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first generation MAV optimization study are shown in
Table 2. The objective function was to maximize the
endurance of the MAV. In the MAV MDO code, the
optimization is performed by a genetic algorithm.
Table 1: Subsystem model descriptions
Subsystem Model Description
Vehicle
aerodynamics
Lifting line theory for induced drag,
Blasius skin friction formulas for
friction drag, Hoerner equations for
interference drag, and equivalent
parasite areas for protuberance drag
Propeller
aerodynamics
Minimum induced loss methodology
Motor
performance
Analytic motor model with coefficients
adjusted to match experimental data for
each motor
Battery
performance
Curve fits of battery endurance vs.
power draw based on experimental data
Weight buildup Mass budget of all fixed components,
and simple weight equations for variable
masses
Table 2: MAV design variables
Design Variable Range/Options
Battery type 2
Motor type 9
Gearbox type 4
Motor power draw 1-5 W
Propeller diameter 2-4 in
Wing tip chord 0-6 in
Loiter velocity 20-40 mph
The vehicle aerodynamics model was validated by
performing wind tunnel tests on a variety of wing
configurations. This allowed validation of the induced
drag and friction drag parts of the code. The
protuberance and interference drag components were
then added individually.
The propeller aerodynamics model was validated
by testing four different propellers in the wind tunnel
over a range of velocities, airspeeds, and power levels.
Both direct drive and geared props were tested.
The motor model was validated by using the Solver
in Excel to adjust the coefficients in the analytic motor
model equations to minimize the error between the
model predictions and experimental performance
measurements over a range of shaft loads and power
levels. Most of the motor models show less than 5%
error from the experimental data.
The battery model is simply a curve fit through
experimental discharge data at different power loads, so
no validation was necessary.
Most of the early MAV prototype vehicles were
flown with direct drive propellers. A few geared
propeller configurations were built, but they had
marginal performance. However, it was felt that the
geared prop concept still had enough potential to merit
further study for the first generation of the Black
Widow. Therefore two optimum configurations—a
direct drive prop and a geared prop—were created as
candidates for the final configuration.
Even though the entire vehicle was optimized for
each of the drivetrain types, the tip chords of both
configurations were roughly the same, and the loiter
velocities were roughly the same. The optimizer also
selected the same battery and the same motor for both
configurations. Therefore these parameters were all
frozen to the same values, to allow a normalized
comparison between the direct drive and geared
propulsion systems. Table 3 shows the wing shape
parameters, and Table 4 shows a comparison of the
direct drive and geared propulsion systems.
Table 3: Wing shape parameters (common to
both direct drive and geared prop designs)
Wing span 6.0 in
Wing centerline chord 5.4 in
Chord at spanwise breakpoint 5.4 in
Wing tip chord (in) 3.9 in
Spanwise position of breakpoint 1.5 in
Wing thickness/chord ratio 8.4%
American Institute of Aeronautics and Astronautics
3
Table 4: Propulsion system parameters for
direct drive and geared propeller configurations
Geared
Prop (4:1)
Direct
Drive Prop
Required thrust 9.9 g 9.4 g
Propeller diameter 3.81 in 2.67 in
Propeller RPM 5,365 22,400
Propeller efficiency 80% 68%
Gearbox efficiency 81% N/A
Motor RPM 21,460 22,400
Motor efficiency 62% 63%
Total propulsion efficiency 40% 43%
Power draw from batteries 4.65 W 4.35 W
Battery endurance 30.2 min 33.4 min
The optimization code predicts that the endurance
of the geared prop configuration is 30.2 minutes, while
the direct drive prop configuration has an endurance of
33.4 minutes. The direct drive prop configuration
achieves about 10% greater endurance than the geared
prop configuration. This is mainly due to the efficiency
loss in the gearbox, the added weight of the gearbox,
and a larger and heavier propeller.
In order to increase our confidence in this
prediction, both propulsion systems were tested in the
AeroVironment wind tunnel over a range of operating
conditions. Figure 2 shows the propeller efficiency,
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Development of the Black Widow Micro Air Vehicle(2)
