16.4. Longitudinal moment. A position of the airplane aerodynamic center.
As well as other aerodynamic characteristics, the longitudinal moment of airplane aerodynamic forces is determined as a sum of moments of its separate parts. Strictly speaking, the longitudinal moment is created by full aerodynamic force. However, it is possible to consider only the aerodynamic lift moment if to neglect the drag force moment. In general, it is necessary also to take into account the engine thrust moment.
It is necessary to have in view, that the moment value depends on location of an axis relatively to which it is calculated. While calculation it is convenient to determine the moment relatively to fuselage nose. Then, if necessary, it is easy to recalculate it relatively to other point (axis).
Let's assume: the lifting (normal) force of the engine nacelle is applied to nacelle shear; the lifting (normal) force of lifting surfaces in the airplane system is applied to the wing or horizontal tail aerodynamic center; fuselage additional lift which arises because of lifting surface and fuselage interference is applied also in the aerodynamic center of the wing or horizontal tail .
For solution of flight dynamics problems it is convenient to allocate items relating to the airplane without horizontal tail and airplane in a whole in a moment:
,
.
(16.24)
16.4.1. Derivatives of the pitch moment factors by the angle of attack.
Let's determine the moment for the considered scheme (Fig. 16.6). It is convenient to take fuselage length as characteristic length for calculation of moment relatively to fuselage nose. In this case aerodynamic center location to be determined relatively to fuselage nose in shares of its length.
Fig. 16.6.
The values of derivatives
and
also are determined under the formulae:
,
(16.25)
,
,
,
.
(16.26)
The parameters and are also determined in the airplane system (in view of flow deceleration and mutual influence).
By known values
and
,
and parameters
and
the aerodynamic center location of the airplane in a whole and the
airplane without horizontal tail relatively to fuselage nose in
shares of its length is determined as follows
,
.
(16.27)
If it is required to know the aerodynamic center location relatively to mean aerodynamic chord nose expressed in shares of MAC length, then pass to new values by the formulae:
,
,
(16.28)
where
and
- mean aerodynamic chord of the wing and distance from MAC nose up to
the leading edge of the root chord.
The displacement of aerodynamic center due to
horizontal tail influence expressed in MAC shares is equal
.
16.4.2. Moment coefficient at zero lift
It is possible to present the formula for
determination of the longitudinal moment factor at airplane zero lift
in a whole and airplane without horizontal tail as
,
,
(16.29)
.
Moment coefficient components are determined by
the following formulae (fuselage length is used as characteristic
length
;
if it is necessary to pass to other characteristic length, for
example to MAC length
,
then the expressions are multiplied on
):
,
,
,
.
The characteristics
and
are also determined in the airplane system,
,
where
- setting angle of engine nacelles axes in relation to fuselage axis
(
if the axis is directed upwards).
Calculation of the characteristics
,
,
… is performed by reduced formulae with replacement of
on
.
Fig. 16.7. The characteristic form of function
The airplane without horizontal tail, as a rule, is unstable (and is not balanced); horizontal tail provides the airplane stability and balancing.