Top Banner
NACA 0012 Standard C81 Table CL M alpha 0 0.2 0.3 0.4 0.5 0.6 -180 0 0 0 0 0 0 -172.5 0.78 0.78 0.78 0.78 0.78 0.78 -161 0.62 0.62 0.62 0.62 0.62 0.62 -147 1 1 1 1 1 1 -129 1 1 1 1 1 1 -49 -1.18 -1.18 -1.18 -1.18 -1.18 -1.18 -39 -1.18 -1.18 -1.18 -1.18 -1.18 -1.18 -21 -0.8 -0.8 -0.81 -0.83 -0.85 -0.85 -16.5 -1.007 -1.007 -0.944 -0.96 -0.965 -0.965 -15 -1.19 -1.19 -1.09 -1.055 -0.99 -0.98 -14 -1.333 -1.333 -1.22 -1.096 -1 -0.97 -13 -1.334 -1.334 -1.28 -1.12 -1 -0.96 -12 -1.255 -1.255 -1.26 -1.13 -1 -0.947 -11 -1.161 -1.161 -1.19 -1.12 -0.994 -0.93 -10 -1.055 -1.055 -1.01 -1.082 -0.985 -0.91 -8 -0.844 -0.844 -0.88 -0.907 -0.922 -0.87 -6 -0.633 -0.633 -0.66 -0.684 -0.741 -0.77 -4 -0.422 -0.422 -0.44 -0.456 -0.494 -0.544 -2 -0.211 -0.211 -0.22 -0.228 -0.247 -0.272 0 0 0 0 0 0 0 2 0.211 0.211 0.22 0.228 0.247 0.272 4 0.422 0.422 0.44 0.456 0.494 0.544 6 0.633 0.633 0.66 0.684 0.741 0.77 8 0.844 0.844 0.88 0.907 0.922 0.87 10 1.055 1.055 1.1 1.082 0.985 0.91 11 1.161 1.161 1.19 1.12 0.994 0.93 12 1.255 1.255 1.26 1.13 1 0.947 13 1.334 1.334 1.28 1.12 1 0.96 14 1.333 1.333 1.22 1.096 1 0.97 15 1.19 1.19 1.09 1.055 0.99 0.98 16.5 1.007 1.007 0.944 0.96 0.965 0.965 21 0.8 0.8 0.81 0.83 0.85 0.85 39 1.18 1.18 1.18 1.18 1.18 1.18 49 1.18 1.18 1.18 1.18 1.18 1.18 129 -1 -1 -1 -1 -1 -1 147 -1 -1 -1 -1 -1 -1 161 -0.62 -0.62 -0.62 -0.62 -0.62 -0.62 172.5 -0.78 -0.78 -0.78 -0.78 -0.78 -0.78 180 0 0 0 0 0 0
53

Propeller or Rotor in Axial Flight

Aug 21, 2014

Download

Documents

Peter Jonathan
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1: Propeller or Rotor in Axial Flight

NACA 0012Standard C81 Table

CL Malpha 0 0.2 0.3 0.4 0.5 0.6 0.7

-180 0 0 0 0 0 0 0-172.5 0.78 0.78 0.78 0.78 0.78 0.78 0.78

-161 0.62 0.62 0.62 0.62 0.62 0.62 0.62-147 1 1 1 1 1 1 1-129 1 1 1 1 1 1 1-49 -1.18 -1.18 -1.18 -1.18 -1.18 -1.18 -1.18-39 -1.18 -1.18 -1.18 -1.18 -1.18 -1.18 -1.18-21 -0.8 -0.8 -0.81 -0.83 -0.85 -0.85 -0.85

-16.5 -1.007 -1.007 -0.944 -0.96 -0.965 -0.965 -0.965-15 -1.19 -1.19 -1.09 -1.055 -0.99 -0.98 -0.98-14 -1.333 -1.333 -1.22 -1.096 -1 -0.97 -0.97-13 -1.334 -1.334 -1.28 -1.12 -1 -0.96 -0.96-12 -1.255 -1.255 -1.26 -1.13 -1 -0.947 -0.94-11 -1.161 -1.161 -1.19 -1.12 -0.994 -0.93 -0.923-10 -1.055 -1.055 -1.01 -1.082 -0.985 -0.91 -0.9

-8 -0.844 -0.844 -0.88 -0.907 -0.922 -0.87 -0.84-6 -0.633 -0.633 -0.66 -0.684 -0.741 -0.77 -0.75-4 -0.422 -0.422 -0.44 -0.456 -0.494 -0.544 -0.578-2 -0.211 -0.211 -0.22 -0.228 -0.247 -0.272 -0.3130 0 0 0 0 0 0 02 0.211 0.211 0.22 0.228 0.247 0.272 0.3134 0.422 0.422 0.44 0.456 0.494 0.544 0.5786 0.633 0.633 0.66 0.684 0.741 0.77 0.758 0.844 0.844 0.88 0.907 0.922 0.87 0.84

10 1.055 1.055 1.1 1.082 0.985 0.91 0.911 1.161 1.161 1.19 1.12 0.994 0.93 0.92312 1.255 1.255 1.26 1.13 1 0.947 0.9413 1.334 1.334 1.28 1.12 1 0.96 0.9614 1.333 1.333 1.22 1.096 1 0.97 0.9715 1.19 1.19 1.09 1.055 0.99 0.98 0.98

16.5 1.007 1.007 0.944 0.96 0.965 0.965 0.96521 0.8 0.8 0.81 0.83 0.85 0.85 0.8539 1.18 1.18 1.18 1.18 1.18 1.18 1.1849 1.18 1.18 1.18 1.18 1.18 1.18 1.18

129 -1 -1 -1 -1 -1 -1 -1147 -1 -1 -1 -1 -1 -1 -1161 -0.62 -0.62 -0.62 -0.62 -0.62 -0.62 -0.62

172.5 -0.78 -0.78 -0.78 -0.78 -0.78 -0.78 -0.78180 0 0 0 0 0 0 0

Page 2: Propeller or Rotor in Axial Flight

CD Malpha 0 0.18 0.28 0.38 0.48 0.62 0.72

-180 0.022 0.022 0.022 0.022 0.022 0.022 0.022-175 0.062 0.062 0.062 0.062 0.062 0.062 0.062-170 0.132 0.132 0.132 0.132 0.132 0.132 0.132-165 0.242 0.242 0.242 0.242 0.242 0.242 0.242-160 0.302 0.302 0.302 0.302 0.302 0.302 0.302-140 1.042 1.042 1.042 1.042 1.042 1.042 1.042-120 1.652 1.652 1.652 1.652 1.652 1.652 1.652-110 1.852 1.852 1.852 1.852 1.852 1.852 1.852-100 2.022 2.022 2.022 2.022 2.022 2.022 2.022

-90 2.022 2.022 2.022 2.022 2.022 2.022 2.022-80 1.962 1.962 1.962 1.962 1.962 1.962 1.962-70 1.842 1.842 1.842 1.842 1.842 1.842 1.842-60 1.662 1.662 1.662 1.662 1.662 1.662 1.662-50 1.392 1.392 1.392 1.392 1.392 1.399 1.392-30 0.562 0.562 0.562 0.562 0.562 0.562 0.562-21 0.332 0.332 0.332 0.332 0.332 0.332 0.332-16 0.155 0.155 0.181 0.207 0.235 0.257 0.274-15 0.102 0.102 0.148 0.181 0.209 0.233 0.252-14 0.038 0.038 0.099 0.146 0.18 0.212 0.233-13 0.0264 0.0264 0.0455 0.094 0.148 0.191 0.216-12 0.022 0.022 0.03 0.06 0.111 0.164 0.198-11 0.0196 0.0196 0.0232 0.038 0.078 0.135 0.17-10 0.0174 0.0174 0.0189 0.0259 0.053 0.105 0.145-9 0.0154 0.0154 0.0159 0.0187 0.0351 0.077 0.122-8 0.0138 0.0138 0.0138 0.0147 0.022 0.053 0.101-7 0.0122 0.0122 0.0122 0.0123 0.0141 0.035 0.082-6 0.011 0.011 0.011 0.011 0.011 0.0212 0.0615-5 0.01 0.01 0.01 0.01 0.01 0.0132 0.038-4 0.0093 0.0093 0.0093 0.0093 0.0093 0.01 0.0167-3 0.0088 0.0088 0.0088 0.0088 0.0088 0.009 0.0102-2 0.0085 0.0085 0.0085 0.0085 0.0085 0.0085 0.0086-1 0.0083 0.0083 0.0083 0.0083 0.0083 0.0083 0.00830 0.008 0.008 0.008 0.008 0.008 0.008 0.0081 0.0083 0.0083 0.0083 0.0083 0.0083 0.0083 0.00832 0.0085 0.0085 0.0085 0.0085 0.0085 0.0085 0.00863 0.0088 0.0088 0.0088 0.0088 0.0088 0.009 0.01024 0.0093 0.0093 0.0093 0.0093 0.0093 0.01 0.01675 0.01 0.01 0.01 0.01 0.01 0.0132 0.0386 0.011 0.011 0.011 0.011 0.011 0.0212 0.06157 0.0122 0.0122 0.0122 0.0123 0.0141 0.035 0.0828 0.0138 0.0138 0.0138 0.0147 0.022 0.053 0.1019 0.0154 0.0154 0.0159 0.0187 0.0351 0.077 0.122

