aircraft centerline.
Wingspan
The wingspan is the dimension b, the distance between the two wingtips. The distance
b/2 from each tip to the centerline is the wing semi-span.
e
edg
Wing tip
Le
Root
Fuselage side
ng
adi
c0
Fuselage side
CL
X
ΛLE
Direction
of flight
ΛTE
edge
Trailing
X
s
s
b = 2s
FIGURE 1.5
Wing planform geometry.
cT
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CHAPTER 1 Basic Concepts and Definitions
Chords
The two lengths cT and c0 are the tip and root chords, respectively; with the alternative convention, the root chord is the distance between the intersections with the
fuselage centerline of the leading and trailing edges produced. The ratio cT /c0 is the
taper ratio λ. Sometimes the reciprocal of this, c0 /cT , is taken as the taper ratio. For
most wings, cT /c0 < 1.
Wing Area
The plan-area of the wing including its continuation in the fuselage is the gross wing
area SG . The unqualified term wing area S usually means this gross wing area. The
plan-area of the exposed wing (i.e., excluding the continuation in the fuselage) is the
net wing area SN .
Mean Chords
A useful parameter is the standard mean chord or the geometric mean chord, denoted
c̄ and defined by c̄ = SG /b or SN /b. It should be clear whether SG or SN is used. The
definition may also be written as
b/2
c̄ =
c dy
−b/2
b/2
dy
−b/2
where y is distance measured from the centerline toward the starboard tip (right-hand
to the pilot). “Standard mean chord” is often abbreviated as “SMC.”
Another mean chord is the aerodynamic mean chord (AMC) which is denoted c̄A
or c̄¯ and is defined by
b/2
c̄ =
c2 dy
−b/2
b/2
c dy
−b/2
Aspect Ratio
Aspect ratio is a measure of the narrowness of the wing planform. It is denoted AR
and is given by
span b2
=
area
c
Note that only for a rectangular wing does AR = b/c.
AR =
Wing Sweep
The sweep angle of a wing is that between a line drawn along the span at a constant
fraction of the chord from the leading edge, and a line perpendicular to the centerline.
It is usually denoted . Sweep-back is commonly measured on the leading edge
1.5 Dimensional Analysis
Γ
Γ
FIGURE 1.6
Dihedral angle.
(LE ), on the quarter-chord line (i.e., the line one-quarter of the chord behind the
leading edge (1/4 )), or on the trailing edge (TE ).
Dihedral Angle
If an airplane is viewed from directly ahead, it is seen that the wings are generally
not in a single geometric plane but instead inclined to each other at a small angle.
Imagine lines drawn on the wings along the locus of the intersections between the
chord lines and the section noses, as in Fig. 1.6. Then the angle 2 is the dihedral
angle of the wings. If the wings are inclined upward, they are said to have dihedral;
if inclined downward, they have anhedral.
Incidence, Twist, Wash-out, and Wash-in
When an airplane is in flight, the chord lines of the various wing sections are not
normally parallel to the direction of flight. The angle between the chord line of a
given airfoil section and the direction of flight or of the undisturbed stream is the
geometric angle of attack α.
Carrying this concept of incidence to the twist of a wing, it may be said that, if
the geometric angles of attack of all sections are not the same, the wing is twisted.
If the angle of attack increases towards the tip, the wing has wash-in; if it decreases
towards the tip, the wing has wash-out.
1.5 DIMENSIONAL ANALYSIS
1.5.1 Fundamental Principles
The theory of dimensional homogeneity has more uses than those described in
Section 1.2.3. By predicting how one variable may depend on a number of others, that
variable may be used to direct an experiment, analyze experimental results, derive
analytical results, or minimize computational effort. For example, when fluid flows
past a circular cylinder the axis of which is perpendicular to the stream, eddies are
formed behind the cylinder at a frequency that depends on factors such as the size of
the cylinder, the speed of the stream, and so forth.
In an experiment to investigate the variation of eddy frequency, the obvious procedure is to take several sizes of cylinder, place them in streams of various fluids at
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