# prop

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This worksheet uses a simple model of a propeller. It consists of an airfoil of area (Area) whirling around at a radius,
The foil makes an angle beta (b) to the plane of the propeller. The airplane moves forward at a fixed speed
density rho_0. The foil has a lift coefficient given by C_l=C_l1*alpha, where alpha is the angle of attack, and drag coefficien
C_d=C_d0+C_d2*alpha^2 . In practice these forms would only be appropriate up to some maximum (stalling) angle of attac
alpha_max.
Given the RPM, the spreadsheet calculates the following:

omega w       angular velocity of the prop in radians/sec
J           the propeller advance ratio, defined as pV/Rw
phi f         the angle between the relative wind and the prop plane
alpha a       the prop foil angle of attack = b-a
C_l, C_d        the lift and drag coefficients
V_tot          the total velocity of the relative wind
L            blade lift (perp to rel wind)
D             blade drag (parallel to rel wind)
T            thrust (lb) (negative means airplane drag)
Q            torque (ft-lb) (negative means the prop is turning the engine)
BHP           brake horse power
THP           thrust HP
eta h         propeller efficiency = THP/BHP
FParea        equivalent flat plate area (negative for drag)- compare to Area for the drag of a stationary plot

Bold values can be input. Others are calculated. BHP and THP are plotted vs RPM (for alpha<alpha_max) on the chart HP
Prop efficiency (eta) is plotted vs advance ratio J (It depends on this combination of RPM and airspeed) on the chart etavsJ
You can compare different conditions (different velocity, blade pitch etc by entering different values in the two data sheets

The spreadsheet illustrates a few points.
(1) Thrust increases monotonically with RPM and engine torque. Zero thrust occurs at a small positive torque. Zero torque
(freely windmilling) gives a small drag.
(2) Windmilling with engine braking (negative Q) gives greater drag than free windmilling- limited by prop stall.
(3) Increasing velocity shifts the peak efficiency to higher RPM. Increasing blade angle brings the peak back to
lower RPM.

This worksheet is purely for educational/entertainment purposes. No warranties are expressed or implied!

Ed Williams 72347,1516

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) whirling around at a radius, R.
ard at a fixed speed V_k through air of
e angle of attack, and drag coefficient
me maximum (stalling) angle of attack,

g of a stationary plot

or alpha<alpha_max) on the chart HPvsRPM.
PM and airspeed) on the chart etavsJ
erent values in the two data sheets)

a small positive torque. Zero torque

limited by prop stall.
brings the peak back to

expressed or implied!

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etavsJ

Propeller Efficiency as a function of Advance ratio J

1

0.9

0.8

0.7

0.6
Efficiency

eta1
0.5
eta2

0.4

0.3

0.2

0.1

0
0.5   0.6   0.7         0.8           0.9            1         1.1   1.2   1.3

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HPvsRPM

HP vs RPM (fixed pitch)

250

200

150

100                                                               BHP1
THP1
BHP2

50                                                               THP2

0
0   500   1000       1500             2000   2500   3000

-50

-100
RPM

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858a8d05-c346-40ce-a325-4309192842e5.xls

Propeller Performance Worksheet
INPUT
Blade Area (sq feet)       Area                  1              500 52.36     4.05     52.19      -30.19
Drag coefft (alpha=0)      C_d0              0.01               600 62.83     3.37     47.04      -25.04
Drag coefft                C_d2              0.36               700 73.30     2.89     42.63      -20.63
Lift slope (C_l/alpha)     C_l1                  3              800 83.78     2.53     38.85      -16.85
Airspeed (knots)           V_k                140 236.13 V_fps 900 94.25      2.25     35.60      -13.60
Air density (slugs/ft^3)   rho         0.0023769               1000 104.72    2.02     32.79      -10.79
alpha_max            12             1100 115.19    1.84     30.36        -8.36
1200 125.66    1.69     28.23        -6.23
1300 136.14    1.56     26.36        -4.36
1400 146.61    1.45     24.71        -2.71
1500 157.08    1.35     23.24        -1.24
1600 167.55    1.27     21.93         0.07
1700 178.02    1.19     20.76         1.24
1800 188.50    1.12     19.69         2.31
1900 198.97    1.07     18.73         3.27
2000 209.44    1.01     17.86         4.14
2100 219.91    0.96     17.06         4.94
2200 230.38    0.92     16.32         5.68
2300 240.86    0.88     15.65         6.35
2400 251.33    0.84     15.03         6.97
2500 261.80    0.81     14.45         7.55
2600 272.27    0.78     13.92         8.08

