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,L
The Mach number is defined as the ratio of velocity of the body Va, to the speed
of sound a.
M Voo (1.9)
a
1
= (,::.:,)
l71 = pL3
2 PERFORMANCE, STABILI-fY, DYNAMICS, AND CONTROL
Chordline
Lowcr surface
a) Arirforl at posib:ve angle of attack
UWer Su~cc
Chordlinc
b) Airfoil at negatrve angle of attack
Fig.'l.l DeffiuOon ofangle ofattack.
The attitude of the body relative to the airstream is also known as the angle of
attack a, which is defined as the angle between the airstream and a reference line
fixed to the body as shown in Rg. 1.1. For airplane wings and horizontal tail, the
reference line is typically the chordline and, for fuselages, it is the centerline.
1.2 Fluid Flow over Wings and Bodies
The hydrodynanuc theory of fluids deals with inviscid or ideal fiuid fiows. This
theory predicts that the fluid fiow always closes behind the body no matter what
the body shape is. The ideal fluid fiow pattern for a two-dimensional wing and a
circular cylinder are schematically shown in Fig. 1.2. This theory also states that
there is no loss of energy in the flow. However, all the real flurds have viscosit)r to
varying degrees. Because ofviscosity, a realfiuid always sticks to the body surface.
In other words, the fluid velocity at any point on the body surface is always zero.
However, the ideal fluid theory predicts a finite, nonzero velocir}r on the body
surface. In fact, in the ideal fluid theory, the body surface is a part ofjthe stagnation
streamline. At the front and rear stagnation points (Si and S2 in Fig. 1.2), the
fiuid velocity is zero. Downstream of the front stagnation point Si, the velocity
increases and may even exceed the freestream value and then drop back to zero at
the rear stagnation point S2. A typical variat.ion of the velocity on the surface of
an airfoil and a circular cylinder in crossfiow are shown in Figv1.3. For a circular
cylinder, the peak velocit)r occurs at the maximum thickness point and is equal to
2 Vw, where Va, iS the freestream velocity.
In real fiuid flow, the velocity on the surface of the body is equal to zero and rises
rapidly to thelocal value Vt within a small distance 8 as shownin Fig. 1.4a. The thin
layer in which the increase from zero to local value Vi occurs is called the bound-
ary layer. The concept of boundary layer was introduced by L. Prandtl in 1904.1
REVIEW OF BASIC AERODYNAMIC PRINCIPLES 3
Positivc
Pret
~
a) Streamlined body (airfoil)
V
Voo
b) Bluff body (circular cylinder)
Fig. 1.2 Ideal fluid flow over bodies.
Z
90
e
180
Fig. 1.3 lrelocity distribution over bodies in ideal fluid flow.
Negaji'e Pressure's
4 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
y
y
0 V
a) Dypical boundary-layer profile
V(y)
Equal Areas
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