10 0.0174 0.0174 0.0189 0.0259 0.053 0.105 0.14511 0.0196 0.0196 0.0232 0.038 0.078 0.135 0.1712 0.022 0.022 0.03 0.06 0.111 0.164 0.19813 0.0264 0.0264 0.0455 0.094 0.148 0.191 0.21614 0.038 0.038 0.099 0.146 0.18 0.212 0.233

Page 3: Propeller or Rotor in Axial Flight

15 0.102 0.102 0.148 0.181 0.209 0.233 0.25216 0.155 0.155 0.181 0.207 0.235 0.257 0.27421 0.332 0.332 0.332 0.332 0.332 0.332 0.33230 0.562 0.562 0.562 0.562 0.562 0.562 0.56250 1.392 1.392 1.392 1.392 1.392 1.392 1.39260 1.662 1.662 1.662 1.662 1.662 1.662 1.66270 1.842 1.842 1.842 1.842 1.842 1.842 1.84280 1.962 1.962 1.962 1.962 1.962 1.962 1.96290 2.022 2.022 2.022 2.022 2.022 2.022 2.022

100 2.022 2.022 2.022 2.022 2.022 2.022 2.022110 1.852 1.852 1.852 1.852 1.852 1.852 1.852120 1.652 1.652 1.652 1.652 1.652 1.652 1.652140 1.042 1.042 1.042 1.042 1.042 1.042 1.042160 0.302 0.302 0.302 0.302 0.302 0.302 0.302165 0.242 0.242 0.242 0.242 0.242 0.242 0.242170 0.132 0.132 0.132 0.132 0.132 0.132 0.132175 0.062 0.062 0.062 0.062 0.062 0.062 0.062180 0.022 0.022 0.022 0.022 0.022 0.022 0.022

Page 4: Propeller or Rotor in Axial Flight

0.75 0.8 0.9 10 0 0 0

0.78 0.78 0.78 0.780.62 0.62 0.62 0.62

1 1 1 11 1 1 1

-1.18 -1.18 -1.18 -1.18-1.18 -1.18 -1.18 -1.18-0.71 -0.68 -0.64 -0.64

-0.795 -0.76 -0.7 -0.7-0.83 -0.79 -0.72 -0.72-0.84 -0.805 -0.73 -0.73-0.85 -0.815 -0.735 -0.735-0.85 -0.82 -0.74 -0.74-0.85 -0.81 -0.74 -0.74

-0.845 -0.805 -0.73 -0.73-0.82 -0.77 -0.695 -0.695-0.77 -0.72 -0.593 -0.593

-0.627 -0.603 -0.396 -0.396-0.35 -0.395 -0.2 -0.2

0 0 0 00.35 0.395 0.2 0.2

0.627 0.603 0.396 0.3960.77 0.72 0.593 0.5930.82 0.77 0.695 0.695

0.845 0.805 0.73 0.730.85 0.81 0.74 0.740.85 0.82 0.74 0.740.85 0.815 0.735 0.7350.84 0.805 0.73 0.730.83 0.79 0.73 0.73

0.795 0.76 0.7 0.70.71 0.68 0.64 0.641.18 1.18 1.18 1.181.18 1.18 1.18 1.18

-1 -1 -1 -1-1 -1 -1 -1

-0.62 -0.62 -0.62 -0.62-0.78 -0.78 -0.78 -0.78

0 0 0 0

-50 -40 -30 -20 -10 0 10 20 30 40 50

-1.5

-1

-0.5

0

0.5

1

1.5

Page 5: Propeller or Rotor in Axial Flight

0.77 0.82 0.92 10.022 0.022 0.022 0.0220.062 0.062 0.062 0.0620.132 0.132 0.132 0.1320.242 0.242 0.242 0.2420.302 0.302 0.302 0.3021.042 1.042 1.042 1.0421.652 1.652 1.652 1.6521.852 1.852 1.852 1.8522.022 2.022 2.022 2.0222.022 2.022 2.022 2.0221.962 1.962 1.962 1.9621.842 1.842 1.842 1.8421.662 1.662 1.662 1.6621.392 1.392 1.392 1.3920.562 0.562 0.562 0.5620.332 0.332 0.342 0.3420.292 0.305 0.342 0.3420.271 0.282 0.298 0.2980.249 0.26 0.293 0.2930.231 0.239 0.272 0.2920.211 0.22 0.252 0.2910.192 0.202 0.232 0.2750.176 0.186 0.213 0.2540.159 0.172 0.199 0.2320.14 0.155 0.183 0.214

0.111 0.139 0.169 0.1920.082 0.12 0.14 0.170.054 0.088 0.111 0.140.03 0.0575 0.095 0.112

0.0175 0.0355 0.086 0.1020.0117 0.024 0.081 0.0980.0091 0.0175 0.078 0.096

0.008 0.0137 0.078 0.0950.0091 0.0175 0.078 0.0960.0117 0.024 0.081 0.0980.0175 0.0355 0.086 0.102

0.03 0.0575 0.095 0.1120.054 0.088 0.111 0.140.082 0.12 0.14 0.170.111 0.139 0.169 0.1920.14 0.155 0.183 0.214

0.159 0.172 0.199 0.2320.176 0.186 0.213 0.2540.192 0.202 0.232 0.2750.211 0.22 0.252 0.2910.231 0.239 0.272 0.2920.249 0.26 0.293 0.293

-50 -40 -30 -20 -10 0 10 20 30 40 500

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Page 6: Propeller or Rotor in Axial Flight

0.271 0.282 0.298 0.2980.292 0.305 0.342 0.3420.332 0.332 0.342 0.3420.562 0.562 0.562 0.5621.392 1.392 1.392 1.3921.662 1.662 1.662 1.6621.842 1.842 1.842 1.8421.962 1.962 1.962 1.9622.022 2.022 2.022 2.0222.022 2.022 2.022 2.0221.852 1.852 1.852 1.8521.652 1.652 1.652 1.6521.042 1.042 1.042 1.0420.302 0.302 0.302 0.3020.242 0.242 0.242 0.2420.132 0.132 0.132 0.1320.062 0.062 0.062 0.0620.022 0.022 0.022 0.022

Page 7: Propeller or Rotor in Axial Flight

-50 -40 -30 -20 -10 0 10 20 30 40 50

-1.5

-1

-0.5

0

0.5

1

1.5

Page 8: Propeller or Rotor in Axial Flight

-50 -40 -30 -20 -10 0 10 20 30 40 500

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Page 9: Propeller or Rotor in Axial Flight

Atmospheric Inputs Geometric InputsDensity 0.00238 slugs/ft^3 Nb, number o 3V_∞ 0.00000 mph Disk Diamete 8.00V_∞ 0.00000 ft/s Disk Radius 4.00V_∞ 0.00000 knots Disk Area 50.27V_∞ 0.00000 m/s c, Chord 0.42RPM 2000 rev/min σ, Solidity 0.09931268RPS 33.3333333 rev/srad/s 209.43951 rad/sV_tip 837.758041 ft/s

λ, Inflow Rav_i v_i Thrust Ct Ct, hover onl Power (ideal)(mph) (ft/s) lbs check (ft*lb/s)

