# Category Model Aircraft Aerodynamics

## DESIGNING NEW AEROFOILS

A mathematical method of working out new ordinates, starting from a chosen camber line and a symmetrical thickness form, is given in the standard text, Theory of Wing Sections by Abbott and Von Doenhoff. Although not a quick procedure, the calculations required are not difficult Failing this method, a modeller may devise his own wing sections by the graphical method outlined in Fig. A 8. The camber line is plotted first then at each station a circle is drawn, the radius being taken from the ordinates for the thickness form, and the centre being on the camber line at the appropriate point Finally a smooth curve is drawn tangentially to aU the circles and the nose radius to produce the aerofoil.

WORKING OUT THE CAMBER

Many aerofoil designations contain information about camber and thickness. The NACA systems are described in Chapter 7, with further information in Abbott and Von

Doenhoff as above. The Benedek Aerofoils give the camber, in percent of chord in the last digit, thus В 10355 is cambered 5 percent, 8356, 6 percent and so on. The first figure gives the profile thickness, the central figure or figures the position of the maximum thickness point, hence Benedek В 12355 is 12% thick at 35%, and cambered 5%.

In other cases it is sometimes possible to work out the maximum camber arithmetically. This is applicable only where the aerofoil ordinates are based on a chord • line running through the leading edge and trailing edge. In these cases, by finding the thickness of the profile at a number of stations and subtracting half this figure, at each place, from the upper surface ordinate, the approximate ordinate for the camber line is found and the maximum value then easily discovered. Note that in finding the profile thickness in this way, minus signs below the chord line must be allowed for. This method of halving the thickness will not produce accurate ordinates for the aerofoil camber line, especially near the nose and trailing edge, but it will produce a correct figure for the maximum camber and its location.

The camber of other aerofoils, plotted on tangential chord lines or on other arbitrary reference lines, may be estimated by measuring from the plotted profile. The true chord line, nose to trailing edge, must first be drawn in, then the half thickness plotted as accurately as possible, and the camber measured.

More accurate estimates of camber from the ordinates may – be carried out by somewhat more complex arithmetic, but this is seldom necessary.

Fig. A8 Fig. A8

 i take ordinates of desired camber line, and plot. ii take radii ot circles from desired thickness and draw on arc as shown. Hi draw smooth curved lines tangential to circles. INDEX OF AEROFOILS

Mean lines, low drag bodies and symmetrical profiles are grouped at the beginning of this section. The N. A. C. A. ‘6’ thickness forms are arranged in order of increasing laminar flow (min. pressure point at 30, 40, 50% chord etc), and in increasing thickness (6, 9, 10, 12, 15, 18% etc.) In the section devoted to cambered profiles, the N. A. C. A. 6 series aerofoils are arranged in order of increasing thickness (9 to 18%), then by increasing camber (shown by the third figure from the right which indicates the ‘ideal’ ci in tenths -.2, .3, .4, .6 etc), and then by increasing proportion of laminar flow (given by the second digit from the left, 30%, 40%, 50% etc.) The various letters and other additions indicate minor modifications to the profiles (e. g., A =0.5 indicates the use of A = 0.5 mean line instead of the usual A = 1).

MEAN LINES

 Reflex for zero pitching moment, каі« to reqd camber NACA 210. CL Ideal 0.3 NACA A • 0.0 NACA A-0.5 NACA A-0.9 NACA A – 1.0 Chord Upper Chord Upper Chord Upper Chord Upper Chord Upper Chord Upper Station Surface Station Surface Station Surface Station Surface Station Surface Station Surface XU vu XU VU XU YU XU vu XU vu XU YU .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 000 5.000 3.240 1050 S96 .500 480 500 .345 .500 .289 .500 .250 10.000 5.770 2.500 .928 .750 .841 .750 .485 .750 979 .750 .350 15.000 7.850 5.000 1.114 1.250 .964 1.250 .735 1.250 .577 1.250 .535 20.000 8.940 7.500 1.087 2.500 1.641 2.500 1.295 2.500 1.008 2.500 .930 25.000 9.700 10.000 1.058 5.000 2.693 5000 2.205 5 000 1.720 5.000 1.580 30.000 9S90 15000 899 7.500 3.507 7.500 2.970 7.500 2.318 7.500 2.120 35.000 9080 20.000 840 10.000 4.161 10.000 3.830 10.000 2835 10.000 2.585 40.000 9.4Э0 25.000 881 15.000 5.124 15.000 4.740 15.000 3.707 15.000 3.385 45.000 8.700 30.000 .823 20.000 5.747 20800 5920 20.000 4.410 20.000 3.980 60.000 7.780 40.000 .705 25.000 8.114 25800 6910 25.000 4.980 25.000 4.475 55.000 8.880 50.000 .588 30.000 8877 30.000 8840 30.000 5.435 30.000 4860 50.000 5.480 80.000 .470 35.000 6.273 35.000 7915 35.000 5.787 35.000 5.150 55.000 4040 70.000 .353 40.000 6.130 40.000 7.430 40.000 6.045 40.000 5.355 70.000 3.040 80.000 .235 45.000 5971 45.000 7.490 45.000 6.212 45.000 5.475 75.000 1040 90.000 .118 50.000 5.516 50.000 7950 50.000 6.290 50.000 80.000 090 •95.000 .059 56.000 5.081 55.000 8865 55.000 6.279 85.000 060 100.000 .000 60.000 4.581 60.000 8.405 60.000 6.178 60.000 90.000 -.190 85.000 4.032 65.000 5.725 85.000 5.981 85.000 5.150 95.000 -.300 70.000 4.955 70.000 5.681 70.000 100.000 .000 75.000 2836 75.000 4.130 75.000 5.265 75.000 4.475 80.000 3.285 80.000 4.714 80.000 3.980 85.000 2995 85.000 3.987 85.000 3.365 90.000 90.000 1.535 90.000 2.984 90.000 2.585 95.000 .467 95.000 .720 95.000 1.503 95.000 1.580 .000 100.000 .000 100800 .000 100.000 .000

 REFLEX MEAN LINE FOR ZERO PITCHING MOMENT SCALE TO REQUIRED CAMBER

NACA 210 MEAN LINE CL IDEAL 0.3

NACA A ** 0.0 MEAN LINE

 NACA A – 0.6 MEAN LINE

0.9 MEAN LINE

 NACA A – 1.0 MEAN LINE

1.10 Percent

0.89 Percent

 Chord Upper Chord Lower Station Surface Station Surface XU vu XL YL .000 .000 .000 .000 .500 .749 .500 -.749 .750 .906 .750 -.906 1.350 U151 1.350 -1.151 3.500 1.583 3.500 -1.583 5.000 3.196 5.000 -3.198 7.500 3.655 7.500 -3.655 10.000 3.034 10.000 -3.034 15.000 3.591 15.000 -3.591 30.000 3.997 30.000 -3.997 30.000 4.443 30.000 -4.443 40.000 4.447 40.000 -4.447 50.000 4.056 50.000 -4.056 60.000 3.358 60.000 -3.358 70.000 3.458 70.000 -3.458 80.000 1.471 80.000 -1.471 90.000 .550 90.000 -.550 95.000 .196 95.000 -.196 100.000 .000 100.000 .000

 Chord Upper Chord Lower Station Surface Station Surface XU YU XL YL .000 .000 .000 .000 .050 .160 .050 -.160 .100 .340 .100 -.240 .300 .350 .300 -.350 .400 .500 .400 -.500 .500 .503 .500 -.503 .750 .609 .750 -.609 1350 .771 1.250 -.771 3.500 1.057 2.500 -1.057 5.000 1.463 5.000 -1.462 7.500 1.766 7.500 -1.766 10.000 3.010 10.000 -2.010 15.000 3.386 15.000 -2386 30.000 3.656 20.000 -2.656 30.000 3.954 30.000 -2.954 40.000 2.971 40.000 -2.971 50.000 2.723 60.000 -2.723 60.000 2.267 60.000 -2.267 70.000 1.670 70.000 -1.670 80.000 1.008 80.000 -1.008 90.000 .383 90.000 -.383 95.000 .138 95.000 -.138 100.000 .000 100.000 .000

 Chord Upper Chord Lower Station Surface Station Surface XU YU X ■< r .000 .000 .000 .000 300 .620 300 -.620 .400 .910 .400 -.910 .600 1.130 .600′ -1.120 900 1.350 .800 -1.250 1350 1.578 1.350 -1.578 2.500 2.178 2.500 -2.178 5.000 2.962 5.000 -3.962 7.500 3.500 7.500 -3.SOO 10.000 3.902 10.000 -3.902 15.000 4.455 15.000 -4.455 20.000 4.782 30.000 -4.782 25.000 4.952 35.000 -4.953 30.000 5.002 30.000 -5.003 40.000 4337 40.000 -4337 50.000 4.412 50.000 -4.412 60.000 3303 60.000 -3303 70.000 3.053 70.000 -3.053 80.000 2.187 80.000 -2.187 90.000 1.207 90.000 -1.207 95.000 .672 95.000 -.672 100.000 .105 100.000 -.105

