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}=0.7729
m
2^2
, wing chord
cref=0.2544c_{ref}=0.2544
m, and wing span
bref=3.0381b_{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
Vref=25|\mathbf{V}_{ref}|=25
m/s and the reference density, pressure and viscosity are evaluated at an altitude of
h=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{,}
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}=-0.5504
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}=-0.5250
m. 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.
Fixed-wing UAV forced roll oscillation
Fixed-wing UAV forced pitch oscillation
Fixed-wing UAV forced yaw oscillation

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