0 0 0 0 0 0 0 01 0.003501 2 2.93 2.06 0.000025 0.000025 6.03 2 0.007003 4 5.87 8.23 0.000098 0.000098 48.27 3 0.010504 6 8.80 18.51 0.000221 0.000221 162.91 4 0.014006 8 11.73 32.91 0.000392 0.000392 386.17 5 0.017507 10 14.67 51.43 0.000613 0.000613 754.23 6 0.021008 12 17.60 74.05 0.000883 0.000883 1,303.32 7 0.02451 14 20.53 100.79 0.001201 0.001201 2,069.62 8 0.028011 16 23.47 131.65 0.001569 0.001569 3,089.34 9 0.031513 18 26.40 166.62 0.001986 0.001986 4,398.69

10 0.035014 20 29.33 205.70 0.002452 0.002452 6,033.87 11 0.038515 22 32.27 248.90 0.002967 0.002967 8,031.08 12 0.042017 24 35.20 296.21 0.003531 0.003531 10,426.53 13 0.045518 26 38.13 347.63 0.004144 0.004144 13,256.41 14 0.04902 28 41.07 403.17 0.004806 0.004806 16,556.94 15 0.052521 30 44.00 462.83 0.005517 0.005517 20,364.31 16 0.056023 32 46.93 526.59 0.006277 0.006277 24,714.73 17 0.059524 34 49.87 594.47 0.007086 0.007086 29,644.40 18 0.063025 36 52.80 666.47 0.007944 0.007944 35,189.53 19 0.066527 38 55.73 742.58 0.008852 0.008852 41,386.32 20 0.070028 40 58.67 822.80 0.009808 0.009808 48,270.96

0.000 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0.080 0.090 0.1000.0000

0.0010

0.0020

0.0030

0.0040

0.0050

0.0060

0.0070

0.0080

0.0090

0.0100

Thrust Coefficient, Ct

Pow

er C

oeff

icie

nt, C

p

Michael DuffyAE 6070, HW 2Sep. 10th, 2006

Page 10: Propeller or Rotor in Axial Flight

0.000 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0.080 0.090 0.1000.0000

0.0010

0.0020

0.0030

0.0040

0.0050

0.0060

0.0070

0.0080

0.0090

0.0100

Thrust Coefficient, Ct

Pow

er C

oeff

icie

nt, C

pMichael DuffyAE 6070, HW 2Sep. 10th, 2006

Page 11: Propeller or Rotor in Axial Flight

Power Corrections1.100

ft Cd_0 0.010ftft^2ft

Power (ideal) Power (ideaCp,simple Cp_i Cp_0 Cp_correct FM Cp/σ Ct/σ(HP) (kW) induced profile

0 0 0 0.0000000 0.000124 0.0001241 0 0.00125 0 0.01097 0.00818 0.0000001 0.0000001 0.000124 0.0001242 0.0006911 0.001251 0.00 0.08777 0.06545 0.0000007 0.0000008 0.000124 0.0001249 0.00549919 0.001258 0.000988 0.29621 0.22088 0.0000023 0.0000025 0.000124 0.0001267 0.0182969 0.001276 0.002222 0.70212 0.52357 0.0000055 0.0000060 0.000124 0.0001302 0.04220633 0.001311 0.00395 1.37133 1.02260 0.0000107 0.0000118 0.000124 0.0001359 0.07894105 0.001369 0.006172 2.36967 1.76706 0.0000185 0.0000204 0.000124 0.0001445 0.12829955 0.001455 0.008888 3.76294 2.80602 0.0000294 0.0000324 0.000124 0.0001565 0.18812456 0.001576 0.012098 5.61698 4.18858 0.0000440 0.0000484 0.000124 0.0001725 0.25483286 0.001737 0.015801 7.99762 5.96382 0.0000626 0.0000688 0.000124 0.0001930 0.32430844 0.001943 0.019998 10.97067 8.18083 0.0000859 0.0000944 0.000124 0.0002186 0.39277914 0.002201 0.024689 14.60197 10.88868 0.0001143 0.0001257 0.000124 0.0002498 0.45737888 0.002516 0.029874 18.95732 14.13647 0.0001484 0.0001632 0.000124 0.0002873 0.51632025 0.002893 0.035553 24.10257 17.97328 0.0001886 0.0002075 0.000124 0.0003316 0.56877902 0.003339 0.041725 30.10353 22.44820 0.0002356 0.0002591 0.000124 0.0003833 0.61464576 0.003859 0.048391 37.02602 27.61030 0.0002898 0.0003187 0.000124 0.0004429 0.65426502 0.004459 0.055551 44.93588 33.50868 0.0003517 0.0003868 0.000124 0.0005110 0.68822291 0.005145 0.063205 53.89892 40.19241 0.0004218 0.0004640 0.000124 0.0005881 0.71719905 0.005922 0.071352 63.98096 47.71060 0.0005007 0.0005508 0.000124 0.0006749 0.74187524 0.006796 0.079994 75.24785 56.11231 0.0005889 0.0006478 0.000124 0.0007719 0.76288586 0.007772 0.09 87.76538 65.44664 0.0006868 0.0007555 0.000124 0.0008797 0.78079555 0.008857 0.10

Κ, Induced Power correction factor

0.000 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0.080 0.090 0.1000.0000

0.0010

0.0020

0.0030

0.0040

0.0050

0.0060

0.0070

0.0080

0.0090

0.0100

Thrust Coefficient, Ct

Pow

er C

oeff

icie

nt, C

p

Michael DuffyAE 6070, HW 2Sep. 10th, 2006

Page 12: Propeller or Rotor in Axial Flight

0.000 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0.080 0.090 0.1000.0000

0.0010

0.0020

0.0030

0.0040

0.0050

0.0060

0.0070

0.0080

0.0090

0.0100

Thrust Coefficient, Ct

Pow

er C

oeff

icie

nt, C

p

Michael DuffyAE 6070, HW 2Sep. 10th, 2006

Page 13: Propeller or Rotor in Axial Flight

Ct/Cp_ Ideal

1000285.5993142.799795.1997871.3998357.1198747.59989

40.799935.6999231.7332628.5599325.9635823.7999421.9691820.3999519.0399617.8499616.7999615.8666315.0315414.27997

Page 14: Propeller or Rotor in Axial Flight

USER INPUTS QUIK CALCS250 ktas Temperature, T 44.756 at the given alt for the given day type (NOT USED, BUT FOR YOU INFO)

Pressure Altitude, h 4000 ft Delta 0.8637Type of Day std std/trop/hot Theta 1.0694

Temperature, T 95 Sigma 0.8076Density 1.920E-03m 3.937E-07n 2.051E-04M 0.365a, Speed of Sound 1154.546 ft/sec

Airspeed, V 224.6716393 kcas

Airspeed, V o F

o Fslugs/ft3

ft2/sec

INPUT HERE:

OUTPUT HERE:

Page 15: Propeller or Rotor in Axial Flight

at the given alt for the given day type (NOT USED, BUT FOR YOU INFO)

Page 16: Propeller or Rotor in Axial Flight

INSTRUCTIONS

Propeller calculator instructions:1) Open MS Excel before loading the spreadsheet, should have a blank workbook.2) Click Tools -> Add-ins -> Check the 'SOLVER' Check box3) Click Tools -> Options -> 'Calculation' Tab -> Check the 'Iteration' Check Box -> then hit ok4) Click Tools -> Macro -> Visual Basic Editor (or hit Alt + F11), this will open Visual Basic Editor5) In Visual Basic Editor Click Tools -> References.. -> Check the 'SOLVER' check box6) Now you can open 'PROPELLER_OR_ROTOR_IN_AXIAL_FLIGHT.xls' in MS Excel7) When prompted -> Click on 'Enable Macros' 8) Change the Blue values to you design, and click on the 'Calculate Button'

Note: If you get 'NaN' in any cell you can either restart the program by closing and reopening, or put zero's in cells 'N7, N8, T3, and T4' this will fix almost any problem, then you can start turning things back on until you find the problem.

Page 17: Propeller or Rotor in Axial Flight

3) Click Tools -> Options -> 'Calculation' Tab -> Check the 'Iteration' Check Box -> then hit ok4) Click Tools -> Macro -> Visual Basic Editor (or hit Alt + F11), this will open Visual Basic Editor

Note: If you get 'NaN' in any cell you can either restart the program by closing and reopening, or put zero's in cells 'N7, N8, T3, and T4' this will fix almost any problem, then you can start turning things back on until you find the problem.

Page 18: Propeller or Rotor in Axial Flight

Note: If you get 'NaN' in any cell you can either restart the program by closing and reopening, or put zero's in cells 'N7, N8, T3, and T4' this will fix almost any problem, then you can start turning things back on until you find the problem.