 Chord Upoer Chord Lower Stanon! Surface Station Surface XU YU XL YL .000 .000 000 000 .200 490 .700 – 490 .400 .870 400 – 870 .600 1 010 .600 ■1 0Ю .800 1.170 BOO -1 170 1 250 1.420 1.750 -1 470 3.500 1.961 2500 -1 961 s. ooo 3666 5.000 -7666 7.500 3.150 7 500 -3 150 10.000 3512 10.000 – 3517 15.000 4.009 15.000 -4.009 20.000 4.303 30.000 -4 303 25.000 4.456 25.000 -4.456 30.000 4.501 30.000 -4.501 40.000 4.352 40000 -4 357 50.000 3.971 50.000 -3.971 60.000 3.423 60.000 -3.473 70.000 2.748 70.000 – 2.748 80.000 1.967 80.000 -1.967 90.000 1.086 90.000 -1.086 95.000 .605 95.000 -.605 100.000 .095 100.000 -.095

NACA 63 009

XL YL.000 .000 M0 – IMS.7» -1.837

1.350 -3.537

3.500 -3.577

5.0 -5.0S5

7.600 -5.183

10.0 -7880

15.0 -8.441

30.0 -9410

30.0 -10413

40.0 -10.398

50.0 -9JOS

80.0 -7441

70.0 -5390

80800 -3.064

90.0 -1.113

95.0 -.392

100.000 .000

NACA 64 0Ю LE RADIUS 0.720 PERCENT

NACA 64 000 LE RA0IUS 0.576 PERCENT

 NACA 65 A 006 NACA 65 006 NACA 64 2 016 L. E. rebut 1.590 Percent NACA 64 1012 Chord Upper Chord Lower Chord Upper Chord Lower Chord Upper Chord Lower Chord Upper Chord Lower Station Surface Station Surface Station Surface Station Surface Station Surface Station Surface Station Surface Station Surface XU YU XL YL XU YU XL YL XU YU XL YL XU YU XL YL 800 .000 .000 .000 800 .000 .000 .000 800 800 800 .000 .000 .000 800 800 .500 .615 800 -815 800 .476 .500 -.476 800 1808 800 -1808 800 878 800 -878 .750 .746 .750 -.746 .750 874 .750 -.574 .750 1.456 .750 -1/456 750 1.179 .750 -1.179 1.260 851 1850 -851 I860 .717 1850 -.717 I860 1842 1850 -1842 I860 1.490 I860 -1.490 2800 1.303 2800 -1803 2800 .956 2800 -856 2800 2828 2800 -2828 2800 2.035 2800 -2835 5.000 1.749 5.000 -1.749 5.000 1.310 5.000 -1810 5800 3804 5800 -3.604 6.000 2810 5800 -2810 7800 2.120 7.500 -2.120 7800 1869 7800 -1.589 7800 4840 7800 -4840 7800 3894 7800 -3894 10.000 2.432 10.000 -2.432 10800 1824 10.000 -1824 10.000 4842 10.000 -4842 10800 3871 10800 -3871 15.000 2826 16800 -2826 15.000 2.197 16800 -2.197 15800 5.786 15800 -6.785 15800 4820 15.000 -4820 20800 3.301 20.000 -3.301 20.000 2.482 20.000 -2.482 20800 6.480 20.000 -6.480 20800 6.173 20800 -5.173 30800 3.791 30.000 -3.791 30800 2852 30.000 -2852 30800 7819 30800 -7819 30.000 5844 30800 -5844 40.000 3895 40800 -3.995 40.000 2888 40800 -2888 40800 7.473 40.000 -7.473 40800 5881 40800 -5881 50.000 3895 60.000 -3895 50800 2800 50.000 .-2800 50800 6810 50800 -6810 50.000 5.480 50800 -5.480 60800 3.456 60800 -3.456 60800 2818 60.000 -2818 60800 6820 60800 -8820 60800 4848 60.000 -4.548 70.000 2.763 70.000 -2.763 70800 1835 70.000 -1835 70.000 4.113 70800 -4.113 70800 3850 70.000 -3860 80.000 1898 80.000 -1898 80800 1833 80800 -1833 80800 2.472 80.000 -2.472 80800 2.029 80800 -2.009 90.000 860 90.000 -860 90800 810 90800 -810 90.000 850 90800 -.950 90800 .786 90800 -.785 95.000 .489 96800 -.489 95.000 .195 95800 -.195 95800 846 95800 -845 95800 286 95.000 -886 100.000 818 100800 -.018 100.000 800 100.000 .000 2 100.000 93 800 100.000 800 > 100.000 800 100800 800
 NACA 65 3 018 L. E. radtu*

 XL YL.000 .000 600 – 765 .750 *628 1650 -1.163 2600 -1.673 5.000 -2.182 7600 -2.650 10.0 -3.040 15.0 -3658 20.0 -4.127 30.0 -4.742 40.0 -4.995 50.0 -4663 60.0 -4604 70600 -3.432 80.0 -2.332 90.0 -1.188 95.0 – 604 100.000 -.021

Wortmenn FX LIIM42/K 25
For 25 percent flep

CLARK Y

Gottingen 548
(1930 to 1950 period)

Gottingen 804 (Eppler EA 8 (-11
-12 06) L. E. radius.5 camber 0.67
at SO

 Chord Upper Chord Lamar Chard Upper Chord Lower Station Surface Station Surface Station Surface Station Surface XU YU XL YL XU YU XL YL .000 OOO .000 .000 .000 OOO OOO OOO .000 050 .200 *.430 OOO 1000 000 – ooo 200 1050 .400 -000 .400 1060 OOO -.770 MO 2000 .600 ‘040 OOO .1800 OOO ‘050 Я00 2.270 OOO ‘060 OOO 0060 OOO ‘1.120 1250 1730 1050 -1030 1050 2.440 1060 -1.430 2.S00 3000 2000 ‘1040 2000 3.390 2000 -1060 SJOOO 6060 5000 -1.990 5.000 4.730 6.000 -2.490 7900 6.570 7000 ‘2050 7000 5.780 7000 ‘2.740 10900 7080 10.000 ‘1090 10.000 8090 10000 -2060 15.000 9.180 15.000 ‘1070 15000 7080 15000 -2080 20.000 10040 20000 -1060 20000 8000 20.000 ‘2.740 »j000 11.140 25000 -.780 25000 9010 25000 ‘2000 30.000 11050 30000 -080 30000 9.780 30000 -2060 40900 IIOOO 40000 OOO 40000 9000 40.000 -1000 50000 11.180 50000 050 80000 9.190 50000 ‘1.400 60Л00 9050 60000 .780 80000 9.140 60.000 -1.000 70.000 8030 70000 050 70.000 6080 70000 -050 80000 6030 80000 .730 80000 4080 80000 – 090 90.000 Э. ЗЭ0 90.000 .390 90.000 2.710 90000 *230 95.000 1.790 95.000 .180 95000 1.470 95000 -130 100000 .120 100000 -.120 100.000 .130 100.000 -.180

 Chord Upper Chord Lower Chord Upper Chord Lower Station Surface Station Surface Station Surface Station Surface XU YU XL YL XU YU XL YL OOO OOO OOO.000 .000 OOO .000 .000 OOO 020 OOO ‘.610 1008 1094 1.402 -1.448 .400 1.280 OOO ‘OOO 2.297 2.411 2.703 -1027 OOO 1010 OOO ‘1.100 4.742 3.420 5058 -2.462 OOO 1.730 OOO ‘1091 7317 4.168 7.783 -2009 1.260 2.150 1050 -1060 9.710 4.786 10090 -3.016 2.600 2080 2000 ‘2070 14.722 5065 15078 -3.227 5000 4.130 5.000 -3.010 19.781 6076 20039 -3076 7000 4080 7000 ‘3.480 24014 6.668 25.166 -3.230 10000 6030 10.000 -3.750 29076 6075 30.125 -3.125 15000 6010 15000 -4.100 40000 6037 40.000 -2037 20.000 7060 20.000 ‘4030 50.049 6.356 49051 -2.468 25.000 7070 25.000 -4.220 60.005 5.580 59015 -2.024 30000 7080 30.000 -4.120 79.W2 4.551 89098 ‘1.551 40.000 7000 40000 ‘3000 80087 3.296 79003 -1 074 60000 7040 50000 -3040 90087 1016 89033 -.594 60000 6080 80000 ‘2.780 95.041 090 94059 -.352 70.000 5.180 70.000 ‘2.140 100000 .105 IOOOOO -.105 80000 3.750 80.000 -1.600 90000 2.080 90000 -020 95000 1.140 96.000 -.480 100.000 .130 100.000 -.130

