15.2.1. Fuselage influence onto wing (horizontal tail).
Let's
consider the wing - fuselage system set in a flow under the angle of
attack
(a fig. 15.7). Let's assume, that the fuselage is a body of
revolution close to cylindrical, and the wing is located on it under
the mid-wing scheme. Let's factor the incoming undisturbed flow
moving with speed
into two components: directed along fuselage axis with speed
and normal to it with speed
.
At flow about fuselage cylindrical part by this transversal flow the
speed
is increased in comparison to
.
Fig. 15.7. The scheme of flow about wing - fuselage system
Supposing speeds small, from the theory of potential flow about cylinder by transversal flow with speed for local streamlining speeds we obtain
.
The
influence of fuselage onto wing has an effect in changing of the wing
angle of attack, which is equal to
.
At
the wing angle of attack is increased twice. So it follows, that for
a wing which span with ventral part differs a little from
we shall have
.
Approximately, for a wing set by the mid-wing scheme
,
,
where
.
For a wing
set on the fuselage of round cross-section by the low-wing or
high-wing configurations, wing distance from fuselage axis influences
on the interference factor
,
,
.
For such
configuration at
:
,
,
.
15.2.2. Wing (horizontal tail) influence onto fuselage
The wing influence onto fuselage has double effect.
At first, the lift of the fuselage part is increased by "carry" of raised pressure under the wing and reduced above the wing on fuselage (Fig. 15.8, a).
Secondly, the lift of fuselage part behind the wing decreases because of presence flow downwash (Fig. 15.8, b).
Fig. 15.8. Wing influence onto fuselage
As a result the additional lift on the fuselage is equal to
.
Let's mark,
that the position
depends on number
at
.
With increasing of
a point of
applying displaces back.
15.3. Moment of pitch and position of aerodynamic center of the wing - fuselage system.
Strictly
speaking, the moment of pitch is created by full aerodynamic force
or, in the most cases, by normal forces. Approximately it is possible
to consider that the moment of pitch is created by lifting forces of
wing, fuselage and additional lifts caused by interference. At that,
we neglect moments of drag forces. Proceeding from mentioned above we
accept:
,
,
,
where
- lift of an isolated fuselage,
- lift of wing installed on the fuselage (
),
- additional lift on the fuselage from wing influence.
The point
of wing lift applying generally places a little ahead of the
aerodynamic center of isolated wing (
),
however, it is possible to accept without large error, that the point
of lift applying
coincides
to aerodynamic center of isolated wing
.
Using fig.
15.9, we shall make an equation for moment of pitch
for wing - fuselage system relatively to fuselage nose.
Fig. 15.9.
Here
- moment at zero lift of isolated parts and their interference.
.
The last
item in equation for
is small, because of small force value and small arm (especially at
)
and it can be neglected. The summarized value
represents wing lift in the system
and then
.
Let's pass
to the factor of moments, for that divide right and left parts of
equation on dynamic pressure, characteristic area and characteristic
length
.
It is possible to accept as characteristic length
,
for example, length of a fuselage:
(15.16)
Here
,
,
,
,
location of
the wing relatively to fuselage nose, position of aerodynamic centers
of the fuselage and wing are expressed in shares of fuselage length
,
,
.
Let's
differentiate the equation (15.16) for
on
:
.
Position of aerodynamic center of the wing - fuselage system relatively to fuselage nose in shares of fuselage length are determined
.
Fig.
15.10.
(Fig. 15.10):
.
Substituting
in expression for
(15.16) parameter
,
we obtain the moment factor at zero lift
As
and
, then
,
where
,
.