Page 19: Propeller or Rotor in Axial Flight

Air Properties: Rotor Properties:Density 0.00191967 slugs/ft^3 Blade Pitch 0 deg.Temp 95 °F Blade Pitch 0 rad.

0.00020507 ft^2/s θ_tip 6.208 deg.3.9367E-07 lb.s/ft^2 θ_tip 0.10835 rad.

a, Speed of Sound 1,154.55 ft/s θ_.75 14.452 deg.θ_twist -20 deg.Blades, Nb 4 NbRadius, R 23.5 ftr_root cut out 0 ftDiam. 47 ftRoot Chord, c_root 31.12122 inTip Chord, c_tip 10.37374 inn_elements 20Ω,RPM 264.15 rev/minΩ,RPS 4.4025 rev/sΩ,rad/s 27.66172 rad/sV_tip 650.0505 ft/sM_tip 0.56 compressibleX_tsr #DIV/0! tip speed ratioV_∞ 0.000 mphV_∞ 0.000 ft/sλc 0.0000Twist Dist 1 1 = linear, 0 = IdealChord Dist 1 2 = constant, 1 = linear taper, 0 = ideal taper

elemey_location of element dy Chord Chord Twist dist. Twist dist. θft ft in ft deg. deg. deg.

Ideal Input Local Blade Pitch1 1.175 1.175 31.12122 2.593435 124.16 28.45 28.452 2.35 1.175 30.02924 2.502437 62.08 27.45 27.453 3.525 1.175 28.93727 2.411439 41.39 26.45 26.454 4.7 1.175 27.8453 2.320442 31.04 25.45 25.455 5.875 1.175 26.75333 2.229444 24.83 24.45 24.456 7.05 1.175 25.66135 2.138446 20.69 23.45 23.457 8.225 1.175 24.56938 2.047448 17.74 22.45 22.458 9.4 1.175 23.47741 1.956451 15.52 21.45 21.459 10.575 1.175 22.38544 1.865453 13.80 20.45 20.45

10 11.75 1.175 21.29346 1.774455 12.42 19.45 19.4511 12.925 1.175 20.20149 1.683458 11.29 18.45 18.4512 14.1 1.175 19.10952 1.59246 10.35 17.45 17.4513 15.275 1.175 18.01755 1.501462 9.55 16.45 16.4514 16.45 1.175 16.92557 1.410465 8.87 15.45 15.4515 17.625 1.175 15.8336 1.319467 8.28 14.45 14.4516 18.8 1.175 14.74163 1.228469 7.76 13.45 13.4517 19.975 1.175 13.64966 1.137471 7.30 12.45 12.4518 21.15 1.175 12.55768 1.046474 6.90 11.45 11.45

ν, Kinematic Viscosityμ, Dynamic Viscosity

(V∞)/ΩR

Important note:Must have:-Tools-Options-Calculation Tab – Iteration check box checked on for this program to work:-Tools-Addi-ins-Solver =>Add-in must be checked-In Visual Basic Tools -References-Solver Must be checked

Hit F9 to Recalculate or Calculate Button

Items in BLUE are INPUTSItems in BLACK are Calculated via magic

H25
Michael Duffy: Choose Linear or Ideal Twist Dist.
H26
Michael Duffy: Choose Constant, linear or ideal taper for chord distribution
Page 20: Propeller or Rotor in Axial Flight

19 22.325 1.175 11.46571 0.955476 6.53 10.45 10.4520 23.5 1.175 10.37374 0.864478 6.21 9.45 9.45

Total:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.00

5.00

10.00

15.00

20.00

25.00

30.00Angle (deg)

EFF. ALPHA INFLOW ANG LOCAL PITCH

x/R

Ang

le (d

eg)

Page 21: Propeller or Rotor in Axial Flight

Airfoil Propeties:Cl Cl_α CdSection Lift Coeffecient Section Drag Coeffecient

For Ideal Twist 0.0000 #DIV/0! 0.0080 Table Look Up5.7 0.0087 Polynomial or Constant

For Linear Twist Compressiblity 1 1 = on, 0 = off Table Look up 0 1 = table look up, 0 = linear approx.

7.1628 m0 m

14.3256 m0.79047891655 m0.26349297218 m Propeller calculator instructions:

1) Open MS Excel before loading the spreadsheet, should have a blank workbook.2) Click Tools -> Add-ins -> Check the 'SOLVER' Check box3) Click Tools -> Options -> 'Calculation' Tab -> Check the 'Iteration' Check Box -> then hit ok4) Click Tools -> Macro -> Visual Basic Editor (or hit Alt + F11), this will open Visual Basic Editor5) In Visual Basic Editor Click Tools -> References.. -> Check the 'SOLVER' check box

compressible 6) Now you can open 'PROPELLER_OR_ROTOR_IN_AXIAL_FLIGHT.xls' in MS Exceltip speed ratio 7) When prompted -> Click on 'Enable Macros'

0 m/s 8) Change the Blue values to you design, and click on the 'Calculate Button'

Note: If you get 'NaN' in any cell you can either restart the program by closing and reopening, or put zero's in cells 'N7, N8, T3, and T4' this will fix almost any problem, then you can start turning things back on until you find the problem.1 = linear, 0 = Ideal2 = constant, 1 = linear taper, 0 = ideal taper

θ φ φ α α r dr σ, Solidityrad. deg. rad. deg. rad.

Local Blade Pitch Inflow Angle Effective Angle of Attack local solidi0.49658 24.35 0.42503 4.10 0.07155 0.05 0.05 0.1405130.47913 20.96 0.36584 6.49 0.11329 0.1 0.05 0.1355830.46167 18.09 0.31574 8.36 0.14593 0.15 0.05 0.1306530.44422 15.86 0.27675 9.60 0.16747 0.2 0.05 0.1257220.42677 14.14 0.24684 10.31 0.17993 0.25 0.05 0.1207920.40931 12.80 0.22332 10.66 0.18600 0.3 0.05 0.1158620.39186 11.68 0.20392 10.77 0.18794 0.35 0.05 0.1109320.37441 10.72 0.18718 10.73 0.18723 0.4 0.05 0.1060010.35695 9.87 0.17226 10.58 0.18470 0.45 0.05 0.1010710.33950 9.09 0.15872 10.36 0.18079 0.5 0.05 0.0961410.32205 8.38 0.14629 10.07 0.17576 0.55 0.05 0.091210.30459 7.72 0.13480 9.73 0.16979 0.6 0.05 0.086280.28714 7.11 0.12411 9.34 0.16303 0.65 0.05 0.081350.26969 6.54 0.11409 8.91 0.15559 0.7 0.05 0.076420.25223 6.00 0.10468 8.45 0.14755 0.75 0.05 0.0714890.23478 5.49 0.09582 7.96 0.13896 0.8 0.05 0.0665590.21733 5.02 0.08757 7.43 0.12976 0.85 0.05 0.0616290.19988 4.60 0.08030 6.85 0.11957 0.9 0.05 0.056698

M5
Michael Duffy: Based on Table look up
O5
Michael Duffy: Based on Table look up
N7
Michael Duffy: Compressiblity effects tend to increase rotor thrust by 10%; however, tip losses usually offset this
N8
Michael Duffy: 1 = table look up (you can supply your own, warning, this is kinda wierd) 0 = linear approx.
Page 22: Propeller or Rotor in Axial Flight

0.18242 4.36 0.07612 6.09 0.10630 0.95 0.05 0.0517680.16497 9.37 0.16349 0.08 0.00148 1 0.05 0.046838

0.0937

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.00

5.00

10.00

15.00

20.00

25.00

30.00Angle (deg)

EFF. ALPHA INFLOW ANG LOCAL PITCH

x/R

Ang

le (d

eg)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.000000

0.020000

0.040000

0.060000

0.080000

0.100000

0.120000

0.140000

0.160000

0.180000INFLOW RATIO

INFLOW GUESS INFLOW FROM MOMENTUM

x/R

INFL

OW

RA

TIO

Page 23: Propeller or Rotor in Axial Flight

Correction Factors: Output:Prandtl Tip Loss 1 1 = on, 0 = off Ct Cp/σ Ct/σPrandtl Root Loss 1 1 = on, 0 = off 0.01066 0.0125 0.1421

Polynomial or Constant

1 = table look up, 0 = linear approx.Check Convergence:Converged

1) Open MS Excel before loading the spreadsheet, should have a blank workbook.2) Click Tools -> Add-ins -> Check the 'SOLVER' Check box3) Click Tools -> Options -> 'Calculation' Tab -> Check the 'Iteration' Check Box -> then hit ok4) Click Tools -> Macro -> Visual Basic Editor (or hit Alt + F11), this will open Visual Basic Editor5) In Visual Basic Editor Click Tools -> References.. -> Check the 'SOLVER' check box6) Now you can open 'PROPELLER_OR_ROTOR_IN_AXIAL_FLIGHT.xls' in MS Excel7) When prompted -> Click on 'Enable Macros' 8) Change the Blue values to you design, and click on the 'Calculate Button'

Note: If you get 'NaN' in any cell you can either restart the program by closing and reopening, or put zero's in cells 'N7, N8, T3, and T4' this will fix almost any problem, then you can start turning things back on until you find the problem.