NACA 4415 LE RAOIUS 2.49 PERCENT

 NACA 64409 NACA 63*209 NACA 23012 L. E. radius 1.68 percent NACA 4415 L. E. radius 2.48 percent Chord Upper Chord Lesser Chord Upper Chord Lesser Chord Upper Chord Lessor Cherd Upper Chord Lesser Station Surface Station Surface Station Surface Station Surface Station Surface Station Surface Station Surface Station Surface XU VU XL YL XU YU XL YL XU YU XL YL XU YU XL YL OOO .000 OOO.000 OOO OOO .000 OOO .000 .000 .000 900 900 .000 .000 .000 077 029 023 ‘029 .437 .798 .583 ‘098 OOO 1.300 900 -.488 .000 940 200 -.550 013 1.021 087 -.741 080 073 020 -033 .400 1680 .400 -.730 .200 1950 .400 -.920 1095 1031 1.405 -003 1.170 1056 1030 -1041 OOO 1920 900 -.910 900 2950 .600 ‘1.180 2022 1095 2078 -1.151 2.408 1.768 2092 -1093 OOO 2.200 900 -1930 900 2950 900 -1.400 4003 2.732 5.197 ‘1.468 4097 20Ю 5.103 -1078 1050 2970 1950 -1930 1.250 3.070 1.250 -1.790 7.297 3.383 7.703 -1087 7094 3077 7008 -2.229 2000 3910 2900 -1.710 2.500 4.170 2.500 -2.480 9.798 3026 10002 -1057 9094 3038 10.106 ‘2006 5000 4910 5900 -2960 5.000 5.740 6.000 -3.270 14010 4.795 15.190 -2.104 14001 4083 16099 -2.917 7000 5800 7900 -2910 7900 6.910 7.500 -3.710 19030 5.458 20.170 -2072 19012 4.792 20088 ‘3000 10000 6930 10900 -2920 10.000 7940 10.000 -3.980 24054 5067 25.146 -2077 24025 5.169 25075 ‘3079 16000 7.190 15900 -3900 16.000 9.270 15.000 -4.180 29082 6.315 30.118 -2.427 29040 5414 30.080 -3.470 20000 7900 20.000 ‘3.970 20.000 10.250 20.000 -4.150 34.912 6038 35.088 ‘2.418 34056 6030 36.044 -3.470 25.000 7900 25.000 -4260 25.000 10920 25900 -3.980 39.942 8.632 40.058 -2048 38071 5.518 40029 -3078 30.000 7950 30900 ‘4.480 30.000 11.250 30.000 -3.7S0 44.972 6.564 45.028 -2.174 44088 5091 «014 -3001 40.000 7.140 40900 -4.480 40.000 11.250 40.000 -3.250 50.000 6042 50.000 -1030 50.000 5.159 60000 ‘2053 50.000 8.410 50900 -4.170 50.000 10.530 50.000 -2.720 60.045 6094 59056 ‘1.310 60.022 4.429 55978 -2.287 80.000 6.470 60.000 -3970 60900 9.300 60900 -2.140 70089 4004 60031 -016 70.033 3.430 88087 -1.486 70.000 4980 70900 -3900 70.000 7.630 70.000 -1950 80088 3.154 79031 -.030 80.032 2087 79068 ‘075 80.000 3980 80900 -2.160 80.000 5.550 80.000 -1.030 90.043 1044 89079 .424 90019 1067 88.981 ‘.033 90.000 1980 90.000 -1930 90.000 3.000 90.000 -.570 95.021 058 94.979 .406 95008 .612 94.991 .120 95.000 920 95.000 -.700 95.000 1970 95.000 -.360 100.000 .000 100.000 .000 IOOOOO .000 IOOOOO .000 100.000 .130 100.000 -.130 100.000 .160 100.000 -.160

 Chord Upper Chord Lower Chord Upper Chord Lower Chord Tppar Chord 14МЄГ Chord Upper Chord Lower Station Surface Station Surface Station Surface Station Surface Station Surface Station urface Station Surface Station Surface XU YU XL YL XU YU XL YL XU YU XL YL XU YU XL YL .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 400 400 .000 450 402 450 -478 499 473 401 -.723 .424 466 470 -.744 .423 468 477 -756 М2 1.112 418 -.796 .638 1.068 462 -458 4S5 1444 .035 -488 464 1.058 436 -.900 1.0S9 1.451 1.441 -409 1.123 1.379 1.377 -1.067 1.153 1442 1447 -1.100 1.151 1487 1449 -1.125 2476 2495 2.724 -1451 2.353 1461 2447 -1.403 2457 1455 2413 -1.473 2454 1444 2416 -1422 4.740 3.034 5451 -1492 4437 2.759 5.163 -1447 4474 2465 6.126 -1463 4405 2.769 5.131 -2.047 7.230 3465 7.770 -1419 7432 3.436 7468 -2.164 7469 3455 7.931 -2416 7464 3.400 7453 -2.428 9.737 4490 10463 -1496 9432 3.970 10.168 -2.420 9459 3.792 10.132 -2400 •463 3417 10.137 -2.725 14.748 5466 15452 -2444 14442 4419 15.158 -2409 14474 4482 20.116 -3430 14469 4.729 15.131 -3.157 10.770 6.126 20430 -2.406 19459 6.464 20.141 -3475 19485 5400 10.116 -3440 19482 5428 20.118 -3.469 24,800 6.705 25400 -2.499 24479 6446 25.121 -3462 24400 5456 25.100 -3464 24498 5.764 25.102 -3462 29434 7.13» 30.166 -2437 29.902 6494 30498 -3478 29417 5.994 30.083 -3.688 29.916 6.060 30.064 -3.764 34471 7.414 35.129 -2.518 34427 6413 35473 -3.423 34435 6.192 35405 -3.744 34436 6419 36465 -3.771 39410 7452 40.090 -2.436 39452 6401 40.048 -3489 35455 6474 40.045 -3.718 39456 9447 40.045 -3489 44450 7422 46.050 -2.266 44477 6436 45.023 -3452 44475 6406 46.026 -3.680 44.976 9.151 45425 -3423 40009 7444 50.011 -2424 50.000 6434 50.000 -3.030 45475 6414 50405 -3464 49.994 5443 50.005 -3483 60.067 6424 69443 -1.418 60.039 5427 69461 -2.415 50425 6423 59472 -2.719 90.029 5445 50472 -2.641 70.108 5.490 69492 -.760 70.063 4.584 69437 -1468 70454 4410 •9445 -1.944 70.052 4427 09448 -1461 90.151 3.967 79449 -429 80470 3496 79.930 -.908 50.076 3407 79424 -1.167 90.074 2.974 79426 -1.104 90.104 2438 90496 -.076 90466 1436 89444 -.296 80.062 1.551 85445 -471 90.090 1419 •9460 -439 95.053 1428 94447 -.048 96.038 1414 94482 -485 96427 .795 94474 -405 95.029 .769 94.974 -479 100.000 421 100.000 -.021 100.000 .021 100.000 -.021 100.000 421 100.000 -421 100.000 .021 100.000 -.021 МАСА 63-1-212 г 2 2 о e 1 МАСА 94-A410 ІАЦ>4МОО) Chord Upper Chord Lower Chord Upper Chord Lower Chord Upper Chord Lower Chord Upper Chord Lower Station Surface Station Surface Station Surface Station Surface Station Surface Station Surface Station Surface Station Surface XU YU XL YL XU YU XL YL XU YU XL YL XU YU XL YL .000 .000 .000 .000 400 400 400 400 .000 .000 400 .000 400 400 .000 .000 .417 1.032 .583 -432 .435 419 485 -.712 415 477 .795 -427 414 479 .786 -426 JS57 1460 443 -1.120 478 499 422 -459 494 1461 1418 -499 481 1j550 1419 -.666 1.145 1422 1.355 -1.408 1.169 1473 1431 -1469 2472 2.470 2428 -.799 2.084 2.476 2439 -.767 2478 2494 2422 -1412 2.408 1.757 2492 -1485 4420 3405 5.480 -466 4408 3.719 5.494 -432 4453 3438 5.137 -2406 4498 2.491 5.102 -1469 7403 4450 7497 -453 8484 4.703 8419 -411 7458 3463 7442 -3.115 7494 3489 7406 -2421 9403 5.457 10.457 -.434 9.479 6441 10421 -.771 9459 4454 10.141 -3420 9494 3456 10.106 -2421 14430 6414 16.470 -.756 14.500 •402 16400 -456 14488 5.470 15.132 -4.124 14499 4438 16.101 -2492 10479 7433 20.422 -496 16443 7468 20.457 -.526 19482 6.137 20.118 -4445 19409 4438 20491 -3446 24439 6420 25451 -.595 24401 8.795 25499 -483 34400 6.606 25.100 -4416 24421 6497 26479 -3407 29.707 0402 30 493 -.454 29468 9.420 30432 -432 29420 6401 30490 -4457 29436 5.732 30484 -3.788 34.790 9.596 35420 -.328 34.742 9457 35459 -.065 34441 7430 35450 -4470 34451 6454 35.049 -3494 39455 9413 40.145 -.174 38420 10.107 40.190 .123 39482 6491 40438 -4449 39.966 8467 40432 -3425 44430 9422 45470 .034 44.900 10.150 45.100 .354 44482 9.799 45.018 -4409 44494 6488 45418 -3488 50400 9449 60400 400 49477 10405 80.023 437 90.000 6.473 50400 -4467 50.000 5416 50400 -3.709 00.117 9439 50453 401 •0.114 9425 89496 1.187 80429 5.491 59471 -3449 80427 6417 59473 -3476 70.150 7.496 50411 1453 70415 7450 69.795 1410 70443 4.182 69457 -2438 70443 4.128 89457 -2.194 •0405 6475 79.792 1.495 •0400 5419 79.700 1457 80442 2498 79.958 -1.109 90444 2.793 79458 -1.191 50.166 3475 •9435 1477 90404 3.004 89.799 420 90425 1.224 99.975 -.190 90428 1427 89472 -493 •6.112 1451 94488 493 •5.104 1412 •4499 .450 95.012 468 94498 496 95414 422 94496 410 100400 .009 100.000 400 100.000 421 100400 -.021 100400 400 100.000 .000 100.000 400 100400 400
 МАСА 64-А-410

