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