6.1.2. Drag.
There
is only pressure drag which determines wave drag and induced drag
in an inviscid supersonic flow. As the wing leading edge is
supersonic, then there is no sucking force and
(for
flat wing). As
and
,
then
;
.
At that influence of
onto
at
is weaker than in subsonic flow (for example at
).
The wave drag
is defined by airfoil drag
and multiplier
which is taking into account span finite. Let's notice, that in case
of unswept wing, the same multiplier is included in the formula for
(6.4). As well as
,
the value of parameter
with increasing of
and
(more precisely
).
It is explained by narrowing of Mach cone and reduction of lateral
edges influence. It is possible to consider that at
(error
).
The ratio
is depended only on reduced aspect ratio and factor of the airfoil
plan form
i.e.
.
6.1.3. Location of aerodynamic center.
Fig.
6.6
(Fig. 6.6). The location of aerodynamic center is a function of
aspect ratio
.
At
.
Approximately
at
with an error less than
.
At
difference from
-
.
6.2. Triangular wings with subsonic leading edges.
Fig.
6.7. A triangular wing with subsonic edges
Fig.
6.8. Pressure distribution in wing cross-section
and
.
Thus
triangular wing with subsonic edges has reduced aspect ratio less
than
(
).
In this case there is an overflow from the lower surface to the upper
surface The sucking force is realized on the leading edge what
reduces induced drag. There is also non-linear additive to a lift
coefficient
. Pressure distribution along wing surface (fig. 6.8) submits to the
law within the linear theory (
)
,
.9)
where
and
(refer to fig. 6.7); it is possible approximately define
- the elliptical integral of II type dependent on parameter
,
by the formula
.
It
follows from the formula (6.9) for
that on each ray
value of
,
that is the feature of conical flows. At
i.e. at approach to the leading edge
(the similar situation takes place in a subsonic flow). For a sharp
edge the site in nose section is equal to zero. Multiplying
onto the nose section area and expanding the uncertainty
,
we receive final force value which projection onto incoming flow
direction creates force
reducing induced drag. This is the sucking force. The aerodynamic
characteristics of a triangular wing with subsonic edges are
determined by the following formulae:
,
;
(6.10)
;
(6.11)
;
(6.12)
;
(6.13)
;
,
(6.14)
where
- a factor of realization of sucking force (
),
it is possible to adopt for sharp leading edges, that
;
for rounded edges -
at
,
further
.
For
a triangular wing
.
The last result follows from consideration of conical flow with
constant pressure
on rays outgoing from the wing top.