 МАСА 64^910

 МАСА 64^.210

 МАСА вЗА-210

Chord Lower Station Surface

XL VL.000 300

MO -.350 .400 -.410 300 -.560 1.250 -500 2.500 -1500

5.0 -2300

10.0 -3300

20.0 -4.000 30300 -5.000

40.0 -4.900

50.0 -4.500

60.0 -4300 70300 -3.500

80.0 -2300 90300 -1.500

100.000 .000

Sigurd Isaacson 53507 L. E. radius 0.5 percent

Sigurd Isaacson 64009 L. E. radius 0.3 percent

Sigurd Isaacson 73508 L. E. radius 0.4 percent

Sigurd Isaacson 53009 L. E. radius 0.8 percent

 Benedek В669вС L. E. radius Benedek 995668 LE. radios Benedek 984S6F Benedek 8635568 L. E. radius 0Л Percent 0.7 Percent 0.7 Percent Chord Ifooer Chord Lower Chord Upper Chord Lower Chord Upper Chord .ewer Chord Upper Chord Lower Station Surface Station Surface Station Surface Station Surface Station Surface Station Surface Station Surface Station Surface XU YU XL YL XU YU XL YL XU YU XL YL XU YU XL YL .000 1.000 .000 1.000 300 1.000 .000 1300 .000 .760 .000 .750 .000 .700 .000 .700 .200 1.450 .200 .590 300 (300 300 300 .200 1310 .200 .320 .200 1.200 .200 320 .400 1.700 .400 .440 .400 1.770 300 360 .400 1300 .400 .160 .400 1.400 .400 .080 jBOO 1.900 .900 .480 .600 1.960 300 300 300 1330 300 .090 300 1300 .700 .000 JBOO 2.100 300 .330 300 2.150 300 .280 300 2.100 300 .030 300 1.800 .800 310 1.250 2.500 1.250 350 1350 2300 1350 300 1.250 2.600 1.250 .000 1.250 2.180 1.250 .030 2.800 3.400 2300 .000 2300 3300 2300 .000 2.500 3.900 2.500 .200 2.500 3.140 2.500 .150 5.000 4.600 5.000 .200 5.000 4.280 5300 360 5.000 4.950 6300 .500 6.000 4.550 6.000 .420 7.800 5.400 7.500 .450 7.500 5300 7300 .400 7300 6.000 7.500 300 7300 5350 7.500 .780 10.000 9.160 10.000 .750 10.000 5.750 10300 .700 10300 6.900 10.000 1.100 10.000 6.530 10.000 1.120 15.000 7.250 15.000 1.300 15,000 6300 15300 1.200 15300 8300 15.000 1.500 16.000 7.780 16000 1.850 30.000 8.000 20.000 1300 20.000 7.700 20.000 1.750 20.000 8.700 20.000 2.200 20.000 8.550 20.000 2.450 25.000 9.550 25.000 2.350 25.000 8300 25300 2.250 25.000 8.950 25.000 2300 25.000 9.000 25.000 2.920 30.000 8.980 30.000 2.700 30.000 8.750 30300 2300 30300 9.000 30300 3.250 30.000 9.150 30.000 3350 40.000 9.400 40300 3360 40300 9.150 40300 3300 40300 8.900 40.000 4.000 40.000 8.990 40.000 3370 80.000 9.300 50.000 3300 50.000 9.100 50300 3.750 50.000 8300 50300 4.500 50.000 8.230 50.000 3350 00.000 8.750 60.000 4.000 60.000 8350 60300 3360 60.000 7.500 50.000 4.500 60.000 7.100 80.000 3.500 70.000 7.950 70.000 3300 70300 7300 76.000 3300 70.000 6.400 70.000 4.050 70.000 3750 70.000 3.000 80.000 5.900 80.000 2350 80.000 6.000 80.000 3.000 80.000 5.060 80300 3.300 80.000 4.080 80.000 2.220 90.000 3.550 90.000 1.500 90.000 3.700 90300 1.750 90.000 3.700 90.000 2.000 90.000 2.230 90.000 1.190 96.000 2.000 95.000 300 98300 2.100 95300 350 95.000 2.600 95300 1.100 100.000 320 100.000 .000 100.000 .400 100.000 .000 100.000 .450 100.000 .000 100.000 .500 100.000 .000 Benedek 993569 L. E. radius Benedek 883068 L. E. radius Benedek 974560 Benedek 87406F 0 A Percent 0.9 Percent Chord Upper Chord Lower Chord Upper Chord Lower Chord Upper Chord Lower Chord Upper Chord Lower Station Surface Station Surface Station Surface Station Surface Station Surface Station Surface Station Surface Station Surface XU YU XL YL XU YU XL YL XU YU XL YL XU YU XL YL .000 1.110 300 1.110 .000 1.180 .000 1.180 .000 350 .000 350 .000 300 .000 .900 .000 1.400 .200 .MO .200 1.740 .200 300 .200 1350 .200 350 .200 1.500 .200 .420 .200 1.810 .400 Ж .400 2.050 .400 .420 .400 1320 .400 350 .400 1.900 .400 .300 .400 2.070 300 .390 .900 2.310 .600 320 .600 1330 300 .ISO .600 2.200 300 .220 300 2.530 300 .300 300 2350 .800 .270 300 2.080 .800 .030 300 2.490 300 .170 1.250 3.000 1.250 .170′ 1.250 3.020 1.260 .170 1350 2.500 1.250 .000 1350 2.950 1.250 .100 2.500 4.150 2300 .030 2300 4.110 2.500 .000 2.500 3.480 2.500 .200 2.500 3.950 2.500 .100 5.000 5330 5.000 .050 5.000 5330 5.000 .070 5.000 4.900 5.000 .450 5.000 5.800 5.000 .450 7.500 7.090 7.600 .250 7.500 7.130 7.500 380 7.500 5.950 7.500 .700 7300 8.800 7.500 300 10.000 8.000 10.000 .500 ta. ooo 8.180 10.000 .960 10.000 6.700 10.000 350 10.000 7.400 10.000 1.000 18.000 9.150 15300 1.190 15300 9.500 16.000 1.470 15.000 8.000 15.000 1.450 16.000 8.550 16000 1.500 20.000 9370 20.000 1370 20.000 10.220 20.000 2.130 20.000 8.700 20.000 1350 20.000 8.200 20.000 1.950 25.000 10380 25300 2350 25.000 10310 25.000 2.560 25.000 9.000 25.000 2.600 25300 9.580 25.000 2.400 30.000 10.370 30.000 2.700 30.000 10300 30.000 2.830 30.000 9350 30.000 3.000 30.000 9.850 30.000 2300 40.000 9.910 40.000 3.050 40.000 9.900 40.000 3.000 40.000 8300 40.000 4.000 40.000 9.300 40.000 3.400 60.000 8380 50.000 2.980 «0.000 8330 50.000 2.900 50.000 8.000 50.000 4.500 50.000 9.800 50.000 3300 90.000 7.500 90.000 2.670 60.000 7.470 60.000 2.820 60.000 6300 60.000 4.000 60.000 7.700 60.000 3.750 70.000 5.900 70.000 2.220 70.000 5350 70.000 2.170 70.000 5.500 70.000 3.000 70.000 8350 70.000 3.400 80.000 4.200 80.000 1320 80.000 4.150 80.000 1.530 60.000 3.950 80.000 2.000 80.000 5.400 80.000 2350 90.000 2320 90.000 390 90.000 2.330 90.000 .830 90.000 2350 90.000 1.000 90.000 3.950 90.000 1.600 100.000 .330 100.000 .000 100.000 .350 100.000 .000 95.000 1.400 95.000 .500 95.000 2.900 95.000 .900 100.000 .500 100300 .000 100.000 .500 100.000 .000
 Benedek 885578 I E. rediu* 0.6 Percent

