Section 2. Aerodynamics of body of revolution Theme 13. Drag coefficient of a fuselage
Drag of body of revolution can be presented as several components. On the one hand, the drag can be presented as pressure drag and friction drag. The pressure drag is caused by forces of pressure which act along perpendicular to the body surface. The friction drag is caused by forces which act along tangent to the body surface.
At flow about the body of revolution with a blunt base, behind which there is no jet stream from the engine, the drag from pressure on the blunt base occurs in addition.
On the other hand, the drag is divided into drag which is not connected with lifting force, and induced drag connected with presence of lift. In this case, the drag coefficient at small angle of attack can be presented as
,
(13.1)
where
- drag coefficient at zero lift,
- induced drag, which is determined similarly to low-aspect-ratio
wing
,
(13.2)
where
- relative factor of sucking force, if to neglect it, then the factor
of a polar pull-off will be equal
.
Generally drag coefficient at zero lift is equal
,
(13.3)
where
- factor of profile drag;
- factor of a wave drag;
- factor of base drag.
At
subsonic speeds the drag consists of drag of friction in
and drag of pressure in
.
At transonic and supersonic speeds
the drag of pressure in
times exceeds drag of friction (due to occurrence of wave drag).
At
the wave drag is equal to zero
.
The critical Mach number of the body of revolution depends on its aspect ratio and aspect ratio of its nose
.
(13.4)
13.1. Wave drag
At first we shall consider a wave drag. This is drag of pressure, therefore it is determined by known distribution of the factor of pressure along lateral surface of the body of revolution
.
(13.5)
It
is convenient to present the factor of wave drag as a sum of drag
coefficients of pressure of the nose
and rear
parts (the cylindrical part does not create the wave drag)
(13.6)
If considered body differs from a body of revolution then factor of wave drag includes an additional addend
,
(13.7)
where
- sum of wave drags of various sources. Such sources of an additional
wave drag of the fuselage can be: canopy, lateral and ventral air
intakes, coupled nozzles in the rear part and so on.
13.1.1. Wave drag of a nose part
Fig.
13.1. Drag of pressure of a nose of the body of revolution
At subsonic speeds there is a reduced pressure on some sites of a surface, owing to that the sucking force can appear, and the drag can be negative. At supersonic speeds pressure is increased on the nose surface, due to that drag of pressure appears (Fig. 13.1).
For
calculation of the wave drag
at
simple engineering method exists - method
of local cones
(Fig. 13.2).
Fig. 13.2.
Let's write down ratios
,
,
.
The factor of pressure on the ray which is going out from cone top has constant value and is determined by the ratio
,
(13.8)
from here
.
(13.9)
It
is possible to define size of
by known value of the factor of pressure
integrating its analytically or numerically. In particular, for the
conical shape of nose:
|
|
;
.
(13.10)For the parabolic nose:
|
|
.
(13.11)
Generally
will depend on the nose shape. If the head fuselage part has
bluntness or air intake, its drag coefficient
varies in comparison with fuselage without bluntness or air intake.
At
bluntness, as a rule, increases drag of the head part. Besides, flow
rate coefficient through the air intake provides the essential
influence onto character of flow about nose of the body of revolution
with a channel. In this case, drag of the fuselage is increased on
some size called as additional drag of the air intake.