that
the
tips
a:re
subsonic, while the leading and
trailing
edges are supersonic.
The
co1'l'esponding change
in
the
quantity
apia.
=
(Ph

Pu)/a.
near a
tip
with the distance from the leading edge (in per cent of
the
chord)
evaluated
for a wing
with
a pentagonal planform
at
M...,
=
=
1.61
is shown in Fig.
B.10.2.
The coefficient
apia.
is
constant
in
the
region between
the
leading edge aud the Mach cones issuing
from
the
vertex and
tips
of
the
wing, on the section confined by
the
tips
and
trailing
edges, and also
by
the
Mach waye reflected from a
tip.
A break in the curve cliaracterizing a change in the pressure
drop coeRicient occurs on the
Mr.lch
lines
and
is a l'esult of the break
in
the configuration
of
the wing tip.
The found pressure distribution
sud
formulas (8.9.27)
flnd
(8.9.28)
are used to determine the lift, momeut and ccntreolpressure coeffi
den
ts. Figure
B.9.4
shows curves characterizing tIlc change in
the
values of
C'II
and
c
p
for a pentagonal wing. These values should
be
Ch.
S.
A
Wing
in
.!I
Supersonic Flow
3S1
fig.
8.10.2
Distl'ihuliul\
of
the quantity
~l/~=le~;;:~~1
~1~~
a\\"~th
supersonic
lea(liDg
I'liges
(s~c
tioo
:1.4)
determined provided
that
i
...
·VM;'

t
>
I.",
tlln
XI'
i.e.
if
the
leading edge is supersonic.
If
a
wing
has
subsonic iealling edges (see
Fig. 8.8.1),
Lhe
flow
oYer
Lhe
section of
the
surface ilt'lweell the eligt·s
and
the
Mach lines issuing from points
E
and
}{
is
aHect('d
llr
a \'ol'tex
sheel. The calculation of lilis
flow
is associated \\·ith solution of
integral
equation
(8.2.t6) anf! the
u~e
of
boundar~
conditions m.1.15)
and
(S.1.1G). Such a solution is
treated
in
drtail
in
Itil.
8.
t
t.
Drag of Wings
with Subsonic Leading Edges
Let
us
consider
the
calculation
of
the drag
of
SW('pt
wings with
subsonic leadin.g edges
ill
a
supersonic
flow
at an angle of aUl\ci..
We
already
kno\\'
that
the
disturbed flo\\' normal to the I!'luling edge is
subsonic near such wings. Such
a
no\\'
is
all('ntied
I)y
the
o/;er,flow
of the gas from the region of increased pressure inlo the region where
the
pressure is reduced and is
the
calise of
the
corresponding force
action on
the
\ving. To calculate
this
acLion,
we
cun lise
the
results
of
investigating
the
disturhed
Ilow
of
an
incompl'essible fluid near
an airfoil in
the
form of a
nat
plale
arranged in
the
flo\\'
at
an angle
of attacl, (sec Sec.
G.3).
The
drag coerficient for a
thin
winq
with
subsonic iea(ling edges
in a supersonic
now
is
(8.11.1)
in
which
ex
T
is
the coefficient of
the
\\'ing sllction force depen(ling
on the sweep anglo
Y.
of the
leadin~
euge and the number
M
...
:
CX•T
=
T/(q
""Sv.)
(8.11.2)
\\'here
T
is
lhe suction force,
q~
=
p«>Vcoi2
is the \elocity hea(I,
anf!'
S",
is
the>
area of
the
wing planform.
3B2
pt. I. Theory. Aerodynllmics
of
lin
Airfoil
lind
II
Wing
~:.
tt:'~~leulation
of
the
suc·
tion
force
for
a triangular wing
with subsonic leading
edgl!s
To detarmine the force
T,
we
can use tbe relations obtained in
Sec. 7.6
for
an
infinitespan
swept wing. This follows
from
the fact
that
in accordance with (7.6.18) and (7.6.19), the suction force
depends
on
the change in the axial component of the velocity in the
close vicinity of the leading edge
of
tile
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 Summer '16
 Fluid Dynamics, The Land, gas flow, AERODYNAMIC FORCES