 .000 .400 .000 .790 .200 1.000 .400 1.220 800 1800 1.290 1.970 2800 3.000 9.000 4.730 7.900 8.170 10.0 7830 19.0 9.*20 20.0 10890 29800 10.470 30.0 10830 40800 10830 90.0 9.470 90.0 8.200 70.0 8.800 80800 4870 90.0 2.900 100.000 .100

 Pfenning Laminar 11 LE. radiu* 08 Percent

 AIRFOIL 64 6.45* 2*00 e. oo AIRFOIL 65 e •88« 6.00 N A Y N A T V-DISTR. FOR the above ALPHA REL . ZERO-LIFT LINE 0 00000 0.0000Q 0*862 0*854 0 1.00006 0 00000 J7»19 0.S7T l 99679 0*00076 0*891 0*888 1 0.99660 0 00070 0.699 0.895 2 98761 0*00311 0*947 0*948 2 0.96762 0 00260 0.969 0.951 Э 9t324 0*00686 1*006 1*013 3 0.97319 0 00639 1.005 1.012 4 95409 0*01145 1*042 1.05S 4 0.95367 0 01060 1.035 1.066 5 93022 0*01659 1*057 1.077 5 0.92963 0 01563 1.062 1.061 6 90185 0*02223 1*073 1*099 6 0.90067 0 02079 1.0S1 1.077 7 86942 0*02829 1*090 1*123 7 0.06763 0 02075 1.063 1.09S 8 8ЭЭЭ6 0*03455 1*105 1*146 8 0.03062 0 03321 1.076 1.116 9 79408 0*04081 1*119 1*167 9 0.79010 0 06006 1.092 1.139 10 75200 0*04691 1*132 1*188 10 0,76727 9 06713 1.110 1,166 11 70756 0*05267 1*143 1*208 11 0.70230 0 05621 1.130 1.195 12 66122 0*05793 1*153 1*228 12 0.65560 0 06100 1.1S2 1.227 13 61344 0*06257 1*161 1*246 13 0.00056 0 06739 1.170 1.262 14 56469 0*06646 1*168 1*264 14 0.56091 0 07286 1.201 1.300 15 51543 0*06950 1*173 1*281 15 0.51352 9 07697 1.229 1.362 16 46615 0*07162 1*177 1*298 16 0.60626 0 07915 1.222 1.366 17 41731 0*07275 1 • 1179 1.315 17 0.61697 0 07976 1.215 1.356 18 36938 0*07288 1*180 1*331 18 0.37226 9 07905 1.206 1.361 19 32280 0.07197 1*178 1*348 19 0.32656 9 07716 1.197 1.369 ao 27803 0*07004 1*175 1*365 20 0.26233 9 07622 1.165 1.377 U 23547 0*06710 1*168 1*382 21 0.26007 9 07026 1.171 1.385 22 19553 0*06322 1*159 1.401 22 0.20017 9 06530 1.154 1.395 23 15858 0*05844 1*145 1*420 23 0.16305 9 05966 1.133 1.605 24 12494 0*05285 1*124 1*441 24 0.12905 9 05326 1.100 1.617 25 09490 0*04653 1*095 1*464 25 0.09651 9 06627 1.070 1.630 26 06872 0*03960 1*052 1*487 26 0.07170 9 03680 1.022 1.666 27 04658 0*03221 0*986 1*511 27 0.06660 9 03119 0.956 1.661 28 0?863 0*02453 0*861 1*531 28 0.03022 9 02363 0.652 1.660 29 Of 496 0*01680 0.70S 1.543 29 0.01569 9 01563 0.686 1.502 30 0<) 560 0*00931 0*382 1*525 30 0.00600 9 00605 0.361 1.519 31 06056 0.002S8 0*286 1*429 31 0.00061 9 00261 0.306 1.519 32 00075 •0*00255 1*503 0.752 32 0.00079 •9 00236 1.506 0.752 33 06675 •0*00664 1*390 0*199 33 0.00693 •9 00629 1.390 0.199 34 01818 -0*01038 1*318 0.S29 34 0.01636 •9 00993 1.316 0.5Э0 35 03477 -0*01348 1*260 0*683 35 O. OSSOO -9 01295 1.260 0.663 36 05640 -0*01582 1*215 0*766 36 0.05066 -9 01522 1.216 0.766 37 08293 -0*01735 1*178 0*814 37 0.06317 -9 01670 1.178 0.616 38 11415 •0*01810 1*146 0*843 38 0.11639 •9 01761 1.166 0,663 39 14979 •0*01809 1*118 0*861 39 0.15006 •9 01730 1.116 0.661 60 18954 -0*01740 1*093 0*872 40 0.16979 -9 01006 1.096 0.673 41 23300 -0*01610 1*071 0!* 879 41 0.23325 •9 01533 1.071 0,679 42 27973 -0*01431 1*051 0*882 42 0.27990 •9 01352 1.05І 0.663 4*% 32924 -0*01212 1*032 0*884 43 0.32950 •9 01131 1.033 0.666 44 38098 -0*00965 1*01S 0*883 44 0.36126 •9 00866 1.0І6 0.6*6 45 43439 -0*00701 0*999 0*882 45 0.6Э66Т •9 00021 0.999 0,6*2 46 48884 -0*00434 0*984 0*879 46 0.66912 •9 00356 0.966 o. tao 47 54370 -0*00173 0*970 0*876 47 0.56399 -9 00095 0.970 0.876 48 59831 0*00069 0*956 0*873 48 0.59661 9 00165 0.956 0.673 49 65199 0*00284 0*943 0*869 49 0.05230 9 00357 0.963 0.669 50 70409 0*00461 0..9Э0 0*864 50 0.70660 9 00531 0.930 0.666 51 75392 0*00595 0*918 0*859 51 0.75626 9 00661 0.916 0.660 52 80082 0*00678 0*906 0*8S5 52 0.60115 9 00760 0.906 0.655 53 84416 0*00709 0*894 0*849 S3 0.06650 9 00705 0.696 0.650 54 88331 0*00686 0*883 0*844 54 0.06305 9 00730 0.663 0,666 55 91770 0*00612 0*871 0*839 55 0.91603 9 00656 0.672 0.639 56 94675 0*00491 0*861 0*833 56 0.96709 9 00522 0.661 0.636 57 96990 0*00333 0*857 0*83\$ 57 0.97019 9 00350 0.660 0.637 58 98661 0*00169 0*861 0*843 58 0.98660 9 00175 0.670 0.652 59 99665 0*00046 0*865 0*853 59 0.99071 9 00066 0.660 0.667 60 00000 0*00000 0*862 0*854 60 1.00000 9 00000 0.679 0.871 ALPHAO « 4«SS DEGREES CMO a-0*1222 ALPNAt * 6.56 oegrees CNO >«0.1206 ETA « 1*071 ETA « 1.072
 WARNING * SUBROUTINE SMOOTH HAS SLOPES WARNING – SUBROUTINE SMOOTH HAS SLOPES •0.3B0 *N0-0*482 BETWEEN POINTS 32 ANO 3 «0.406 ANO-0.691 BETWEEN POINTS 32 AND