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C_l     C_d C_l/C_d V_tot L        D       T          Q          BHP       THP       eta    FParea
-1.58   0.11 -14.38 298.90 -167.82 11.67    -112.11   -438.97     -41.79    -48.13    1.152   -1.69
-1.31   0.08 -16.65 322.68 -162.22 9.74     -117.69   -392.25     -44.81    -50.53    1.128   -1.78
-1.08   0.06 -19.06 348.69 -156.05 8.19     -120.36   -348.79     -46.49    -51.68    1.112   -1.82
-0.88   0.04 -21.45 376.48 -148.57 6.93     -120.06   -307.27     -46.80    -51.54    1.101   -1.81
-0.71   0.03 -23.52 405.67 -139.24 5.92     -116.67   -266.82     -45.72    -50.09    1.096   -1.76
-0.57   0.02 -24.81 436.00 -127.66 5.14     -110.10   -226.85     -43.19    -47.27    1.094   -1.66
-0.44   0.02 -24.78 467.23 -113.53 4.58     -100.28   -186.98     -39.16    -43.05    1.099   -1.51
-0.33   0.01 -22.88 499.20 -96.62 4.22       -87.12   -146.94     -33.57    -37.40    1.114   -1.31
-0.23   0.01 -18.90 531.78 -76.76 4.06       -70.58   -106.56     -26.38    -30.30    1.149   -1.07
-0.14   0.01 -13.14 564.85 -53.83 4.10       -50.61     -65.73    -17.52    -21.73    1.240   -0.76
-0.07   0.01   -6.40 598.34 -27.71 4.33      -27.17     -24.36     -6.96    -11.66    1.677   -0.41
0.00   0.01    0.35 632.19   1.67 4.75       -0.22      17.61      5.36     -0.10   -0.018    0.00
0.07   0.01    6.41 666.33  34.38 5.37       30.25      60.21     19.49     12.99    0.666    0.46
0.12   0.01  11.41 700.72   70.48 6.18       64.27    103.47      35.46     27.59    0.778    0.97
0.17   0.01  15.32 735.33 109.99 7.18       101.86    147.42      53.33     43.73    0.820    1.54
0.22   0.01  18.26 770.13 152.97 8.38       143.03    192.07      73.14     61.41    0.840    2.16
0.26   0.01  20.42 805.10 199.43 9.77       187.80    237.41      94.93     80.63    0.849    2.83
0.30   0.01  21.96 840.21 249.41 11.36      236.17    283.48    118.74    101.39     0.854    3.56
0.33   0.01  23.06 875.44 302.92 13.14      288.15    330.25    144.62    123.71     0.855    4.35
0.37   0.02  23.81 910.79 359.98 15.12      343.75    377.75    172.62    147.58     0.855    5.19
0.40   0.02  24.32 946.24 420.60 17.29      402.98    425.97    202.76    173.01     0.853    6.08
0.42   0.02  24.66 981.77 484.80 19.66      465.84    474.91    235.10    200.00     0.851    7.03

