Page 126 - Aeronautical Engineer Data Book

102 Aeronautical Engineer’s Data Book
the principle of moments the following expres­
:
sion can be derived for k CP
x AC
k CP = –
C M AC
c C L cos + C D sin
Assuming that cos 1 and C sin 0 gives:
D
x AC
k CP –
C M AC
c C L
6.6 Supersonic conditions
As an aircraft is accelerated to approach super­
sonic speed the equations of motion which
describe the flow change in character. In order
to predict the behaviour of airfoil sections in
upper subsonic and supersonic regions,
compressible flow equations are required.

6.6.1 Basic definitions
M Mach number
M ∞ Free stream Mach number
Critical Mach number, i.e. the value of
M c
which results in flow of M ∞ = 1 at some
location on the airfoil surface.
Figure 6.6 shows approximate forms of the
pressure distribution on a two-dimensional airfoil
around the critical region. Owing to the complex
non-linear form of the equations of motion which
describe high speed flow, two popular simplifica­
tions are used: the small perturbation approxima­
tion and the so-called exact approximation.

6.6.2 Supersonic effects on drag
In the supersonic region, induced drag (due to
lift) increases in relation to the parameter
2
M – 1 function of the plan form geometry of
the wing.
6.6.3 Supersonic effects on aerodynamic centre
Figure 6.7 shows the location of wing aerody­
namic centre for several values of tip chord/root
chord ratio ( ). These are empirically based
results which can be used as a ‘rule of thumb’.