EPPLER 205 EPPLER 207 EPPLER 209

PROF1L E 205 10.484b PROFIL E 207 12.04% PROFIL E209 13.78%

 N X Y X Y X Y 0 100.000 0.000 100.000 0.000 100.000 0.000 1 99.655 .039 99.647 .045 99.639 .052 2 98.649 .174 98.625 .202 98.600 .232 3 97.049 .427 97.011 .489 96.969 .557 4 94.916 .778 94.870 .881 94.821 .992 5 92.285 1.196 92.238 1.337 92.187 1.488 6 89.175 1.668 89.128 1.841 89.077 2.027 7 85.624 2.199 85.576 2.400 85.523 2.615 8 81.684 2.786 81.633 3.011 81.577 3.253 9 77.412 3.419 77.357 3.666 77.295 3.930 10 72.866 4.088 72.806 4.352 72.738 4.634 11 68.108 4.777 68.043 5.055 67.968 5.352 12 63.204 5.470 63.132 5.759 63.049 6.065 13 58.218 6.147 58.139 6.441 58.047 6.753 14 53.217 6.782 53.129 7.079 53.028 7.393 15 48.265 7.342 48.169 7.638 48.058 7.949 16 43.410 7.785 43.306 8.075 43.185 8.380 17 38.680 8.081 38.567 8.362 38.436 8.657 18 34.101 8.214 33.981 8.483 33.841 8.764 19 29.699 8.177 29.573 8.430 29.424 8.694 20 25.496 7.970 25.363 8.205 25.208 8.448 21 21.508 7.606 21.371 7.819 21.211 8.037 22 17.764 7.111 17.626 7.300 17.461 7.490 23 14.302 6.507 14.162 6.669 13.997 6.830 24 11.157 5.811 11.018 5.944 10.854 6.073 25 8.360 5.040 8.225 5.143 8.065 5.237 26 5.937 4.211 5.808 4.282 5.656 4.341 27 3.909 3.344 3.791 3.383 3.651 3.406 28 2.292 2.461 2.189 2.468 2.066 2.454 29 1.097 1.589 1.015 1.565 .916 1.517 30 .331 .766 .279 .714 .216 .635 31 .002 .055 .000 -.015 .007 -.106 32 .233 -.506 .304 -.626 .398 -.775 33 1.065 -.988 1.212 -1.204 1.379 -1.467 34 2.419 -1.420 2.628 -1.750 2.852 -2.140 35 4.291 -1.776 4.543 -2.234 4.804 -2.765 36 6.669 -2.053 6.943 -2.649 7.219 -3.329 37 9.534 -2.252 9.807 -2.991 10.073 -3.821 38 12.864 -2.378 13.109 -3.257 13.340 -4.233 39 16.627 -2.436 16.817 -3.448 16.986 -4.561 40 20.783 -2.435 20.893 -565 20.974 -4.799 41 25.290 -2.384 25.292 -3.611 25.258 -4.943 42 30.097 -2.292 29.966 -3.586 29.793 -4.985 43 35.149 -2.168 34.861 -3.487 34.524 -4.909 44 40.388 -2.021 39.937 -3.302 39.430 -4.683 45 45.751 -1.859 45.165 -3.044 44.516 -4.322 46 51.174 -1.689 50.495 -2.744 49.749 -3.884 47 56.591 -1.516 55.860 -2.425 55.057 -3.409 48 61.938 -1.345 61.189 -2.102 60.368 -2.923 49 67.149 -1.180 66.414 -1.787 65.609 -2.446 50 72.160 -1.023 71.467 -1.488 70.708 -1.993 51 76.911 -.876 76.283 -1.212 75.594 -1.576 52 81.343 -.740 80.796 -.963 80.197 -1.205 53 85.400 -.614 84.948 -.744 84.451 -.884 54 89.034 -.380 91.942 -.390 91.665 -.400 55 92.195 -.380 91.942 -.390 91.665 -.400 56 94.860 -.252 94.699 -.239 94.522 -.222 57 97.017 -.125 96.930 -.108 96.834 -.089 58 98.635 -.036 98.598 -.026 98.558 -.014 59 99.651 -.003 99.643 -.000 99.633 .003 60 100.000 .000 100.000 .000 100.000 -.000 CM = -.0460 fi « 2.37° CM = -.0499 fi = 2.33е CM * -.0547 fi = 2.28°

 XU YU .000 900 .026 .190 .466 .915 1.344 1.740 2.652 2906 4.363 3.487 6.525 4.352 9.061 5.161 11.957 5.957 15.218 5.663 19780 7.284 22920 7905 26.595 6.213 30.967 8.487 39403 8.603 39.979 8951 44973 8.332 49.458 7.954 54.305 7.438 59.186 8908 64.052 8.112 56939 6.381 73.484 4.842 77.923 3.914 82.096 3.214 85.945 2.558 89.414 1957 92.452 1.415 95.023 932 97.106 .522 98.674 .220 99.661 .051 100.000 .000

XL YL.000 000 .129 -.375 919 -.938 2.044 -1.252 3.791 -1.598 6.049 -1841 8901 -2.010 12.026 -2.098 15.697 -2.112 19.778 -2.061 24.227 -1.955 28.998 -1.807 34.035 -1.628 39.280 -1.430 44.672 -1.244 50.145 -1.019 55.630 – 824 61.059 -.645 66.384 -.486 71.479 -950 76.339 -.239 80982 -.153 85.050 -.091 88.788 -.048 92.048 -.018 94.794 .010

97.003 .032

98.640 .034

99.655 .014

100.000 .000

 Wortmann FX 38*153 Camber 2.1 fercant

 AIRFOIL 0008 10 .80X AIRFOIL 12 9.27X AIRFOIL 14 8.47X N X Y N К Y N X Y 0 100.000 0. 0 0 100. .000 0.0 0 100.000 0.0 1 99.664 0. 082 1 99. .665 0.052 1 99.667 0.045 2 98.714 0. 338 2 98. .701 0.219 2 98.707 0.195 3 97.253 0. 740 3 97, .190 0.497 3 97.194 0.446 4 95.321 1. 211 4 95 .174 0 .837 4 95.169 0.760 5 92.908 1. 712 5 92 .660 1.213 5 92.645 1.112 6 90.028 2. 250 6 89 .671 1.629 6 89.647 1.506 7 86.722 2. 819 7 86. .251 2.080 7 86.218 1.937 8 83.033 3. 407 8 82 .447 2.557 8 82.405 2.394 9 79.007 4. 001 9 78 .304 3.047 9 78.255 2.867 10 74.689 4. 586 10 73 .875 3.538 10 73.817 3.344 11 70.131 5. 147 11 69 .209 4.018 11 69.145 3.811 12 65.381 5. 672 12 64 .361 4.472 12 64.292 4.256 13 60.492 6. 147 13 59 . 384 4.889 13 59.310 4.666 14 55.516 6. 558 14 54 .331 5.256 14 54.254 5.029 15 50.504 6. 895 15 49 .257 5.562 15 49.178 5.334 16 45.508 7. 146 16 44 .213 5.795 16 44.133 5.570 17 40.577 7. 303 17 39 .251 5.948 17 39.172 5.727 18 35.760 7. 359 18 34 .419 6.013 18 34.343 5.800 19 31.103 7. 309 19 29 . 765 5.984 19 29.692 5.780 20 26.649 7. 149 20 25 .331 5.857 20 25.262 5.666. 21 22.440 6. 878 21 21 .158 5.631 21 21.095 5.456i 22 18.512 6. 498 22 17 .282 5.308 22 17.226 5.151 23 14.898 6. 013 23 13 .>36 4.892 23 13.689 4.755 24 11.627 5. 431 24 10 .551 4.391 24 10.513 4.275 25 8.724 4. 763 25 7 .750 3.815 25 7.725 3.721 26 6.211 4. 023 26 5 .357 3.176 26 5.344 3.104 27 4.105 3. 230 27 3 .389 2.492 27 3.388 2.439 28 2.421 2. 405 28 1 .859 1.779 28 1.867 1.744 29 1.169 1. 577 29 0 .772 1.067 29 0.786 1.048 30 0.360 0. 779 30 0 .140 0.393 30 0.150 0.390 31 0.004 0. 079 31 0. .026 -0.161 31 0.022 -0.139 32 0.219 -0. 521 32 0. .486 -0.652 32 0.465 -0.595 33 1.024 -1. 097 33 1 .483 -1.155 33 1.447 -1.055 34 2.328 -1. 645 34 2 .985 -1.618 34 2.938 -1.468 35 4.124 -2. 137 35 4 .983 -2.030 35 4.931 -1.824 36 6.398 *2. 559 36 7 .462 -2.382 36 7.412 -2.116 37 9.136 -2. 903 37 10 .404 -2.673 37 10.363 -2.346 38 12.318 -3. 170 38 13 .781 -2.903 38 13.756 -2.515 39 15.914 •3. 363 39 17 .558 -3.074 39 17.559 -2.629 40 19.884 -3. 484 40 21 .697 -3.190 40 21.730 -2.690 41 24.185 -3. 538 41 26, .153 -3.252 41 26.227 -2.705 42 28.769 -3. 525 42 30. .876 -3.266 42 30.998 -2.680 43 33.580 -3. .446 43 35. .813 -3.235 43 35.989 -2.619 44 38.562 -3. .299 44 40. .907 -3.161 44 41.144 -2.527 45 43.655 -3. .069 45 46. .098 -3.046 45 46.401 -2.409 46 48.825 -2. .728 46 51. .327 -2.891 46 51.701 -2.267 47 54.071 -2. .287 47 56. .530 -2.694 47 56.979 -2.105 48 59.361 -1. .802 48 61. .646 -2.448 48 62.175 -1.921 49 64.626 ►1. .317 49 66. .629 -2.128 49 67.227 -1.718 50 69.792 -0, .862 50 71. .476 -1.732 50 72.073 -1.480 51 74.784 -0. .463 51 76. .164 -1.318 51 76.689 -1.194 52 79.524 -0. .138 52 80. .621 -0.934 52 81.057 -0.890 53 83.934 0. .102 53 84. .773 -0.604 53 85.121 -0.612 54 87.940 0. .252 54 88. .550 -0.342 54 88.811 -0.382 55 91.469 0. .315 55 91. .881 -0.155 55 92.063 -0.209 56 94.456 0. .302 56 94. 705 -0.039 56 94.817 -0.091 57 96.845 0. .233 57 96. .969 0.020 57 97.026 -0.019 58 98.586 0. .133 58 98. ‘632 0.032 58 98.654 0.012 59 99.645 0. .040 59 99. 654 0.014 59 99.659 0.008 60 100.000 0. .000 60 160. 000 0.0 60 100.000 0.0 ALPHAO CMO = – = 3.74 DEGREES 0.1028 ALPHAO cno s 2. =-0. 07 0527 DEGREES ALPHAO cno и и i Є N* ** V» DEGREES

