APPENDIX A
0.50 0.50
APPENDIX A
0.25 0.25
MARTIAN ATMOSPHERIC COMPOSITION
[~] [~] 0.00 0.00
The composition of the Martian atmosphere is
y/c y/c -0.25 -0.25 presented in Table A1 .
-0.50 -0.50 0.00 0.50 1.00 0.00 0.50 1.00 Table A1 . Mars atmospheric composition comparison [45] station 1, r/R = 0.0908, x/c [~] station 2, r/R = 0.2000, x/c [~] Gas Earth Mars 0.50 0.50 O 2 (oxygen) 21% 0.1% 0.25 0.25 CO 2 (carbon dioxide) < 0.1% 95% [~] [~] N (nitrogen) 78% 2.7% 0.00 0.00 y/c y/c Ar (argon) 0.9% 1.6% -0.25 -0.25 Others 0.1% 0.6% -0.50 -0.50 0.00 0.50 1.00 0.00 0.50 1.00 station 3, r/R = 0.2950, x/c [~] station 4, r/R = 0.3903, x/c [~]
APPENDI X B
Figure B2 . The normali zed airfoil profile s for the MH rotor
ROTOR PARAMETERS
Figure B1 shows the chord, thickness, and twist
APPENDIX C
distribution for the MH rotor. Figure B2 shows
LAMINAR SEPARATION PREDICTION
the normalized airfoil cross sections for the MH
Table C1 shows the comparison of the laminar
rotor. The thickness and camber properties of the
separation locations of the present work with the
airfoils are presented in Table B1 .
work by Bussmann et al. [16] .
0.4 [~] Table C1 . Theoretical l aminar separation points (LP6 0.3 c/R criterion), comparison Walz linearization with B ussmann et al.
0.2 Airfoil Source c l 0 .00 0.25 0.5 0 0.75 1 .00 0.1 Present S 0.396 0.351 0.311 0.282 0.246 work normalized chord, 0.0 P 0.394 0.439 0.495 0.543 0.604 J025 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 S 0.403 0.353 0.308 N/A 0.252 radial station, r/R [~] [16] P 0.403 0.435 0.491 N/A 0.592 1.0 [~] S 0.675 0.617 0.558 0.499 0.433 Present t/c 0.8 work P 0.142 0.224 0.329 0.465 N/A J415 0.6 S 0.686 0.630 0.570 N/A 0.476 [16] 0.4 P 0.200 0.283 0.377 N/A 0.494 0.2 Present S 0.749 0. 709 0.674 0.635 0.597 work P 0.039 0.048 0.072 0.116 0.189 0.0 normalized thickness, J815 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 S 0.737 0.685 0.648 N/A 0.594 [16] radial station, r/R [~] P 0.043 0.056 0.093 N/A 0.192 [~] ct ε chordline twist, 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 radial station, r/R [~] Figure B1 . The chord, thickness, an d twist distribution for the MH rotor Table B1 . MH Airfoil thickness and camber details Airfoil t/ c [~ ] x [x/c] f/c [~ ] x [x/c] t/c f/c Station 1 96.201 0.466 0.000 0.000 Station 2 21.985 0.346 5.298 0.594 Station 3 9.800 0.255 5.083 0.591 Station 4 5.899 0.201 4.944 0.597 clf5605 5.000 0.200 4.910 0.593
APPENDIX D ∞
0.20 [~] V
APPENDIX D ∞
c/R 1 LP6 e 0.10
ROTOR STATE CAMRADII
The averaged angle of attack distribution on the limit of stability
0.00
MH rotor in hover obtained from CAMRADII is
-0.10 normalized chord,
shown in Figure D1 and Figure D2 . The error bar
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 suction side radial station, r/R [~] length represents 2 σ .
0.20 [~] V 30.0 30.0 ∞ c/R LP6 0.10 limit of stability 25.0 25.0 0.00 20.0 20.0 [~] -0.10 normalized chord, [~] α α 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 pressure side radial station, r/R [~] 15.0 15.0
Figure E1 . Mars Helicopter upper rotor , approximated
in compressible two - dimensiona l boundary layer state in
10.0 10.0 angle of attack, angle of attack,
hover for Mars Condition 2 at 2,800 RPM
5.0 5.0 0.20 V [~] ∞ LP6 c/R e 0.0 0.0 0.10 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 radial station, r/R [~] radial station, r/R [~] limit of stability 0.00
Figure D1 . Upper rotor average angle of attack dist ribution
over azimuth in hover from CAMRADII
-0.10 normalized chord, 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.0 1.0 30.0 suction side radial station, r/R [~] 0.9 0.9 0.20 [~] V 25.0 0.8 0.8 ∞ c/R 0.10 LP6 0.7 [~] 0.7 [~] l l c c 20.0 limit of stability 0.6 0.6 [~] cient, cient, 0.00 α ffi ffi 0.5 0.5 15.0 -0.10 normalized chord, 0.4 0.4 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 10.0 0.3 0.3 pressure side radial station, r/R [~] section lift coe section lift coe angle of attack,
Figure E2 . Mars Helicopter lower rotor, approximated
0.2 0.2
incompressible two - dimensional boundary layer state in 5.0
0.1 0.1
hover for Mars Condition 2 at 2,800 RPM
0.0 0.0 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.20 radial station, r/R [~] radial station, r/R [~] reattachment V [~] ∞ radial station, r/R [~] possible reattachment c/R possible
Figure D2 . Lower rotor average angle of attack distribution
0.10 limit of stability
over azi muth in hover from CAMRADII 9
e LP6 e LP6 0.00 1.0
APPENDIX E
0.9 -0.10 normalized chord,
BOUNDARY LAYER STATE 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
0.8 suction side radial station, r/R [~]
Figure E1 to Figure E4 show the estimated
0.7 [~] l 0.20 c
boundary layer state for the MH in hover for [~]
V ∞ 0.6 9 e c/R cient,
incompressible flow on M ars and compressible
ffi 0.10 0.5 9 e e limit of stability flow on Earth.