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0.28328995

Filtered for alpha<alpha_max HPvsRPM plot         Filtered for THP>0 etavsJ plot
RPM             BHP1        THP1                  J              eta1
1000 -43.192348 -47.2706455               1.19058824 0.66640965
1000 -43.192348 -47.2706455               1.19058824 0.66640965
1000 -43.192348 -47.2706455               1.19058824 0.66640965
1000 -43.192348 -47.2706455               1.19058824 0.66640965
1000 -43.192348 -47.2706455               1.19058824 0.66640965
1000 -43.192348 -47.2706455               1.19058824 0.66640965
1100 -39.1602758 -43.0523424              1.19058824 0.66640965
1200 -33.5725077 -37.4049883              1.19058824 0.66640965
1300 -26.3764846 -30.3040184              1.19058824 0.66640965
1400 -17.5211633 -21.7293093              1.19058824 0.66640965
1500 -6.95705329 -11.6644136              1.19058824 0.66640965
1600    5.3639132 -0.09587134             1.19058824 0.66640965
1700 19.4885661 12.9873686                1.19058824 0.66640965
1800 35.4626863 27.5944207                1.12444444      0.7781255
1900 53.3311783     43.732841             1.06526316      0.8200239
2000 73.1382186     61.408928                    1.012 0.83962843
2100 94.9273811 80.6279613                0.96380952 0.84936465
2200 118.741741 101.394391                        0.92    0.8539069
2300 144.623958 123.711989                        0.88 0.85540453
2400    172.61635 147.583969              0.84333333 0.85498256
2500 202.760945 173.013082                     0.8096 0.85328603
2600 235.099532 200.001697                0.77846154 0.85071074

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>0 etavsJ plot

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858a8d05-c346-40ce-a325-4309192842e5.xls

Propeller Performance Worksheet
INPUT
Blade Area (sq feet)       Area                  1              500 52.36     4.05     52.19      -32.19
Drag coefft (alpha=0)      C_d0              0.01               600 62.83     3.37     47.04      -27.04
Drag coefft                C_d2              0.36               700 73.30     2.89     42.63      -22.63
Lift slope (C_l/alpha)     C_l1                  3              800 83.78     2.53     38.85      -18.85
Airspeed (knots)           V_k                140 236.13 V_fps 900 94.25      2.25     35.60      -15.60
Air density (slugs/ft^3)   rho         0.0023769               1000 104.72    2.02     32.79      -12.79
alpha_max            12             1100 115.19    1.84     30.36      -10.36
1200 125.66    1.69     28.23        -8.23
1300 136.14    1.56     26.36        -6.36
1400 146.61    1.45     24.71        -4.71
1500 157.08    1.35     23.24        -3.24
1600 167.55    1.27     21.93        -1.93
1700 178.02    1.19     20.76        -0.76
1800 188.50    1.12     19.69         0.31
1900 198.97    1.07     18.73         1.27
2000 209.44    1.01     17.86         2.14
2100 219.91    0.96     17.06         2.94
2200 230.38    0.92     16.32         3.68
2300 240.86    0.88     15.65         4.35
2400 251.33    0.84     15.03         4.97
2500 261.80    0.81     14.45         5.55
2600 272.27    0.78     13.92         6.08