 JANOVEC 8*12

 888*388**38

x у

 1 . иисюи U. UUU1M .99674 .00039 .99707 .00150 .97126 .00367 .94970 .00699 .92292 .01150 .69147 .01713 .69594 .02373 .6169Э .03107 .77501 .03666 .73070 .04669 .66454 .05479 .63700 .06231 .96656 .06920 .53965 .07526 .49073 .06029 .44220 .06416 .39450 .06677 .34605 .06605 .30323 .06794 .26043 .06644 .22002 .06356 .16232 .07934 .14769 .07362 .11622 .06706 .06623 .05927 .06364 .05060 .04320 .04130 .02649 .03166 . 01374 .02205 .00517 .01269 .00077 .00401 .00056 *.00312 .00579 *.00664 .01662 -.01315 .03263 -.01645 .05397 -.01644 .06063 -.01936 .11236 -.01939 .14663 -.01673 .16960 -.01750 .23417 -.01561 .26205 -.01374 .33271 -.01142 .36555 -.00694 .43995 -.00643 .49526 •.00396 .99066 -.00171 .60605 .00029 .66009 .00162 .71216 .00296 .76166 .00367 .60795 .00397 .65036 .00391 .66634 .00354 .92140 .00299 .94911 .00222 .67109 .00144 .96709 .00073 .99674 .00020 1.00000 -.00000
 X У X У X У X У 00000 0.00000 1.00000 0.00000 1.Ос000 0.00000 1.00000 0.ооооо 99679 .00126 .99662 .00093 .99679 .00034 .99677 .00099 96799 .00901 .96666 .00231 .96709 .00147 .96736 .00226 97456 .01036 .97193 .00936 .97129 .00363 .97242 .00921 99696 .01636 .99119 .00939 .94976 .00696 .99237 .00906 93361 .02299 .92601 .01361 .92304 .*01 199 .92746 .01399 90692 .03009 .69611 .01677 .69170 .01729 .69794 .01666 67910 .03766 .86192 .021*22 .69637 .02403 .66424 .02430 63996 .04997 .62393 .03011 .61764 .03191 .82669 .03033 60196 .09396 .76266 .03632 .77610 .03949 .76630 .03697 76043 .06192 .73669 .04271 .73227 .04792 .74310 .04262 71703 .06914 .69260 .04911 .66669 .09941 .69771 .04663 67169 .07619 .64900 .09931 .63971 .06283 .69062 .09439 62932 .06241 .99647 .06102 .99169 .06990 .60229 .09934 97762 .06760 .94793 .06992 .94399 .07320 .99306 .06392 92979 .09167 .49693 .06973 .49922 .07974 .90349 .06663 46196 .09493 .44977 .07232 .44716 .06302 .49401 .06922 43371 .09606 .40160 .07366 .39979 .06492 .40907 .07062 38660 .09626 .39444 .07363 .39346 .06943 .39714 .07102 34064 .09912 .30666 .07280 .30862 .06494 .31066 .07042 29623 .09296 .26476 .07066 .26999 .06226 .26612 .06669 29373 .06671 .22310 .06749 .22460 .07676 .22394 .06631 21390 .06361 .16409 .06333 . 6620 .07414 .18493 .06269 17967 .07741 .14613 .09626 .19074 .06649 .14630 .09649 14120 .07023 .11991 .09243 .11699 .06166 .11999 .09326 10960 .06229 .06699 .04966 .06966 .09436 .06699 .04729 06196 .09361 .06147 .03679 .06493 .04617 .06167 .04060 09792 .04491 .04093 .03131 .04366 .03741 .04093 03323 03769 .03919 .02366 .02360 .02677 .02839 .02437 .02936 02206 .02979 .01163 .01964 .01380 .01936 .01204 .01730 01090 .01649 .00377 .00623 .00903 .01069 .00400 .00939 00313 .00776 .00013 .00131 .00046 .00263 .00021 .00191 00001 .00038 .00192 -.00392 .00079 •.00320 .00119 -.00406 00246 -.00902 .00676 -.00761 .00681 -.00767 .00799 •.00692 01117 •.00919 .02169 -.01116 .01639 -.01209 .01909 -.01317 02993 -.01267 .03990 -.01368 .03499 -.01946 .03994 -.01630 04922 -.01994 .06334 -.01992 .09666 -.01760 .09723 -.01620 07000 -.01634 .09177 -.01729 .06326 -.01906 .06413 -.01911 09999 •.02006 .12494 -.01606 .11474 -.01932 . 1999 -.01920 13368 -.02111 .16249 -.01640 .19069 -.01669 .19247 -.01669 17169 -.02192 .20391 -.01629 .19129 -.01724 .19313 -.01797 21376 -.02129 .24679 -.01771 .23969 -.01926 .23791 -.01609 29666 •.02044 .29*61 -.01671 .26349 -.01292 .26909 -.01417 30669 -.01697 .34696 -.01941 .33413 -.01034 .33937 -.01202 39670 -.01689 .39927 -.01392 .36706 -.00772 .36774 -.00970 40636 -.01409 ..49266 -.01231 .44199 -. 009,16 .44162 •.00726 46124 -.01061 .90711 -.01064 .49702 •.00279 .49640 -.00467 91493 -.00639 .96136 •.00696 .99269 •.00069 .99149 •.00296 96931 -.00192 .61907 -.00731 .60776 .00107 .60606 •.00093 62394 .00324 .66792 ’-. 00979 .66163 .00249 .69997 .00121 67603 .00747 .71609 -.00443 .71396 .00342 .71127 .00260 73071 .0.1064 .76614 •.00326 .76267 .00400 .76091 .00360 76110 .01311 .61109 •.00236 .60693 .00420 .60669 .00416 62629 .01419 .69226 -.00169 .69114 .00406 .64906 .00436 87139 .01390 .68923 -.00113 .66693 .00364 .66717 .00416 90999 .01242 .92149 •.00079 .92163 .00301 .92046 .00363 94190 .00962 .94694 -.00041 .94939 .00229 .94643 .00269 96749 .00646 .97026 -.00003 .97126 .00146 .97066 .00193 96969 .00321 .96646 .00016 .96713 .00074 .96666 .00102 99649 .00069 .99699 .00010 .99677 .00020 .99670 .00029 006oo .OCOOO 1*00046 •40000 1 • 00006 ,йОлло І. ОоООО • 04000

