Wing-tail configuration
Example simulation of a fixed-wing configuration
The wing-tail configuration has a wing aspect ratio
, wing area
m
, wing chord
m. Both the wing and the tail have a taper ratio of 1. The distance between the quarter-chord points of the wing and the tail is
m. A body-fixed coordinate system is placed at the wing quarter-chord point. The reference speed is
m/s and the reference density, pressure, and viscosity are evaluated at an altitude of
m (ISA). An unstructured mesh with 6354 panels is used. The image below shows the pressure coefficient of the wing-tail configuration at an angle of attack
deg.

Wing-tail configuration pressure coefficient
The lift, drag and pitching moment coefficients of the wing-tail configuration are assumed to be given by:
where
is the normalised pitch rate. The
,
, and
are functions of the the angle of attack
, the normalised pitch rate
and the elevator deflection angle
. The aim is to obtain the
,
, and
coefficients and the
,
,
,
,
,
,
,
, and
derivatives using APM.
A simulation of the wing-tail configuration is performed at
rad,
rad/s,
rad. The values for the aerodynamic coefficients are recorded. They are the values of the
- coefficients.
As already discussed, a simulation of the wing-tail configuration is performed at
rad,
rad/s,
rad. The values for the aerodynamic coefficients are recorded. A second simulation of the wing-tail configuration is performed at
rad,
rad/s,
rad. The choice of value for
is arbitrary. Again the aerodynamic coefficients are recorded. To obtain the
- derivatives a simple difference is used:
where
rad. The same method is used to obtain the
- derivatives.
The coordinate system used for the analysis above is fixed to the wing quarter-chord point however, this point does not coincide with the centre of gravity. If one determines the
- derivatives with respect to this coordinate system they will not be representative of the
- derivatives with respect to the centre of gravity. To determine the position of the centre of gravity (often driven by a required static margin), the neutral point position must be found. By definition, the stick-fixed neutral point position is where:
Using the difference method described above, the value of
is obtained for two different locations of the centre of gravity. The first location is when the centre of gravity coincides with the quarter-chord point of the wing
m and the second location is selected forward of the quarter-chord point of the wing
m. The choice of value for
is arbitrary. The equation for
as a function of
is then:
The solution of the equation gives
, for
. This is the location of the stick-fixed neutral point,
, (
=
for
). The centre of gravity location for a 15% static margin is then given by:
with
m. The
- derivatives can now be obtained with respect to this point. A forced sinusoidal motion is imposed on the wing-tail combination:
where
deg is the amplitude of the motion and
Hz is the frequency of the motion. The video below shows the development of the wing-tail configuration wake during the forced sinusoidal motion.
Wing-tail configuration wake development
The values of
with respect to
make a quasi-steady elliptical hysteresis. Two points exist at which the angular velocity is maximum or minimum.
derivative is estimated from the values of the
at these points
where
is the reduced frequency. The same method is used to obtain the other
- derivatives. Below are the wing-tail configuration derivatives estimated by the method.
| | | | |
| -0.0114 | 0.2555 | -0.2491 | -0.0195 |
| -0.3219 | -5.1439 | 2.7170 | -0.8377 |
| 0.0556 | -0.9575 | -20.0581 | -2.3205 |
wing_tail_configuration.zip
375KB
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Last modified 1yr ago