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# Fixed-wing UAV

Example simulation of a fixed-wing configuration
The fixed-wing UAV has a wing aspect ratio
$AR=12$
, wing area
$S_{ref}=0.7729$
m
$^2$
, wing chord
$c_{ref}=0.2544$
m, and wing span
$b_{ref}=3.0381$
m. Both the wing and the tail have a taper ratio of 1. A body-fixed coordinate system is placed at the nose. The reference speed is
$|\mathbf{V}_{ref}|=25$
m/s and the reference density, pressure and viscosity are evaluated at an altitude of
$h=0$
m (ISA). An unstructured mesh of 24674 elements was used. The figures below show the pressure coefficient, the mesh, the panel types, and the doublet potential. Fixed-wing UAV pressure coefficient   The pitching moment coefficient of the Cruiser UAV is assumed to be given by:
$C_{m}=C_{m0}+\frac{x_{cg}}{c_{ref}}C_{Z}\text{,}$
where
$x_{cg}$
is the distance measured along the x-axis. Once the pitching moment coefficient at the origin of the coordinate system
$C_{m0}$
and the Z-force coefficient
$C_{Z}$
are known from the solution, the pitching moment coefficient
$C_{m}$
about an arbitrary point forward or aft of the origin of the coordinate system (along the x-axis) can be obtained. If
$C_ {m0}$
and
$C_{Z}$
are available at two different angles of attack the neutral point location can be found (
$C_{m,\alpha}=0$
). The neutral point is the location of the centre of gravity for which a change in the angle of attack does not create a restoring (negative, nose-down) pitching moment.
$C_{m}\rvert_{\alpha=0}=C_{m0}\rvert_{\alpha=0}+\frac{x_{cg}}{c_{ref}}C_{Z}\rvert_{\alpha=0}\\ C_{m}\rvert_{\alpha=5}=C_{m0}\rvert_{\alpha=5}+\frac{x_{cg}}{c_{ref}}C_{Z}\rvert_{\alpha=5}\\ \frac{\partial C_{m}}{\partial\alpha}=C_{m,\alpha}=\frac{C_{m}\rvert_{\alpha=5}-C_{m}\rvert_{\alpha=0}}{\Delta\alpha}=0\text{.}$
When the first two equations are substituted in the third, the following expression is obtained for the location of the neutral point
$x_{cg}$
:
$x_{cg}=-c_{ref}\frac{C_{m0}\rvert_{\alpha=5}-C_{m0}\rvert_{\alpha=0}}{C_{Z}\rvert_{\alpha=5}-C_{Z}\rvert_{\alpha=0}}$
For the fixed-wing UAV the location of the neutral point is
$x_{cg}=-0.5504$
m. The negative sign means that the point is aft of the nose. For a static margin of 10% the centre of gravity location must be
$x_{cg}=-0.5250$
m. The table below lists the stability derivatives for the fixed-wing UAV evaluated for the center of gravity at
$\vec{r}_{cg}=\{-0.5250,0,0\}^{T}$
m.
 ​ ​$_0$​ ​$\frac{\partial }{\partial\alpha}$​ ​$\frac{\partial }{\partial\beta}$​ ​$\frac{\partial }{\partial\delta_{a}}$​ ​$\frac{\partial }{\partial\delta_{e}}$​ ​$\frac{\partial }{\partial\delta_{r}}$​ ​$\frac{\partial }{\partial\bar{p}}$​ ​$\frac{\partial }{\partial\bar{q}}$​ ​$\frac{\partial }{\partial\bar{r}}$​ ​$C_{X}$​ -0.0273 0.6584 0.0151 -0.0114 -0.0138 -0.0130 ​ -0.0850 ​ ​$C_{Y}$​ ​ ​ -0.3221 0.0192 ​ 0.3318 -0.0864 ​ 0.3365 ​$C_{Z}$​ -0.3755 -5.7537 0.0426 0.0042 -0.5479 0.0015 ​ 11.1781 ​ ​$C_{l}$​ ​ ​ -0.0801 0.2597 ​ 0.0478 -0.5984 ​ 0.1487 ​$C_{m}$​ 0.0384 -0.5750 0.0639 ​ -2.8199 0.0176 ​ -34.9704 ​ ​$C_{n}$​ ​ ​ 0.1199 -0.0091 ​ -0.1504 -0.0172 ​ -0.1413
The deflections of the ailerons
$\delta_{a}$
, elevator
$\delta_{e}$
and rudder
$\delta_{r}$
follow positive conventions. Port aileron down is positive, elevator down is positive, rudder to port is positive. The value for
$C_{m,\alpha}$
is
$-0.5750$
per radian. The negative sign indicates that for a positive increase of the angle of attack there is a negative (nose-down) pitching moment. This shows that the fixed-wing UAV is statically stable in pitch. The signs of the
$C_{l,\beta}$
and
$C_{n,\beta}$
also show that the fixed-wing UAV is statically stable in roll and yaw. The derivatives of the fixed-wing UAV with respect to the rolling, pitching, and yawing were obtained following the approach in the wing-tail configuration example. The figures below show pitch and roll forced oscillations with an amplitude of 5 deg and frequency of 2.5 Hz. The respective derivatives are listed in the table above.   Fixed-wing UAV forced roll oscillation
Fixed-wing UAV forced pitch oscillation
Fixed-wing UAV forced yaw oscillation