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

$C_{l}$

0.2597

0.0478

-0.5984

0.1487

$C_{m}$

0.0384

0.0639

-2.8199

0.0176

-34.9704

$C_{n}$

-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

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