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By a dimensional analysis, it can be shown that a number of these variables can
be grouped into two important nondimensional parameters, the Reynolds number
Re and the Mach number M.
The Reynolds number is the ratio ofinertial forces to viscous forces.
L force
Re = 3 uff (1.1)
s force
We assume
Change in momentum/time
= S~ear stress x Area
d 1
dt = tune
Voo
=L
av voa
ay = L
(1.2)
(1.3)
(1.4)
(1.5)
(1.6)
(1.7)
where L is the characteristic dimension (length) of the body. Then
p Voo L
Re - - (1.8)
,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
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