Prandtl Tip/Root Loss Don't Use Yetσ, Solidity V_tan X_loc f_tip f_root F v_inflow v_inflow

ft/s Prandtl mph mphThrust Weighted local speed ratio using lift curve using tables1.756E-05 32.503 #DIV/0! 89.40 0.25 0.43 10.03 0.00006.779E-05 65.005 #DIV/0! 49.20 0.61 0.63 16.98 3.77590.000147 97.508 #DIV/0! 35.89 1.12 0.79 21.72 7.68220.000251 130.010 #DIV/0! 28.91 1.81 0.89 25.18 7.60690.000377 162.513 #DIV/0! 24.31 2.70 0.96 27.92 8.70680.000521 195.015 #DIV/0! 20.90 3.84 0.99 30.20 9.73620.000679 227.518 #DIV/0! 18.21 5.28 1.00 32.08 10.68930.000848 260.020 #DIV/0! 16.03 7.12 1.00 33.58 11.57630.001023 292.523 #DIV/0! 14.19 9.50 1.00 34.70 12.40990.001202 325.025 #DIV/0! 12.60 12.60 1.00 35.47 13.1983

0.00138 357.528 #DIV/0! 11.19 16.71 1.00 35.92 13.94830.001553 390.030 #DIV/0! 9.89 22.25 1.00 36.07 14.66440.001719 422.533 #DIV/0! 8.68 29.93 1.00 35.94 15.35260.001872 455.035 #DIV/0! 7.51 40.90 1.00 35.55 16.01380.002011 487.538 #DIV/0! 6.37 57.32 1.00 34.92 16.6524

0.00213 520.040 #DIV/0! 5.22 83.49 1.00 34.08 17.27260.002226 552.543 #DIV/0! 4.03 129.42 0.99 33.08 16.06270.002296 585.045 #DIV/0! 2.77 224.16 0.96 32.10 14.5092

Calculate

T3
Michael Duffy: Prandtl tip loss factor, put a 1 to turn it on, and a 0 to turn it off ONLY affects outboard 10 elements
T4
Michael Duffy: Prandtl root loss factor, put a 1 to turn it on, and a 0 to turn it off ONLY affects first 10 elements
Page 24: Propeller or Rotor in Axial Flight

0.002336 617.548 #DIV/0! 1.38 499.20 0.84 32.11 12.64740.002342 650.050 #DIV/0! 0.00 4992.00 0.00 73.11 25.9158

0.0750 1.0000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.000000

0.020000

0.040000

0.060000

0.080000

0.100000

0.120000

0.140000

0.160000

0.180000INFLOW RATIO

INFLOW GUESS INFLOW FROM MOMENTUM

x/R

INFL

OW

RA

TIO

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0.00000

0.00200

0.00400

0.00600

0.00800

0.01000

0.01200

0.01400

0.01600

0.01800

0.02000Cl AND Cd

Cl Cd

x/RC

l Cd

Page 25: Propeller or Rotor in Axial Flight

Thrust 15,000.32

Note: If you get 'NaN' in any cell you can either restart the program by closing and reopening, or put zero's in cells 'N7, N8, T3, and T4' this will fix almost any problem, then you can start turning things back on until you find the problem.

Don't Use Yet BETv_inflow a_induction f λ, Inflow U_vel_vector Re Re Mach Cl_αft/s ft/s check Local

14.711 #DIV/0! 0.022631 35.68 451,193 451,193 0.03 5.70 24.902 #DIV/0! 0.038308 69.61 849,464 849,464 0.06 5.71 31.853 #DIV/0! 0.049001 102.58 1,206,237 1,206,237 0.08 5.72 36.927 #DIV/0! 0.056807 135.15 1,529,310 1,529,310 0.11 5.74 40.950 #DIV/0! 0.062995 167.59 1,822,012 1,822,012 0.14 5.76 44.289 #DIV/0! 0.068132 199.98 2,085,390 2,085,390 0.17 5.78 47.051 #DIV/0! 0.072380 232.33 2,319,646 2,319,646 0.20 5.81 49.248 #DIV/0! 0.075760 264.64 2,524,813 2,524,813 0.23 5.85 50.894 #DIV/0! 0.078292 296.92 2,700,969 2,700,969 0.25 5.89 52.024 #DIV/0! 0.080031 329.16 2,848,233 2,848,233 0.28 5.94 52.680 #DIV/0! 0.081039 361.39 2,966,717 2,966,717 0.31 5.99 52.898 #DIV/0! 0.081375 393.60 3,056,504 3,056,504 0.34 6.06 52.710 #DIV/0! 0.081086 425.81 3,117,657 3,117,657 0.37 6.12 52.143 #DIV/0! 0.080214 458.01 3,150,216 3,150,216 0.39 6.20 51.223 #DIV/0! 0.078798 490.22 3,154,212 3,154,212 0.42 6.29 49.985 #DIV/0! 0.076894 522.44 3,129,669 3,129,669 0.45 6.38 48.511 #DIV/0! 0.074627 554.67 3,076,622 3,076,622 0.48 6.49 47.081 #DIV/0! 0.072426 586.94 2,995,159 2,995,159 0.51 6.61

(V+vi)/ΩR

Page 26: Propeller or Rotor in Axial Flight

47.100 #DIV/0! 0.072456 619.34 2,885,693 2,885,693 0.53 6.75 107.233 #DIV/0! 0.164962 658.84 2,777,356 2,777,356 0.56 6.90

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.0000E+00

1.0000E-04

2.0000E-04

3.0000E-04

4.0000E-04

5.0000E-04

6.0000E-04

7.0000E-04

8.0000E-04

9.0000E-04

1.0000E-03Ct - Thrust Coeff

MOMENTUM THEORY SMALL ANGLE EXACT

x/RC

t - T

hrus

t Coe

ff0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0.00000

0.00200

0.00400

0.00600

0.00800

0.01000

0.01200

0.01400

0.01600

0.01800

0.02000Cl AND Cd

Cl Cd

x/R

Cl Cd

Page 27: Propeller or Rotor in Axial Flight

BETCl Cd dL= dD= dT= dQ=Section Lift CoSection Drag Colbf lbf lbf ft*lb

1 blade 1 blade n blades n blades0.4080 0.00920 1.519 0.034 5.479 3.0900.6468 0.01138 8.845 0.156 32.818 31.1100.8348 0.01406 23.889 0.402 90.333 109.9870.9607 0.01629 45.925 0.779 175.860 249.9851.0359 0.01775 73.157 1.254 282.534 448.6381.0756 0.01851 103.748 1.785 403.104 697.0281.0927 0.01876 136.192 2.338 531.587 982.7281.0953 0.01866 169.266 2.884 663.090 1290.9081.0883 0.01834 201.851 3.402 793.121 1605.3091.0739 0.01786 232.858 3.872 917.278 1909.4281.0536 0.01725 261.254 4.277 1031.359 2187.6351.0283 0.01655 286.103 4.605 1131.554 2426.0150.9986 0.01580 306.589 4.851 1214.522 2612.9850.9650 0.01501 322.018 5.010 1277.417 2739.7490.9278 0.01421 331.814 5.082 1317.867 2800.6370.8872 0.01341 335.480 5.072 1333.824 2793.4070.8423 0.01262 332.454 4.982 1322.976 2719.7330.7906 0.01183 321.441 4.809 1280.079 2586.868

Page 28: Propeller or Rotor in Axial Flight

0.7171 0.01092 296.418 4.512 1180.868 2414.7880.0102 0.00867 4.317 3.669 14.650 406.306

