# 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.

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.

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