6.4.4. Location of aerodynamic center.
Generally,
there is a dependence
,
in which the influence of taper is essential in difference from the
characteristics
and
.
Location of aerodynamic center tend to the position of the center of
mass of a figure presenting the wing plan form with increasing of
reduced aspect ratio. In particular, for wings with unswept edges of
the tapered plan form we have
.
(6.23)
The
reduced formula can be used already at
:
(For
a rectangular wing -
,
;
for
a triangular wing -
,
,
).
Note:
At calculation of the aerodynamic characteristics of the complex plan
form wings (curved edges or the edges with a fracture) approximate
methods replacing variables spanwise
,
,
... by their mean values are used together with precisely numerical
calculations of a particular wing.
6.5. Wing in transonic range of speeds.
Fig.
6.18.
)
are called transonic. All range can be divided on to: area of
subsonic speeds (
),
area of supersonic speeds (
),
flow mode with Mach numbers
.
Features
of the aerodynamic characteristics in subsonic part of transonic
speeds are determined by existence of
mixed
flow including subsonic (outside of the wing) and supersonic (on the
wing and near to it) flow areas. The forward border of supersonic
flow area represents the so-called sound line, along which the
transition from subsonic to supersonic flow is occurred. The flow
remains subsonic outside of zones limited by the sound line. Fig.
6.18 shows the approximate borders of supersonic zones at various
Mach numbers
.
With increasing of Mach number
the shock waves are originally formed on the upper surface and move
to the trailing edge. Then the supersonic area is formed on the lower
surface. The development of supersonic area on the airfoil lower
surface proceeds more intensively, than on lower. The supersonic
areas are finished by shock waves, which with increasing of numbers
displace back and enlarge the extent in the vertical direction. At
a shock wave is theoretically distributed into infinity, at that
there is a head shock wave before the wing also in infinity. The
further increasing of
caused movement of a head shock wave and shock wave on the wing
surface downwards of the flow. The supersonic wing flow mode comes at
values
,
when the shock waves practically do not move any more, and reduce
their angle of inclination with increasing of
.
The
appearance of
transonic parameter of similarity
,
as a result of the non-linear theory, is characteristic for transonic
area. Parameter
influences onto changing of the aerodynamic characteristics so, that:
(Fig.
6.19);
(Fig.
6.20);
(Fig.
6.21).
At
:
the dimensionless parameters
,
,
depend on
,
,
shape of the airfoil and
.
Let's remind, that the taper
continues to play a small role in changing of
and
,
in some cases its influence can be neglected. However, the parameter
plays an essential role for characteristic of aerodynamic center
location, because it effects onto aerodynamic loading distribution
wing spanwise.
For
wings of arbitrary shape the influence of
is investigated a little. More detail research is carried out on
rectangular wings with rhomboid airfoil (
,
,
or
).
it was proved, that for such wings at
and
the value of
.
It can be explained that at
reduced aspect ratio
and we pass to the very low-aspect-ratio wing, for which
.
If
,
then the theory of transonic flows for a rectangular wing gives
.
The
analogous results are received for wave drag:
at
,
at
.
Fig.
6.19. Dependence
on reduced aspect ratio
|
Fig. 6.20. Dependence on reduced aspect ratio |
Fig.
6.21. Dependence of the aerodynamic center location on
,
i.e. the wave drag grows with increasing of
,
though not so fast as in the supersonic flow, in which
.
Change of the aerodynamic center location dependently on
is similar to changes of
(Fig. 6.21). The more
,
then aerodynamic center changing by Mach numbers
behaves more irregularly: drastic displacement forward in subsonic
range is probable with the subsequent displacement backward into
position corresponded to supersonic speeds (displacement of
aerodynamic center for a triangular wing at passage from
to
is determined as
).
Main
measures provided reduction of wing wave drag, improvement of its
lifting properties and smooth change of aerodynamic center in
supersonic range of speeds by Mach numbers
are: reduction of
and
(decreasing of parameter value
) and increasing of
.