3,795.14 63.77 15,000.32 31,016.34 66,724.74 N

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.0000E+00

1.0000E-04

2.0000E-04

3.0000E-04

4.0000E-04

5.0000E-04

6.0000E-04

7.0000E-04

8.0000E-04

9.0000E-04

1.0000E-03Ct - Thrust Coeff

MOMENTUM THEORY SMALL ANGLE EXACT

x/R

Ct -

Thr

ust C

oeff

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.000

10000.000

20000.000

30000.000

40000.000

50000.000

60000.000

70000.000

80000.000

90000.000Power - ft*lb/s

PROFILE POWER INDUCED POWER TOTAL POWER

x/R

Pow

er -

ft*lb

/s

Page 29: Propeller or Rotor in Axial Flight

BET EXACTdP_i= dP_p= dP= dP= dP= dCt dCpft*lb/s ft*lb/s ft*lb/s HP kWinduced profile n blades

81.428 4.056 85.483 0.1554238638 0.11589956 3.8927E-06 9.3439E-08822.781 37.786 860.567 1.5646678947 1.16677265 2.3319E-05 9.4066E-07

2893.303 149.131 3042.434 5.5316973188 4.12498598 6.4186E-05 3.3256E-066525.477 389.551 6915.028 12.572778084 9.37551901 1.2496E-04 7.5586E-06

11619.906 790.188 12410.094 22.563806479 16.8258276 2.0075E-04 1.3565E-0517923.103 1357.891 19280.995 35.056353755 26.1415185 2.8642E-04 2.1075E-0525100.542 2083.411 27183.953 49.425369423 36.8564917 3.7772E-04 2.9714E-0532761.279 2947.471 35708.750 64.925000115 48.4145643 4.7116E-04 3.9032E-0540483.704 3921.913 44405.617 80.73748627 60.2059332 5.6355E-04 4.8538E-0547847.743 4970.332 52818.076 96.032864695 71.6116949 6.5177E-04 5.7734E-0554462.887 6050.869 60513.756 110.02501041 82.0456362 7.3283E-04 6.6145E-0559987.815 7119.946 67107.761 122.01411051 90.9859066 8.0402E-04 7.3353E-0564144.302 8135.378 72279.681 131.41760103 97.9980883 8.6297E-04 7.9006E-0566727.434 9058.751 75786.184 137.7930623 102.752269 9.0766E-04 8.2839E-0567613.527 9856.928 77470.455 140.85537307 105.035834 9.3641E-04 8.4680E-0566768.282 10502.171 77270.453 140.49173283 104.764667 9.4774E-04 8.4462E-0564263.673 10968.829 75232.502 136.7863674 102.001577 9.4004E-04 8.2234E-0560339.421 11217.809 71557.231 130.10405561 97.0185776 9.0956E-04 7.8217E-05

AS33
Michael Duffy: Non dimensionalized by Tip speed for Rotor
AT33
Michael Duffy: Non dimensionalized by Tip speed for Rotor
Page 30: Propeller or Rotor in Axial Flight

55683.350 11113.846 66797.196 121.44944711 90.5648372 8.3906E-04 7.3014E-051827.138 9411.977 11239.115 20.434754713 15.238194 1.0410E-05 1.2285E-05

747,877.10 110,088.23 857,965.3 1,559.94 1,163.24 0.01066 0.00094

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.000

10000.000

20000.000

30000.000

40000.000

50000.000

60000.000

70000.000

80000.000

90000.000Power - ft*lb/s

PROFILE POWER INDUCED POWER TOTAL POWER

x/R

Pow

er -

ft*lb

/s

Page 31: Propeller or Rotor in Axial Flight

SMALL ANGLE APPROX MOMENTUMdCt dCp λ, Inflow Solver v_i_diff dT dCtcheck: check: mph check: check:

3.6173E-06 8.0182E-08 0.022631 0.000000 0.000000 7.2081 2.2013E-062.2064E-05 8.4060E-07 0.038308 0.000000 0.000000 41.3067 1.8586E-056.1677E-05 3.0606E-06 0.049001 0.000000 0.000000 101.3757 5.6756E-051.2135E-04 7.0949E-06 0.056807 0.000000 0.000000 181.6647 1.1553E-041.9634E-04 1.2903E-05 0.062995 0.000000 0.000000 279.2467 1.8993E-042.8149E-04 2.0233E-05 0.068132 0.000000 0.000000 391.9727 2.7470E-043.7251E-04 2.8725E-05 0.072380 0.000000 0.000000 516.1073 3.6553E-044.6591E-04 3.7938E-05 0.075760 0.000000 0.000000 646.2080 4.5893E-045.5846E-04 4.7388E-05 0.078292 0.000000 0.000000 776.4017 5.5164E-046.4700E-04 5.6574E-05 0.080031 0.000000 0.000000 901.4045 6.4049E-047.2849E-04 6.5018E-05 0.081039 0.000000 0.000000 1016.6928 7.2240E-048.0020E-04 7.2294E-05 0.081375 0.000000 0.000000 1118.3340 7.9460E-048.5972E-04 7.8041E-05 0.081086 0.000000 0.000000 1202.9454 8.5466E-049.0498E-04 8.1986E-05 0.080214 0.000000 0.000000 1267.7528 9.0048E-049.3428E-04 8.3948E-05 0.078798 0.000000 0.000000 1310.7793 9.3035E-049.4614E-04 8.3852E-05 0.076894 0.000000 0.000000 1331.4136 9.4277E-049.3890E-04 8.1740E-05 0.074627 0.000000 0.000000 1332.4326 9.3605E-049.0881E-04 7.7823E-05 0.072426 0.000000 0.000000 1328.8260 9.0640E-04

(V+vi)/ΩR

AU30
Michael Duffy: assumes small angle approx.
AV30
Michael Duffy: assumes small angle approx.
AU33
Michael Duffy: Non dimensionalized by Tip speed for Rotor
AV33
Michael Duffy: Non dimensionalized by Tip speed for Rotor
Page 32: Propeller or Rotor in Axial Flight

8.3858E-04 7.2685E-05 0.072456 0.000000 0.000000 1403.8016 8.3644E-041.3605E-05 1.2104E-05 0.164962 0.000000 0.000000 7659.5607 5.4425E-08

0.01060 0.00092 0.000000 22,815.43 0.01050

Page 33: Propeller or Rotor in Axial Flight

test1

Page 33

-218184335

Page 34: Propeller or Rotor in Axial Flight

-60 -50 -40 -30 -20 -10 00.007

0.0075

0.008

0.0085

0.009

0.0095

0.01

0.0105

0.011Cp/σ

Twist from Root to Tip

Cp/

σ

Held Constant:Thrust Weighted Solidity = 0.1Thrust = 15,000lbTip Speed is 650 ft/sRotor Dia = 47 ftRoot Cut-Out = 0 ftHoverTip and Root Losses IncludedCl corrected for Compressibility

-60 -50 -40 -30 -20 -10 00.0094

0.0096

0.0098

0.01

0.0102

0.0104

0.0106Cp/σ

Twist from Root to Tip

Cp/

σ

You are asked to design a rotor that will carry 15000 lbf at 4000 feet pressure altitude at 95 deg F. Due to geometric limitations, the rotor diameter is 43 feet. The designer decides to use a thrust weighted solidity of 0.1, and has chosen the number of blades to be 4. The designer also decides to use a 3 bladed rotor for this design. Because the company has prior experience with NACA 0012 airfoils, a NACA0012 airfoil is also chosen. The tip speed is selected to be 650 feet/sec. Determine the best combinations of linear taper ratio and linear twist that will minimize power consumption. Use combined Blade Element Momentum theory, and Prandtl’s tip loss model F(r). The NACA 0012 airfoil properties are supplied below as a table of alpha and Mach number. Please use these. 1. AE 6070 students only:

The designer seeks your advice on changing solidity (between 0.05, 0.075, or 0.10), and the number of blades (between 2, 3, 4, or 5). Repeat the BEMT simulations for subsets of these combinations and give your recommendation. Note that a very small value of sigma may cause the rotor to stall.

