4.5. Lift-to-drag ratio.
The
ratio of aerodynamic lift to a drag force obtained by dividing the
lift by the drag is called lift-to-drag ratio
:
,
(4.16)
The lift-to-drag ratio is one of the basic characteristics determining efficiency of an airplane.
For
a flat wing -
.
(4.17)
Fig.
4.19. Dependence
is achieved is called as optimal and designated as
and
.
Let's define maximum lift-to-drag ratio. For this purpose differentiate by and from a condition
we shall
define values
at which the lift-to-drag ratio has extremums:
.
We shall receive the formula for calculation of maximum quality having substituted in expression (4.17). We get
;
.
The
value of
is increased with increasing of
,
decreasing of
and
(
for elliptical distribution chordwise). We shall notice, that
and does not depend on
.
For
a non-planar wing -
and
.
It
is easy to find values of
,
,
graphically. From fig. 4.20 follows, that it is necessary to conduct
a beam tangent to polar from origin of coordinates to search
.
The values of
and
in tangency point will correspond to
and
.
Fig.
4.20. Dependencies
,
,
and connection between them.
4.6. Distribution of aerodynamic loading along wing span.
Summarizing
pressure distribution chordwise, we receive
.
At the analysis of influence of wing geometrical parameters in
planform for distribution of aerodynamic loading spanwise it is
convenient to use relative value
.
The function
depends on
,
,
and geometrical twist (refer to Fig. 3.5). Let's consider a flat
wing. The influence of
,
,
is shown on the following diagrams (Figs. 4.21, 4.22, 4.23).
Loading
is distributed spanwise more regular with increasing of aspect ratio
.At
and for an elliptical wing
.
Refer to fig. 4.21.
The
increasing of sweep angle
causes growth of loading in a tip part and reduction in root
cross-section for a swept-back wing (
).
Refer to fig. 4.22.
The influence of wing taper is similar to sweep effect : there is loading growth in wing tip cross-sections with taper increasing. Refer to fig. 4.23.
Distribution of lift along wing span: |
Fig.
4.21. Depending on aspect ratio at condition of
,
|
Fig.
4.22. Depending on sweep at condition of
|
Fig. 4.23. Depending on taper at condition of , |
,
It is possible to write down for an one-profile flat high-aspect-ratio wing approximately:
;
,
Where
,
,
the values of parameter
are undertaken from the reference book or calculated.
Chord
are distributed spanwise for a tapered wing with straight-line edges
as follows:
.
Approximately
,
,
.
4.7. Flow stalling.
Different
values of
along wing span are the reason of flow stalling in one of
cross-sections in which the local value
is reached. For example, the flow stalling on a flat rectangular wing
occurs at increasing of angles of attack in central cross-section. Ii
is evidently shown in fig. 4.24., that the true angle of attack in
central cross-section of a rectangular wing is more than at the tip
,
therefore flow stalling will begin in that place, where the true
angle of attack comes nearer to critical.
Fig. 4.24.
In
general the position of flow stalling spanwise on a tapered unswept
wing can be determined by the formula
, for swept tapered wing the position of stalling spanwise is
determined by the following dependence
,
.
For
improvement of wing aerodynamics at high angles of attack it is
necessary to create a condition of simultaneous flow stalling
spanwise, i.e. uniform distribution of loading spanwise It can be
achieved by geometrical twist application. It is necessary to apply
washin to rectangular wing for the purpose of increasing loading in
tip cross-sections, washout is used for unswept wing, in this case
tip cross-sections are unload. (It has be noticed, that for a wing
with the elliptical law of chords distribution spanwise without
geometrical twist all cross-sections have an identical
,
because
and true angles of attack
are identical for such wing spanwise).