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C_l     C_d C_l/C_d V_tot L        D       T          Q          BHP       THP       eta    FParea
-1.69   0.12 -13.63 298.90 -178.94 13.12    -120.08   -466.60     -44.42    -51.55    1.161   -1.81
-1.42   0.09 -15.70 322.68 -175.18 11.16    -127.55   -422.06     -48.22    -54.76    1.136   -1.92
-1.18   0.07 -17.91 348.69 -171.18 9.56     -132.43   -381.12     -50.80    -56.85    1.119   -2.00
-0.99   0.05 -20.16 376.48 -166.21 8.24     -134.62   -342.40     -52.15    -57.80    1.108   -2.03
-0.82   0.04 -22.27 405.67 -159.72 7.17     -134.05   -304.98     -52.26    -57.55    1.101   -2.02
-0.67   0.03 -23.97 436.00 -151.32 6.31     -130.62   -268.26     -51.08    -56.08    1.098   -1.97
-0.54   0.02 -24.92 467.23 -140.70 5.65     -124.26   -231.82     -48.55    -53.35    1.099   -1.88
-0.43   0.02 -24.73 499.20 -127.63 5.16     -114.89   -195.39     -44.64    -49.33    1.105   -1.73
-0.33   0.01 -23.07 531.78 -111.96 4.85     -102.47   -158.78     -39.30    -43.99    1.119   -1.55
-0.25   0.01 -19.84 564.85 -93.54 4.71       -86.94   -121.87     -32.48    -37.33    1.149   -1.31
-0.17   0.01 -15.23 598.34 -72.27 4.75       -68.27     -84.56    -24.15    -29.31    1.214   -1.03
-0.10   0.01   -9.72 632.19 -48.07 4.94      -46.44     -46.79    -14.25    -19.94    1.399   -0.70
-0.04   0.01   -3.93 666.33 -20.87 5.31      -21.40      -8.51     -2.76     -9.19    3.335   -0.32
0.02   0.01    1.60 700.72   9.37 5.84        6.85      30.30     10.38      2.94    0.283    0.10
0.07   0.01    6.53 735.33  42.70 6.54       38.34      69.67     25.20     16.46    0.653    0.58
0.11   0.01  10.69 770.13   79.16 7.40       73.07    109.61      41.74     31.37    0.752    1.10
0.15   0.01  14.08 805.10 118.77 8.44       111.07    150.14      60.03     47.69    0.794    1.68
0.19   0.01  16.77 840.21 161.55 9.63       152.33    191.27      80.12     65.40    0.816    2.30
0.23   0.01  18.87 875.44 207.54 11.00      196.88    233.00    102.04      84.53    0.828    2.97
0.26   0.01  20.49 910.79 256.74 12.53      244.71    275.34    125.82    105.06     0.835    3.69
0.29   0.01  21.72 946.24 309.17 14.23      295.84    318.28    151.50    127.01     0.838    4.46
0.32   0.01  22.66 981.77 364.85 16.10      350.26    361.84    179.12    150.38     0.840    5.29

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858a8d05-c346-40ce-a325-4309192842e5.xls

Filtered for alpha<alpha_max HPvsRPM plot         Filtered for THP>0 etavsJ plot
RPM             BHP2        THP2                  J              eta2
1100 -48.5519857 -53.348689               1.12444444 0.28328995
1100 -48.5519857 -53.348689               1.12444444 0.28328995
1100 -48.5519857 -53.348689               1.12444444 0.28328995
1100 -48.5519857 -53.348689               1.12444444 0.28328995
1100 -48.5519857 -53.348689               1.12444444 0.28328995
1100 -48.5519857 -53.348689               1.12444444 0.28328995
1100 -48.5519857 -53.348689               1.12444444 0.28328995
1200 -44.6423291 -49.3273973              1.12444444 0.28328995
1300 -39.3014813 -43.9933341              1.12444444 0.28328995
1400 -32.4848777 -37.3269703              1.12444444 0.28328995
1500 -24.1493472 -29.3122998              1.12444444 0.28328995
1600 -14.2530296 -19.9361956              1.12444444 0.28328995
1700 -2.75522235 -9.18786084              1.12444444 0.28328995
1800 10.3837861 2.94162223                1.12444444 0.28328995
1900 25.2028734 16.4596555                1.06526316 0.65308647
2000 41.7402209 31.3724154                       1.012 0.75161115
2100 60.0334315 47.6850841                0.96380952 0.79430882
2200    80.119627 65.4020327                      0.92 0.81630476
2300    102.03553 84.5269688                      0.88 0.82840721
2400 125.817528 105.063053                0.84333333 0.83504306
2500 151.501731 127.012994                     0.8096 0.83836002
2600 179.124015 150.379122                0.77846154 0.83952518

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>0 etavsJ plot

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