Page 35: Propeller or Rotor in Axial Flight

-60 -50 -40 -30 -20 -10 00.0094

0.0096

0.0098

0.01

0.0102

0.0104

0.0106Cp/σ

Twist from Root to Tip

Cp/

σ

-60 -50 -40 -30 -20 -10 00.0094

0.0096

0.0098

0.01

0.0102

0.0104

0.0106Cp/σ

Twist from Root to Tip

Cp/

σ

-60 -50 -40 -30 -20 -10 00.0094

0.0096

0.0098

0.01

0.0102

0.0104

0.0106Cp/σ

Twist from Root to Tip

Cp/

σ

Page 36: Propeller or Rotor in Axial Flight

0 2 4 6 8 10 120.00925

0.0093

0.00935

0.0094

0.00945

0.0095

0.00955

0.0096

0.00965Cp/σ

Taper Ratio Root/Tip

Cp/

σ

-60 -50 -40 -30 -20 -10 00.0094

0.0096

0.0098

0.01

0.0102

0.0104

0.0106Cp/σ

Twist from Root to Tip

Cp/

σ

0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.110.00098

0.001

0.00102

0.00104

0.00106

0.00108

0.0011

0.00112Cp

σ, Solidity, Thrust Weighted

Cp

Page 37: Propeller or Rotor in Axial Flight

0 2 4 6 8 10 120.00925

0.0093

0.00935

0.0094

0.00945

0.0095

0.00955

0.0096

0.00965Cp/σ

Taper Ratio Root/Tip

Cp/σ

Page 38: Propeller or Rotor in Axial Flight

I USED THIS PROGRAM TO DESIGN A ROTOR WHICH FOLLOWED THE CONSTRAINTS IN THIS PROBLEM.

4-BladesData: Sea Level Taper (r:t, 1:1)θ_twist θ_.75 Ct Cp/σ Ct/σ

0 11.137 0.008608 0.00778 0.085997-5 11.124 0.008608 0.007551 0.085993

-10 11.091 0.008608 0.007381 0.085996-15 11.038 0.008608 0.00727 0.085994

min power -20 10.966 0.008608 0.007219 0.085992-25 10.875 0.008608 0.007227 0.085992-30 10.764 0.008608 0.007296 0.085997-35 10.629 0.008608 0.007421 0.085991-40 10.466 0.008608 0.007602 0.08599

Data: 4k, 95 Taper (r:t, 1:1); c = 20.57"θ_twist θ_.75 Ct Cp/σ Ct/σ

0 13.134 0.010658 0.010445 0.106631-5 13.118 0.010658 0.01016 0.106627

-10 13.085 0.010658 0.009937 0.10663-15 13.035 0.010658 0.009774 0.10663-20 12.969 0.010658 0.009671 0.106629

min power -25 12.887 0.010658 0.009629 0.106628-30 12.789 0.010658 0.009646 0.106627-35 12.674 0.010658 0.009723 0.106625-40 12.541 0.010658 0.009858 0.106625-50 12.204 0.010657 0.010293 0.10662

3-BladesData: 4k, 95 Taper (r:t, 1:1); c = 27.43"θ_twist θ_.75 Ct Cp/σ Ct/σ

0 13.242 0.010658 0.010603 0.106615-5 13.218 0.010658 0.0103 0.106613

-10 13.177 0.010658 0.01006 0.106617

-60 -50 -40 -30 -20 -10 00.007

0.0075

0.008

0.0085

0.009

0.0095

0.01

0.0105

0.011Cp/σ

Twist from Root to Tip

Cp/

σ

-60 -50 -40 -30 -20 -10 00.0094

0.0096

0.0098

0.01

0.0102

0.0104

0.0106Cp/σ

Twist from Root to Tip

Cp/

σ

You are asked to design a rotor that will carry 15000 lbf at 4000 feet pressure altitude at 95 deg F. Due to geometric limitations, the rotor diameter is 43 feet. The designer decides to use a thrust weighted solidity of 0.1, and has chosen the number of blades to be 4. The designer also decides to use a 3 bladed rotor for this design. Because the company has prior experience with NACA 0012 airfoils, a NACA0012 airfoil is also chosen. The tip speed is selected to be 650 feet/sec. Determine the best combinations of linear taper ratio and linear twist that will minimize power consumption. Use combined Blade Element Momentum theory, and Prandtl’s tip loss model F(r). The NACA 0012 airfoil properties are supplied below as a table of alpha and Mach number. Please use these. 1. AE 6070 students only:

The designer seeks your advice on changing solidity (between 0.05, 0.075, or 0.10), and the number of blades (between 2, 3, 4, or 5). Repeat the BEMT simulations for subsets of these combinations and give your recommendation. Note that a very small value of sigma may cause the rotor to stall.

Page 39: Propeller or Rotor in Axial Flight

-15 13.119 0.010658 0.009881 0.106617-20 13.045 0.010658 0.009764 0.106617

min power -25 12.955 0.010658 0.009709 0.106616-30 12.849 0.010658 0.009715 0.106614-35 12.726 0.010658 0.009781 0.106609-40 12.586 0.010658 0.009908 0.106615-45 12.425 0.010658 0.010093 0.106616

Comparison3-Blades 4-Bladesc_r/c_t Cp/σ min c_r/c_t Cp/σ min

1 0.009709 1 0.009629 0.82%2 0.009604 2 0.009519 0.89%3 0.009545 3 0.009468 0.81%4 0.009511 4 0.00945 0.64%

-60 -50 -40 -30 -20 -10 00.0094

0.0096

0.0098

0.01

0.0102

0.0104

0.0106Cp/σ

Twist from Root to Tip

Cp/

σ

-60 -50 -40 -30 -20 -10 00.0094

0.0096

0.0098

0.01

0.0102

0.0104

0.0106Cp/σ

Twist from Root to Tip

Cp/

σ

-60 -50 -40 -30 -20 -10 00.0094

0.0096

0.0098

0.01

0.0102

0.0104

0.0106Cp/σ

Twist from Root to Tip

Cp/

σ

Page 40: Propeller or Rotor in Axial Flight

ComparisonData: 4k, 95 Taper (r:t, 1:1); θ_twist = 0 deg. Blades, N chord, c σ, Solidity θ_.75 Ct Cp/σ

2 20.56 0.05 20.105 0.010658 0.0222232 30.87 0.075 15.686 0.010658 0.0144982 41.17 0.1 13.464 0.010658 0.0109213 13.71938 0.05 19.868 0.010659 0.0214893 20.57907 0.075 15.46 0.010658 0.0140493 27.43 0.1 13.242 0.010658 0.0106034 10.28 0.05 19.772 0.010658 0.0211614 15.43 0.075 15.353 0.010658 0.0138314 20.57 0.1 13.134 0.010658 0.0104455 8.23163 0.05 19.699 0.010658 0.0209415 12.34744 0.075 15.29 0.010658 0.0137015 16.46342 0.1 13.069 0.010658 0.010349

Data: 4k, 95 θ_twist = -25 deg.Root ChordTip Chord, Taper r/t θ_.75

20.6 20.6 1 12.87722 20.2 1.089109 12.826 18.9 1.375661 12.62330 17.61111 1.70347 12.45836 15.68189 2.295641 12.2342 13.76462 3.0513 12.022

min power 48 11.84382 4.052748 11.83554 9.92046 5.443296 11.66760 7.95 7.54717 11.524

0 2 4 6 8 10 120.00925

0.0093

0.00935

0.0094

0.00945

0.0095

0.00955

0.0096

0.00965Cp/σ

Taper Ratio Root/Tip

Cp/

σ

-60 -50 -40 -30 -20 -10 00.0094

0.0096

0.0098

0.01

0.0102

0.0104

0.0106Cp/σ

Twist from Root to Tip

Cp/

σ

0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.110.00098

0.001

0.00102

0.00104

0.00106

0.00108

0.0011

0.00112Cp

σ, Solidity, Thrust Weighted

Cp

Page 41: Propeller or Rotor in Axial Flight

0 2 4 6 8 10 120.00925

0.0093

0.00935

0.0094

0.00945

0.0095

0.00955

0.0096

0.00965Cp/σ

Taper Ratio Root/Tip

Cp/σ

Min power consumption is found at a linear twist of -20 deg. and a taper ratio of 6.36 root to chordratio. I only proceed with this iterative process 3 times, I could go back and continue to optimize the twist with this new taper ratio, but this would take a long time. I noticed that as my linear twistrate was decreased the taper ratio wanted to go up. I noticed that the taper was getting a bitun-reasonable and stopped at 6.4:1. I plot this blade in CATIA to see how it looks in terms of feasibility.

Page 42: Propeller or Rotor in Axial Flight

I USED THIS PROGRAM TO DESIGN A ROTOR WHICH FOLLOWED THE CONSTRAINTS IN THIS PROBLEM.

