Scaling Analysis of Propeller-Driven Aircraft for Mars ...
Transcript of Scaling Analysis of Propeller-Driven Aircraft for Mars ...
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Scaling Analysis of Propeller-Driven Aircraft
for Mars Exploration
Tianshu Liu
ISAS, JAXA, Sagamihara, Japan
&
Department of Mechanical & Aeronautical Engineering
Western Michigan University, Michigan, USA
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Objective
To give a criterion for feasible cruising
flight of propeller-driven aircraft on Mars
and provide a guideline for the design of
such a Martian aircraft
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Martian Atmosphere
Density
0142.01087.5 4 HM
Pressure
2.7743.42 HpM
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Martian Atmosphere
Temperature Speed of Sound
8.28622.6 HTM 3.2681.3 HaM
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Martian Atmosphere
Dynamical Viscosity
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Adaption of PIW-VIW Relation in Flight Testing:
Effects of Density and Gravity for Mars Flight
where the standard velocity and the generalized power:
2/1
2/1
)/(
)/(
ref
ref
WW
VVIW
2/3
2/1
)/(
)/(
ref
ref
WW
PPIW
)(
2)(
2
12
3
0VIWS
KWVIWSCPIW
ref
refD
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Power-Velocity Relation on Earth
Related to Martian Parameters
where the velocity and the power are related to those on Mars
EE
EEEDE
VS
KWVSCP
23
0
2
2
1
2/1
2/1
)/(
)/(
EM
EMME
WW
VV
2/3
2/1
)/(
)/(
EM
EMME
WW
PP
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Scaling Relations: Power and Velocity
where
2/1
min, / SWaV EPE 2/3
min, / SWbSP EPE
4/1
0
2
4/1
3
4
DEC
Ka
a
KaCb
E
ED
2
2
1 3
0
Pmin,E
2/1
M
E
2/1
E
M
2/1
E
2/1
M
E
2/1
E
MPmin,M V
g
g
S
W
g
gaV
S/Pg
g
S
W
g
gbS/P Pmin,E
2/1
M
E
2/3
E
M
2/3
E
2/1
M
E
2/3
E
MPmin,M
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Scaling Relations: Power and Velocity
Scaling Relations: Lift Coefficient
In cruising flight on Earth and Mars,
the lift coefficient remains the same, i.e.,
Pmin,MRmax,M V35.1V
Pmin,MRmax,M P146.1P
E,L
2
M
E
M
E
E
MM,L C
V
V
g
gC
E,LM,L CC
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Scaling Relations: Propulsive Power
where the power coefficient is defined as
E
M
E,P
M,P
E,prop
M,prop
c
c
P
P
Propulsive Power Scaling:
3
P
3
AS3
Ppropprop VScVSr
J
C4P
)J/C4(r)VS/(Pc 3
PASprop
3
propP
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Power Criterion for Cruising Flight on Mars
Propulsive Power Available:
Propulsive Power Required:
where the following scaling relations are used
6/7
EPE,prop WP 3/2
ES WS
6/7
E
E
M
E,P
M,P
PM,prop Wc
cP
6/7
E
2/1
M
E
2/3
E
M
2/1
S
Rmax,M Wg
gb146.1P
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Power Criterion for Cruising Flight on Mars
Power Ratio Criterion:
1P/P Rmax,MM,prop
1g
g
c
c
b873.0
P
P2/3
E
M
2/3
M
E
E,P
M,PP
2/1
S
Rmax,M
M,prop
M
1c
c
b106.4
E,P
M,PP
2/1
S3
M
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Further Formulation of Power Criterion
for Cruising Flight on Mars
Weight Constraint:
others,Emotor,Eprop,Ewing,EE WWWWW
322113E CxCxCxS/W
where A/WC prop,E1
E,propmotor,E2 P/WC
S/)WW(C others,Ewing,E3
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Further Formulation of Power Criterion
for Cruising Flight on Mars
Power Ratio Criterion:
1
CxCxC
xxC
2/3
32211
214M
where M1 S/Ax S/Px E,prop2 S/Wx E3
Disk-to-Wing
Area Ratio
Propulsive Power
Per Unit Wing Area Wing Loading
E3
Pprop
M
3
Pprop
E
3
4JC
JC
)S/A(b
106.4C
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Further Formulation of Power Criterion
1)x,x(frC
eARC 21
E,prop
M,prop2/3
E,propmotor4/1
0D
4/3
5M
where
2/3
232121
2121
C/Cxx)C/C(
xx)x,x(f
Power Ratio Criterion:
E3
P
M
3
P
E
2/1
E4
5JC
JC
)S/A(1045.1C
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Further Formulation of Power Criterion
where
2/3
232121
2121
C/Cxx)C/C(
xx)x,x(f
Power Ratio Criterion:
1)x,x(frC
CC 21
E,prop
M,prop2/3
E,propmotor
0D
2/3
E,L
6M
Requirements for Cruising Flight on Mars:
0D
2/3
E,L C/C motorr M,prop1C 3C
E3
P
M
3
P
E
2/1
E5
6JC
JC
)S/A(1063.6C
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Power Criterion for Cruising Flight on Earth:
A Reduced Case Power Ratio Criterion at Altitude H:
1)H(
c
c
b873.0
2/3
SLSL,P
H,PP
2/1
SH
Condition for the Max Altitude of Typical Aircraft:
1H
263.0b095.1/)H( 3/2
P
3/1
S
3/2
SLmax
km9.11Hmax
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Upper Bound of Total Weight
Upper bound by setting 1M
where the weight function is
3/2
21
3/1
2
3/2
121 )yy1(yy)y,y(g
mpw,Emotor,E1 W/Wy mpw,Ewing,E2 W/Wy
3/1
wing,S
3/2
prop,A
3/2
E,propmotorE
3/2
41 )rg(CB
3/13/2
E,prop
3/23/2
4E SPAC)W(UB
)y,y(gWB)W(UB 21mpw,E1E
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Upper Bound of Total Weight: Weight Function
