Fixed-wing UAV

Example simulation of a fixed-wing configuration

The fixed-wing UAV has a wing aspect ratio AR=12AR=12AR=12
, wing area Sref=0.7729S_{ref}=0.7729Sref​=0.7729
m2^22
, wing chord cref=0.2544c_{ref}=0.2544cref​=0.2544
m, and wing span bref=3.0381b_{ref}=3.0381bref​=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 ∣Vref∣=25|\mathbf{V}_{ref}|=25∣Vref​∣=25
m/s and the reference density, pressure and viscosity are evaluated at an altitude of h=0h=0h=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:
Cm=Cm0+xcgcrefCZ,C_{m}=C_{m0}+\frac{x_{cg}}{c_{ref}}C_{Z}\text{,}Cm​=Cm0​+cref​xcg​​CZ​,
where xcgx_{cg}xcg​
 is the distance measured along the x-axis. Once the pitching moment coefficient at the origin of the coordinate system Cm0C_{m0}Cm0​
 and the Z-force coefficient CZC_{Z}CZ​
are known from the solution, the pitching moment coefficient CmC_{m}Cm​
 about an arbitrary point forward or aft of the origin of the coordinate system (along the x-axis) can be obtained. If Cm0C_ {m0}Cm0​
 and CZC_{Z}CZ​
 are available at two different angles of attack the neutral point location can be found (Cm,α=0C_{m,\alpha}=0Cm,α​=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.
Cm∣α=0=Cm0∣α=0+xcgcrefCZ∣α=0Cm∣α=5=Cm0∣α=5+xcgcrefCZ∣α=5∂Cm∂α=Cm,α=Cm∣α=5−Cm∣α=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{.}Cm​∣α=0​=Cm0​∣α=0​+cref​xcg​​CZ​∣α=0​Cm​∣α=5​=Cm0​∣α=5​+cref​xcg​​CZ​∣α=5​∂α∂Cm​​=Cm,α​=ΔαCm​∣α=5​−Cm​∣α=0​​=0.
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​
:
xcg=−crefCm0∣α=5−Cm0∣α=0CZ∣α=5−CZ∣α=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}}xcg​=−cref​CZ​∣α=5​−CZ​∣α=0​Cm0​∣α=5​−Cm0​∣α=0​​
For the fixed-wing UAV the location of the neutral point is xcg=−0.5504x_{cg}=-0.5504xcg​=−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 xcg=−0.5250x_{cg}=-0.5250xcg​=−0.5250
m. The table below lists the stability derivatives for the fixed-wing UAV evaluated for the center of gravity at r⃗cg={−0.5250,0,0}T\vec{r}_{cg}=\{-0.5250,0,0\}^{T}rcg​={−0.5250,0,0}T
m.
​
​0_00​
​
​∂∂α\frac{\partial }{\partial\alpha}∂α∂​
​
​∂∂β\frac{\partial }{\partial\beta}∂β∂​
​
​∂∂δa\frac{\partial }{\partial\delta_{a}}∂δa​∂​
​
​∂∂δe\frac{\partial }{\partial\delta_{e}}∂δe​∂​
​
​∂∂δr\frac{\partial }{\partial\delta_{r}}∂δr​∂​
​
​∂∂pˉ\frac{\partial }{\partial\bar{p}}∂pˉ​∂​
​
​∂∂qˉ\frac{\partial }{\partial\bar{q}}∂qˉ​∂​
​
​∂∂rˉ\frac{\partial }{\partial\bar{r}}∂rˉ∂​
​
​CXC_{X}CX​
​
-0.0273
0.6584
0.0151
-0.0114
-0.0138
-0.0130
​
-0.0850
​
​CYC_{Y}CY​
​
​
​
-0.3221
0.0192
​
0.3318
-0.0864
​
0.3365
​CZC_{Z}CZ​
​
-0.3755
-5.7537
0.0426
0.0042
-0.5479
0.0015
​
11.1781
​
​ClC_{l}Cl​
​
​
​
-0.0801
0.2597
​
0.0478
-0.5984
​
0.1487
​CmC_{m}Cm​
​
0.0384
-0.5750
0.0639
​
-2.8199
0.0176
​
-34.9704
​
​CnC_{n}Cn​
​
​
​
0.1199
-0.0091
​
-0.1504
-0.0172
​
-0.1413
The deflections of the ailerons δa\delta_{a}δa​
, elevator δe\delta_{e}δe​
 and rudder δr\delta_{r}δr​
 follow positive conventions. Port aileron down is positive, elevator down is positive, rudder to port is positive. The value for Cm,αC_{m,\alpha}Cm,α​
 is −0.5750-0.5750−0.5750
 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}Cl,β​
and Cn,βC_{n,\beta}Cn,β​
 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
​
​

Wing-tail configuration

Aerosonde UAV

Last modified 4mo ago

	$_0$	$\frac{\partial }{\partial\alpha}$	$\frac{\partial }{\partial\beta}$	$\frac{\partial }{\partial\delta_{a}}$	$\frac{\partial }{\partial\delta_{e}}$	$\frac{\partial }{\partial\delta_{r}}$	$\frac{\partial }{\partial\bar{p}}$	$\frac{\partial }{\partial\bar{q}}$	$\frac{\partial }{\partial\bar{r}}$
$C_{X}$	-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