12.1.2. Lift of the cylindrical part.
In subsonic
flow (
)
the cylindrical part of a fuselage does not create lift at small
angles of attack. According to the theory, as on the cylindrical part
,
then
.
In the
supersonic flow (
)
there is a lift on the cylindrical part. It happens because of
influence of the nose part. At presence of lift on the nose part
pressure have various values on its upper and lower parts. These
pressure are propagated to the cylindrical part as disturbances after
reflection from a head shock wave. As a result, there is a reduced
pressure on the upper surface in comparison with the lower surface of
the cylindrical part, that causes occurrence of lift on the
cylindrical part
(Fig. 12.3). (In the subsonic flow disturbances are spreaded in
all directions, therefore the upper surface of the nose part effects
both on upper and the lower parts of the cylinder surface. The
influence of the lower surface of the nose part is similar. As a
result of mutual influence at
).
In general,
size of the derivative
depends on the Mach number, aspect ratio of the nose part and type of
coupling of nose and cylindrical parts (Fig. 12.4, 12.5)
.
|
Intersecting coupling
Tangent coupling |
Fig. 12.3. Distribution of lift along length of the cylindrical part |
Fig. 12.4. Types of coupling of nose and cylindrical parts |
Approximately it is possible to estimate size of by the formula
,
(12.9)
where
.
The values
of factors
,
,
and
also can be adopted as the following:
- for
conical nose part
,
,
,
;
- for the
nose with curvilinear generative line and tangent coupling
,
,
,
.
Fig.
12.5.
12.1.3. Lift of the rear part.
The derivative of the lift coefficient of the rear part of the body of revolution does not depend on the shape of the rear part and is determined by the following ratios.
In the
subsonic flow (
)
distribution of lift along body length according to the theory of an
elongated body
,
from here
.
(12.10)
In real
flow (Fig. 12.6) boundary layer
rising happens in the rear part due to influence of viscosity, that
results in the body thickening
and decreasing of angle of declination of generative line.
Fig. 12.6. Thickening of the rear part due to the boundary layer
As a
result, the size of parameter
should decrease on an absolute value. The account of viscosity
influence results in the following computational formula
.
(12.11)
In the supersonic flow ( ) the Mach numbers effect onto amount of the derivative and determination of is performed by the formula
,
.
(12.12)
With increasing of numbers the amount of decreases in an absolute value.
It is necessary to note one more effect, which is not taken into account in the theory of an elongated body. This is an occurrence of the non-linear component on the fuselage due to formation of vortical structures on the upper surface (it is similar to the wing).
The values
are essential in general size
for thin body of revolutions at large angles of attack. For fuselages
of airplanes the occurrence of the non-linear component, as a rule,
is not considered. Also it is necessary to remember, that in the
system of an airplane the non-linear components from a wing and
fuselage decreases.
The size of
zero lift angle of the fuselage
is determined by chamber of its axis which is caused by nose
deflection and splayed rear part. The value of
is calculated by the formula
,
(12.13)
where
- angle of nose deflection;
- angle of taper of the rear part.
The angles and also undertake with positive sign, if the nose is deflected downwards, and the rear part is tapered upwards.