0.4 0.00 0.3 section lift coe -0.10 normalized chord, 0.2 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 pressure side radial station, r/R [~] 0.1
Figure E3 . Mars Helicopter upper rotor, approximated
0.0
compressible two - dimensional boundary layer state in hover
0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 radial station, r/R [~]
on Earth at 2,800 RPM
-1.0 -1.5 -20 -15 -10 -5 0 5 10 15 20 25 angle of attack, α [deg] reattachment 1.0 0.20 possible V ∞ [~] reattachment M = 0.2 (c81) reattachment LP6 possible possible 0.9 M = 0.3 (c81) c/R 9 e e 9 M = 0.4 (c81) 0.10 limit of stability 0.8 M = 0.5 (c81) LP6 LP6 1 M = 0.6 (c81) e [~] 0.00 M = 0.7 (c81) 0.7 d c M = 0.8 (c81) 0.6 M = 0.85 (c81) cient, M = 0.9 (c81) -0.10 normalized chord, ffi 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.5 suction side radial station, r/R [~] 0.4 0.20 V [~] ∞ 0.3 c/R e section drag coe e 0.2 0.10 e limit of stability 0.1 0.00 0.0 -20 -15 -10 -5 0 5 10 15 20 25 -0.10 normalized chord, angle of attack, α [deg] 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 pressure side radial station, r/R [~]
Figure F2 . The drag polar s for the clf 5605 airfoil at
Figure E4 . Mars Helicopter lower roto r, approximated
Station 7 for various Mach numbers
compressible two - dimensional boundary layer state in hover
on Earth at 2,800 RPM
.9
APPENDIX F
.
CFD RESULTS 0
. 9
Figure F1 and Figure F2 show the lift curve and
. 9
the drag coefficients at Station 7 for various Mach 2
.
0. . 9
numbers simulated. Figure F3 and Figure F4
0. 984 988 0. 99 0 0. 0. 992 . 9 9 8 0 .986 6 9 0 .9 7 0 0 .9 0 .9 . 9 8 8 8 9 8 show the non - dimensional density contours for 0 .
0 1. 002 .9 9 0 .9 9 4 8 0 .9 9 Station 3 and 6, respectively.
1.
1 006 1 . 0 0 4 2.0 1 .
0 0 M = 0.2 (c81) M = 0.3 (c81) 1.
1.5 M = 0.4 (c81) M = 0.5 (c81) M = 0.6 (c81) 1.0 [~] M = 0.7 (c81) l c .0 M = 0.8 (c81) 1 M = 0.85 (c81) 0.5 cient, M = 0.9 (c81) ffi 0.0 1 .
0 0 2
Figure F3 . Non - dimensional density contours, 𝜌 𝜌 for
∞ -0.5 section lift coe
Station 3, Mars Condition 2 ( 𝑟 𝑅 = 0 . 30 , 𝛼 = 4 . 82 , 𝑀 =
-1.0
0 . 22 )
-1.5 -20 -15 -10 -5 0 5 10 15 20 25 angle of attack, α [deg]
Fi gure F1 . The lift curve s for the clf 5605 airfoil at Station 7
for various Mach numbers
1.0 M = 0.2 (c81) 0.9 M = 0.3 (c81) M = 0.4 (c81) 0.8 M = 0.5 (c81) M = 0.6 (c81) [~] 0.7 M = 0.7 (c81) d c M = 0.8 (c81) M = 0.85 (c81) 0.6 cient, M = 0.9 (c81) ffi 0.5 0.4 0.3 section drag coe 0.2 0.1 0.0 -20 -15 -10 -5 0 5 10 15 20 25 angle of attack, α [deg] 0 .9 5 .
6 99 0 0.
. 9 4 0. .
0 . 9 3 0.
. 9 .
9 2 0 .
.
0 0 .
0 . 9 . 8 . 9 9 0 4 0 0.
0. . 94 88 0 0 0. 91 . 9 0 . 8 6 0 .8 7 9 . 5 0 . 9 0 . 8 1 0 .8 0 . 9 3 0 . 9 0 . 0 . 9 8 9 6 0. 97 1 . 0 3 1 .0 1 . 0 2 1 1 .
.0 0 0. 99 5 . 0 1 4 . 0 .
0 1.
3 1 0 . 0 . 3
Figure F4 . Non - dimensional density contours, 𝜌 𝜌 for
∞