4-Blades

Thrust15000.7215000.0415000.5915000.21 25.0%14999.8614999.9715000.7714999.7514999.57

Data: 4k, 95 Taper (r:t, 2:1); c_r = 41.5", c_t = 13.833" Data:Thrust θ_twist θ_.75 Ct Cp/σ Ct/σ Thrust θ_twist15000.23 0 13.108 0.010659 0.010137 0.106548 15000.69 014999.73 -5 12.996 0.010658 0.009885 0.106546 15000.33 -515000.17 -10 12.863 0.010659 0.009698 0.106547 15000.58 -1015000.07 -15 12.71 0.010658 0.009575 0.106541 14999.74 -1515000.06 -20 12.539 0.010658 0.009519 0.106543 14999.98 -2014999.85 -25 12.349 0.010658 0.009527 0.10654 14999.59 -2514999.76 -30 12.14 0.010658 0.009601 0.106538 14999.29 -3014999.37 -35 11.911 0.010658 0.00974 0.10654 14999.48 -35

14999.5 -40 11.659 0.010658 0.009943 0.106541 14999.69 -4014998.77 -45 11.378 0.010658 0.010205 0.10654 14999.58 -45

-50 11.053 0.010658 0.010514 0.106538 14999.323-Blades

Data: 4k, 95 Taper (r:t, 2:1); c_r = 44.1", c_t = 22.05" Data:Thrust θ_twist θ_.75 Ct Cp/σ Ct/σ Thrust θ_twist14999.88 0 13.205 0.010658 0.010283 0.106624 15000.04 014999.62 -5 13.085 0.010658 0.010013 0.10662 14999.47 -515000.17 -10 12.946 0.010659 0.009812 0.106628 15000.62 -10

Page 43: Propeller or Rotor in Axial Flight

15000.12 -15 12.787 0.010658 0.009675 0.106627 15000.4 -1515000.15 -20 12.609 0.010658 0.009605 0.10662 14999.48 -2014999.95 -25 12.414 0.010659 0.009604 0.106629 15000.71 -2514999.77 -30 12.199 0.010658 0.009668 0.106625 15000.16 -3014999.06 -35 11.964 0.010658 0.009798 0.10662 14999.52 -3514999.79 -40 11.708 0.010659 0.009996 0.106629 15000.77 -4014999.94 -45

0.5 1 1.5 2 2.5 3 3.5 4 4.50.0094

0.0095

0.0096

0.0097

0.0098

0.0099

0.01Cp/σ w/Optimized Twister for Min Power

Taper Ratio (c_r/c_t)

Cp/

σ w

/Opt

imiz

ed T

wis

t for

Min

Pow

er

Page 44: Propeller or Rotor in Axial Flight

Ct/σ Thrust Cp0.213355 14999.54 0.0011110.142101 14999.74 0.0010870.106551 14999.95 0.0010920.213171 15000.52 0.001074

0.14211 15000.09 0.0010540.106615 14999.88 0.001060.213367 15000.35 0.0010580.142143 14999.41 0.0010370.106631 15000.23 0.0010450.213164 15000 0.0010470.142112 15000.24 0.0010280.106578 14999.53 0.001035

Data: 4k, 95 θ_twist = -20 deg.Ct Cp/σ Ct/σ Thrust Root ChordTip Chord, Taper r/t θ_.75 Ct0.010658 0.009616 0.106474 15000.07 36 15.68189 2.295641 12.442 0.0106580.010658 0.009583 0.10627 14999.61 42 13.76462 3.0513 12.282 0.0106590.010658 0.009549 0.106303 14999.05 48 11.84382 4.052748 12.1405 0.0106580.010659 0.009523 0.106309 15000.49 54 9.92046 5.443296 12.017 0.0106590.010659 0.009496 0.106286 15000.86 57 8.959844 6.361718 11.961 0.0106590.010658 0.009479 0.106211 15000.21 60 7.95 7.54717 11.918 0.0106580.010658 0.009473 0.10615 14999.72 63 6.972974 9.034882 11.872 0.0106580.010658 0.009479 0.106105 14999.94 66 6.010943 10.97997 11.828 0.0106580.010659 0.009508 0.106247 15000.78

Page 45: Propeller or Rotor in Axial Flight

Min power consumption is found at a linear twist of -20 deg. and a taper ratio of 6.36 root to chordratio. I only proceed with this iterative process 3 times, I could go back and continue to optimize the twist with this new taper ratio, but this would take a long time. I noticed that as my linear twistrate was decreased the taper ratio wanted to go up. I noticed that the taper was getting a bitun-reasonable and stopped at 6.4:1. I plot this blade in CATIA to see how it looks in terms of feasibility.

Page 46: Propeller or Rotor in Axial Flight

0.2%1.7%

4k, 95 Taper (r:t, 3:1); c_r = 41.5", c_t = 13.833" Data: 4k, 95 Taper (r:t, 4:1); c_r = 47.52", c_t = 11.88"θ_.75 Ct Cp/σ Ct/σ Thrust θ_twist θ_.75 Ct Cp/σ

13.137 0.010659 0.009973 0.106574 15000.49 0 13.177 0.010659 0.00987312.962 0.010658 0.009748 0.10657 14999.88 -5 12.958 0.010658 0.00966712.766 0.010658 0.009588 0.106573 15000.32 -10 12.718 0.010658 0.00952912.549 0.010658 0.009495 0.106571 15000.09 -15 12.456 0.010658 0.00945512.312 0.010658 0.009468 0.106569 14999.83 -20 12.174 0.010658 0.0094512.055 0.010658 0.009508 0.106567 14999.5 -25 11.871 0.010659 0.00951211.778 0.010658 0.009617 0.106571 15000.08 -30 11.546 0.010658 0.00964111.478 0.010658 0.009791 0.106567 14999.48 -35 11.198 0.010658 0.00983811.153 0.010658 0.010031 0.106571 15000.09 -40 10.823 0.010658 0.01010110.794 0.010659 0.010331 0.106577 15000.93

4k, 95 Taper (r:t, 3:1); c_r = 55.3", c_t = 18.433" Data: 4k, 95 Taper (r:t, 4:1); c_r = 63.4", c_t = 15.85"θ_.75 Ct Cp/σ Ct/σ Thrust θ_twist θ_.75 Ct Cp/σ

13.221 0.010658 0.010104 0.106633 14999.74 0 13.246 0.010659 0.00998313.041 0.010658 0.009864 0.106637 15000.37 -5 13.022 0.010658 0.00976312.839 0.010658 0.00969 0.106635 14999.97 -10 12.778 0.010659 0.009613

Page 47: Propeller or Rotor in Axial Flight

12.617 0.010658 0.009583 0.106635 14999.99 -15 12.512 0.010659 0.00952812.375 0.010658 0.009545 0.106632 14999.6 -20 12.225 0.010658 0.00951112.114 0.010658 0.009577 0.106637 15000.28 -25 11.918 0.010658 0.00956411.832 0.010658 0.009676 0.106633 14999.82 -30 11.591 0.010658 0.00968711.529 0.010659 0.009845 0.106638 15000.44 -35 11.24 0.010658 0.00987911.226 0.010663 0.010086 0.106683 15006.72 -40 10.863 0.010658 0.010138

10.84 0.010658 0.010377 0.106634 14999.83 -45 10.45 0.010658 0.010457

0.5 1 1.5 2 2.5 3 3.5 4 4.50.0094

0.0095

0.0096

0.0097

0.0098

0.0099

0.01Cp/σ w/Optimized Twister for Min Power

Taper Ratio (c_r/c_t)

Cp/

σ w

/Opt

imiz

ed T

wis

t for

Min

Pow

er

Page 48: Propeller or Rotor in Axial Flight

Cp/σ Ct/σ Thrust0.009475 0.106279 14999.90.009437 0.106215 15000.780.009411 0.106154 15000.210.009397 0.106108 15000.420.009394 0.106081 15000.510.009409 0.106243 15000.320.009416 0.106273 14999.40.009421 0.106257 15000.35

Page 49: Propeller or Rotor in Axial Flight

Taper (r:t, 4:1); c_r = 47.52", c_t = 11.88"Ct/σ Thrust0.106618 15000.440.106609 14999.190.106615 15000.010.106612 14999.620.106617 15000.260.106618 15000.420.106613 14999.730.106612 14999.560.106617 15000.24

Taper (r:t, 4:1); c_r = 63.4", c_t = 15.85"Ct/σ Thrust0.106551 15000.460.106542 14999.110.106553 15000.7

Page 50: Propeller or Rotor in Axial Flight

0.106552 15000.590.106545 14999.540.106542 14999.1

0.10655 15000.310.106545 14999.630.106546 14999.690.106545 14999.54