6.4. Wings of any plan form. The qualitative analysis of the aerodynamic characteristics.
The
main feature of the aerodynamic characteristics of all wings: with
increasing of Mach numbers
(more precisely - reduced aspect ratio
)
the aerodynamic characteristics
,
tend to the airfoil characteristics, i.e.
;
.
It can be explained, that the Mach cone is narrowing with increasing
of
(at
)
and each cross-section of a wing also will be isolated streamlined.
It also follows, that the wing aerodynamic center (or center of
pressure) displaces into center of mass of the plan form, i.e.
.
Let's analyze the aerodynamic characteristics of wings.
6.4.1. Lift.
Generally for flat wing , where - the non-linear additive existed only at a subsonic leading edge. It can be estimated by the formula
At
(supersonic edge)
.
There are schedules constructed in a generalized form for definition
of the derivative
,
as dependence
on parameters of similarity:
.
Approximately
it is possible to consider, that the taper
practically does not influence onto lift coefficient. For each wing
the function
is various. However, as it was mentioned above, at
we receive for all wings
.
Practically this dependence can be used at
.
Fig.
6.14.
In a point - the trailing edge passes from subsonic to supersonic flow mode;
In a point - the leading edge passes from subsonic to supersonic flow mode.
In experiment these fractures are smoothed out.
6.4.2. Wave drag.
Generally
.
At
irrespectively of the wing plan form we shall have
-
the characteristic of an airfoil. Practically this formula can be
used at
.
It is necessary to note weak influence of taper onto wave drag. The
presence of fractures on a curve (Fig. 6.15). is characteristics for
general dependence
on reduced aspect ratio.
Fig.
6.15.
Fig.
6.16.
- transition of the maximum thickness line from subsonic to
supersonic flow; in a point
- the leading edge passes from subsonic to supersonic flow mode.
These fractures are not present in experimental dependencies, they
are smoothed out.
The
maximums of curves are observed in the are of transition of the
maximum thickness line (
)
from a subsonic flow mode to supersonic (point
).
For a sound line of maximum thickness
.
It is necessary to pay attention that at subsonic lines of maximum
thickness the wave drag of swept wings is less than drag of unswept
wing. Thus the longer wing aspect ratio (at
),
sweep (at
)
or parameter
,
then the larger profit is received in drag. On the contrary, at a
supersonic line of maximum thickness the wave drag of swept wing is
more than of unswept one (Fig. 6.16).
6.4.3. Induced drag.
If
the leading edge is supersonic, then
or
,
where
- for the flat wing. At the subsonic leading edge it is necessary to
take into account the sucking force. In this case
,
or approximately
;
;
;
(6.22)
Fig.
6.17.
and
- parameters of a triangular wing, which leading edge coincides to
the leading edge of considered wing (fig. 6.17).