Fixed-wing UAV

Example simulation of a fixed-wing configuration

The fixed-wing UAV has a wing aspect ratio AR=12AR=12, wing area Sref=0.7729S_{ref}=0.7729m2^2, wing chord cref=0.2544c_{ref}=0.2544m, and wing span bref=3.0381b_{ref}=3.0381m. 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 Vref=25|\mathbf{V}_{ref}|=25m/s and the reference density, pressure and viscosity are evaluated at an altitude of h=0h=0m (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:

Cm=Cm0+xcgcrefCZ,C_{m}=C_{m0}+\frac{x_{cg}}{c_{ref}}C_{Z}\text{,}

where xcgx_{cg} is the distance measured along the x-axis. Once the pitching moment coefficient at the origin of the coordinate system Cm0C_{m0} and the Z-force coefficient CZC_{Z}are known from the solution, the pitching moment coefficient CmC_{m} about an arbitrary point forward or aft of the origin of the coordinate system (along the x-axis) can be obtained. If Cm0C_ {m0} and CZC_{Z} are available at two different angles of attack the neutral point location can be found (Cm,α=0C_{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.

Cmα=0=Cm0α=0+xcgcrefCZα=0Cmα=5=Cm0α=5+xcgcrefCZα=5Cmα=Cm,α=Cmα=5Cmα=0Δα=0.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 xcgx_{cg}:

xcg=crefCm0α=5Cm0α=0CZα=5CZα=0x_{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 xcg=0.5504x_{cg}=-0.5504m. 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 xcg=0.5250x_{cg}=-0.5250m. The table below lists the stability derivatives for the fixed-wing UAV evaluated for the center of gravity at rcg={0.5250,0,0}T\vec{r}_{cg}=\{-0.5250,0,0\}^{T}m.

0_0

α\frac{\partial }{\partial\alpha}

β\frac{\partial }{\partial\beta}

δa\frac{\partial }{\partial\delta_{a}}

δe\frac{\partial }{\partial\delta_{e}}

δr\frac{\partial }{\partial\delta_{r}}

pˉ\frac{\partial }{\partial\bar{p}}

qˉ\frac{\partial }{\partial\bar{q}}

rˉ\frac{\partial }{\partial\bar{r}}

CXC_{X}

-0.0273

0.6584

0.0151

-0.0114

-0.0138

-0.0130

-0.0850

CYC_{Y}

-0.3221

0.0192

0.3318

-0.0864

0.3365

CZC_{Z}

-0.3755

-5.7537

0.0426

0.0042

-0.5479

0.0015

11.1781

ClC_{l}

-0.0801

0.2597

0.0478

-0.5984

0.1487

CmC_{m}

0.0384

-0.5750

0.0639

-2.8199

0.0176

-34.9704

CnC_{n}

0.1199

-0.0091

-0.1504

-0.0172

-0.1413

The deflections of the ailerons δa\delta_{a}, elevator δe\delta_{e} and rudder δr\delta_{r} follow positive conventions. Port aileron down is positive, elevator down is positive, rudder to port is positive. The value for Cm,αC_{m,\alpha} is 0.5750-0.5750 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 Cl,βC_{l,\beta}and Cn,βC_{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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