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Table 1. Scaling Laws and Derived Results for Propeller Aircraft on Earth
Quantity Scaling Law
Upper Limit or Max TO Weight W282.1WMTO
Wingspan 3/1
wing W462.0b
Wing Area 3/2
wing W0262.0S
Mean Chord 3/1W0567.0c
Aspect Ratio 8.15
Body Length 3/1
body W41.0l
Max Body Diameter 3/1
0 W0481.0d
Wet and Wing Area Ratio 4.35
Body Fineness Ratio 8.52
Wing Loading 3/1W53WL
Reynolds Number 2/14
c W102.6Re
Cruise Speed 6/1
Rmax W52.15V
Cruise Power 6/7
aircraft,Rmax W67.1P
Power Available 13.1
prop W25.5P
Engine Weight 8944.0
engine W327.0W
Max L/D 11.9
Oswald Efficiency 9.06.0e
Parasite Drag 044.002.0CwingPara S,D
Induced Drag e/0032.0CwingIn S,D
Propulsive Efficiency wingS,Dprop C32.29
Note:
(1) Units: Newtons for weight, m for length, m2 for area, m/s for velocity, Watts for power,
kg/m3 for density, and Newtons/m
2 for loading.
(2) The mean relative errors associated with the scaling laws are indicated in Liu (2006).
Scaling Laws for Typical
Propeller Aircraft on Earth
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Disk-to-Wing Area Ratio for
Typical Propeller Aircraft on Earth
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Service Ceiling for Typical Propeller Aircraft
on Earth
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Parametric Domains for Cruising Flight of
1- and 2-Propeller Aircraft on Earth
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Parametric Domain for Cruising Flight of
The Helios Prototype on Mars
Table 2. Parameters of Several Propeller-Driven Aircraft
Parameters S P S/A b Cruise maxH
M
Typical Aircraft 0.0262 5.25 0.18 0.1 11.8 km 0.039
Helios 0.564 0.67 0.24 0.025 16.1 km 0.12
Sample Martial
Aircraft
0.096 31 0.55 0.12 21.5 km 1.07
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Design Parameters of the JAXA Martian Aircraft
Wing Parameters
wb 2.42 m Wing span
wc 0.48 m Mean wing chord
AR 5.11 Wing aspect ratio
S 1.15 m2 Wing area
wing,S 0.343 kg/m2 Wing surface density
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Design Parameters of the JAXA Martian Aircraft
Propulsion Parameters
propD 0.636 m Propeller diameter
proph 5 mm Mean blade thickness
A/S prop 0.3 Propeller solidity
prop 1797 kg/m3 Propeller material density (carbon fiber)
E,prop 0.8 Propeller efficiency on Earth
M,prop 0.8 Propeller efficiency on Mars
n 2 Number of propellers
E)S/A( 0.18 Reference disk-to-wing area ratio
motorr 2720 W/kg Motor power-to-mass ratio
batteriesE 420 kJ/kg Energy density of batteries
Initial Input Aerodynamic Parameters
0DC 0.02 Zero-lift drag coefficient
e 0.8 Oswald efficiency
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Upper Bound of Total Weight
of the JAXA Martian Aircraft
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Parametric Domain for Cruising Flight of
the JAXA Martian Aircraft
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Relation between Motor Power and Mass:
Specific Power of Motor
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JAXA
Noth et al. (2009)
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Table 4. Mass Distribution of Sample Propeller-Driven Martian Aircraft
Em 4.24 kg Total mass
wing,Em 0.394 kg Wing mass
prop,Em 0.175 kg Propeller mass
motor,Em 1.16 kg Motor mass
others,Em 2.51 kg Other mass
Output Parameters of the JAXA Martian Aircraft
Table 5. Performance Parameters of Sample Propeller-Driven Martian Aircraft
M 1.07 Power ratio on Mars
Rmax,MV 65 m/s Cruising velocity on Mars
MR 260 km Cruising range on Mars
ME 1.1 h Cruising endurance on Mars
Rmax,MP 84 W Cruising power required on Mars
M,propP 90 W Propulsive power available on Mars
M,LC 0.46 Lift coefficient on Mars
S/WM 14.5 N/m2 Wing loading on Mars
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Conclusions
The power ratio criterion is given for cruising
flight of propeller-driven aircraft on Mars
The power ratio criterion is validated by
examining typical propeller-driven aircraft
and the Helios on Earth in several
interesting cases
The power ratio criterion indicates that
the preliminary design of the JAXA Martian
aircraft could be feasible for cruising flight
on Mars
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Conclusions
The power-to-weight ratio of a DC motor:
= 3000 W/kg
The propeller efficiency:
= 0.8
Specific Requirements for JAXA Martian Aircraft:
The lift-to-zero-lift-drag ratio:
= 26 0DE,L C/C
Minimizing the weights of wing
and propellers
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Further Topics
Aerodynamics optimization:
Wing/airfoil design and testing
Propeller optimization/design and testing
Optimization under suitable constraints
on solar power source, batteries, structures
etc.