 X У X У X У X У 00000 0.00000 1.ooooo 0.00000 1.оооос 0.00000 1.00000 0.00000 99694 .00023 .99694 .00036 .99690 .00042 .99669 .00043 96621 .00111 .99746 .00196 .99619 .00196 .99679 .00194 96929 .00307 .97209 .00376 .96949 .00461 .97069 .00444 94604 .*00694 .99106 .00702 .94697 .00991 .94993 .00834 91742 .01192 .92493 .01132 .91927 .01444 .92202 .01391 •6429 .01990 .99394 .01661 .99703 .02139 .99094 .01994 94791 .02797 .99961 .02279 .99099 .02939 .99907 .02714 90901 .03749 .91971 .02971 .91146 .03917 .91616 .03916 76666 .04799 .77769 .03719 .76933 .04740 .77439 .04369 72424 .09930 .73313 .04497 .72903 .09674 .73029 .09230 9909Э .06722 .69661 .09290 .67907 .06996 .69439 .06064 63993 .07442 .63999 .06042 .63196 .07443 .63721 .06996 99999 .06029 .99961 .06762 .99414 .09219 .99923 .07640 94234 .09492 .94019 .07420 .93609 .09991 .94091 .08299 49464 .06909 .49093 .07997 .49920 .09406 .49269 .08606 44690 .09996 .44204 .09472 .44079 .09770 .44477 .09187 39997 .09097 .39427 .09929 .39411 .09969 .39761 .09421 39312 .09992 .34799 .09090 .34997 .10001 .39194 .09904 .30909 .09904 .30399 .09119 .30490 .09667 .30694 .09439 29499 .09496 .26126 .09019 .26227 .09971 .26416 .09231 22379 .09044 .22127 .09791 .22219 .09119 .22361 .06809 19912 .07499 .19393 .09329 .19497 .09923 .16969 .06419 .14939 .06997 .14916 .07770 .14971 .07799 .19073 .07922 .11693 .06137 .11797 .07099 .11799 .06963 . 1999 .07113 09909 .09342 .09939 .06323 .09939 .06040 .09072 .06303 .09297 .04494 .06476 .09469 .06437 .09096 .06611 .Q9406 .04177 .03994 .04399 .04993 .04320 .04033 .04930 .04443 .02474 .02697 .02726 .03996 .02602 .03000 .02940 .03437 .01209 .01914 .01467 .02606 .01301 .01997 .01946 .02416 .00392 .00969 .00607 .01606 .00433 .01032 .00643 .01419 00019 .00199 .00129 .00643 .00017 .00193 .00130 .00909 00127 •.00429 .00016 •.00200 .00196 -.00466 .00030 -.00210 00901 -.00994 .00377 -.00914 .00916 -.01099 .00499 -.00721 .02093 •.01294 .01306 •.01234 .02237 -.01621 .01603 -.01117 0394S •.01613 .02779 -.01923 .04069 •.02144 .03260 -.01434 .06167 •.01949 .04791 -.01670 ■ .06399 •.02609 .09491 -.01664 09001 •.02012 .07391 -.01690 .09171 •.03004 .06196 -.01907 12317 •.02113 .10493 -.01964 .12392 -.03322 .11392 -.01669 .16079 •.02160 .14069 -.01417 .16019 -.03999 .19011 -.01897 20229 •.02199 .16140 -.01202 .20012 -.03714 .19099 -.01764 24730 -.02109 .22624 -.00997 .24337 •.03762 .23962 -.01661 29934 -.02016 .27499 •.00696 .29990 -.03766 .29362 -.01903 .34990 -.01999 .32999 -.00433 .*33902 •.03672 .33437 -.01323 39639 -.01739 .37936 -.00176 .39946 -.03497 .39726 -.01133 49219 -.01969 .43UM9 .00060 .44031 -.03249 .44162 -.00942 90667 -.01399 .49043 .00273 .49309 -.02934 .49677 -.00799 96120 -.01202 .94699 .00499 .94629 -.02999 .89203 -.00999 61911 -.01022 .60221 .00601 .99939 -.02139 .60671 -.00429 66779 •.00992 .69660 .00709 .69199 -.07703 .66013 -.00291 71949 -.00696 .70909 .00774 .70341 -.01296 .71162 -.00179 76666 •;00996 .79997 .00900 .79299 -.00910 .76093 -.00079 61169 -.00437 .60964 .00796 .*79966 -.00991 .80627 .00001 69297 •.00337 .64947 .00739 .64299 -.00337 .94833 .00067 99999 •.00297 .69692 .00692 .99219 -.00149 .66622 .00114 92229 -.00193 .92046 .00946 .91664 -.00026 .91946 .00139 94931 -.00140 .94962 .00407 .94976 .0004^ .94797 .00137 97093 •.00097 .97093 .00262 .96909 .00099 .97009 .00110 99669 •.00039 .99703 .00131 .99609 .00043 .96699 .00069 99699 -.00009 .99674 .00039 .99649 .00014 .99661 .00020 OOO0O фОСООО 1.00090 .ООбо* |.90 000 •Од ООО . воем .00ооо

 49 0.66752 -.0.01108 50 0.7)001 *0.01000 51 0.71171 *0.00000 52 0.02490 *0.00705 5) 0.00900 *0.00072 54 0.09707 *0.00557 55 0.92707 >0.00440 SO 0.95270 *0.00917 57 0.97279 *0.00108 50 0.90709 *0.00079 59 0.99000 – O. OGOIO 00 1.00001 *0.00000 ALPHAO – 0.02 DECREES CMO • 0.0004

AIRFOIL SSOlO-Rt К X Y

0 1.00000 0.0

1 0.99674 0.00001

2 0.90707 0.00007

9 0.9710] 0.000jo

4 0.94070 0.00108

5 0.92041 0.00256

6 0.00667 0.00516

7 0.04820 0.00903

0 0.80600 0.01406

9 0.76076 0.02000

10 0.71907 0.02600

11 0.66377 0.09420

12 0.61355 0.04163

19 0.56296 0.04077

14 0.51247 0.05529

15 0.46251 0.06099

16 0.41940 0.06546

17 0.96576 0.06879

10 0.91969 0.07069

19 0.27560 0.07113

20 0.23303 0.07023

21 0.19473 0.06799

22 0.15060 0.06445

29 0.12579 0.05960

24 0.09697 0.03377

25 0.07071 0.04600

26 0.04009 0.09915

27 0.03102 0.03001

20 0.01710 0.02214

29 0.00799 0.01940

90 0.00167 0.00533

91 0.00015 -0.00140

92 0.00424 *0.00650

33 0.01456 *0.01004

94 0.09020 *0.01471

95 0.05129 *0.01004

36 0.07710 *0.02002

37 0.I070S -0.02906

30 0.14291 -0.02401

39 0.10194 -0.02609

40 0.22440 -0.02600

41 0.27000 *0.02715

42 0.91029 *0.02691

43 0.96064 -0.02629

44 0.42035 -0.02517

45 0.47345 -0.02301

46 .0.52673 -0.02219

47 0.37983 -0.02039

40 0.69209 *0.01046

49 0.60292 *0.01645

50 0.73179 -0.01449

51 0.77792 -0.01243

52 0.82095 -0.01049

59 0.06090 -0.00065

54 0.09547 -0.00691

55 0.92603 *0.0052′

56 0.95163 *0.00967

57 0.97211 -0.00212

58 0.90790 -0.00000

59 0.99670 -0.00019

40 1.00001 -0.00000

ЛГ. РКАО «0.64 DECREES

CMO * 0.0006

 X(i) Yo Yu X(i ) Yo Yu 1 0.0000 1 0.OOUO 0.0000 1 0.0000 0.0000 0.0000 г .0050 .0076 -.0054 2 . 0050 . 0084 -.0062 3 .0125 .0115 -.0088 3 .0125 . 0128 -.0101 4 .0250 .0177 -.0128 4 .0250 .0195 -.0147 5 .0500 .0253 -.0175 5 .0500 .0280 -.0202 6 .1000 .0349 -.0229 6 .1000 . 0385 -.0265 7 .1500 .0414 -.0266 7 .1500 . 0456 -.0309 8 .2000 .0448 -.0284 8 .2000 . 0494 -.0325 9 .2500 . 0473 -.0297 9 .2500 .0521 -.0345 10 .3000 .0488 -.0302 10 .3000 .0537 -.0351 11 .3500 . 04V6 -.0304 11 .3500 . 0546 -.0354 12 .4000 . 0490 -.0295 12 .4009 . 0540 -.0344 13 .5000 . 0463 -.0263 13 .5000 .0508 -.0308 14 .6000 .0402 -.0208 14 .6000 . 0440 -.0246 15 .7000 .0312 -.0136 15 .7000 . 0340 -.0164 lb .8000 . 0208 -.0069 16 .8000 .0225 -.0Д87 17 .8500 .0153 -.0042 17 .8500 .0165 -.0054 18 .9000 .0101 -.0021 18 .9000 .0109 -.0029 1? .9500 .0047 -.0006 19 .9500 . 0050 -.0009 20 1.0000 0.0000 0.0000 20 1.0000 0.0000 0.0000 HQ-1,0/10 HQ-1,5/8 X(i) Yo Yu _ X(i> Yo Yu 0.0000 0 . UUOO 1 0.0000 U. 0001) 0 . OOUO 2 .0050 . 0092 – .0070 2 .0050 . 0082 – .0048 3 .0125 .0141 -.0114 3 .0125 .0128 – .0082 4 .0250 . 0214 -.0166 4 .0250 .0189 -.0115 5 . 0500 . 0307 -.0228 5 .0500 . 0273 -.0156 6 . 1000 .0421 -.0301 6 .1000 . 037V -.0199 7 . 1500 . 0499 -.0351 7 .1500 . 0451 – . 0229 8 .2000 . 0540 -.0375 8 .2000 .0489 – . 0243 V .2500 . 0569 -.0393 9 .2500 . 0517 -.Ubjj 10 .3000 . 0586 -.0400 10 .3000 .0534 -.0255 11 .3500 . 0596 -.0404 11 .350 0 . 0544 -.0256 12 .4000 .0589 -.0393 12 .4000 .0534 -.0246 13 .5000 .0554 -.0354 13 .5000 .0513 -.0213 14 .6000 . 0478 -.0284 14 .6000 . 0450 – . 0159 15 .7000 .0368 -.0192 15 .7000 .0356 -.0092 16 .8000 .0243 -.0104 16 .8000 .0243 -.0035 17 .8500 .0177 -.0066 17 .8500 .0181 -.0014 18 .9000 .0117 -.0037 18 .9000 .0121 -.0002 19 .9500 .0054 -.0013 19 .9500 .0057 -.0004 20 1.0000 0.0000 0.0000 20 1.0000 0.0000 0.0000

U5/» І7І —

HQ-1,5/9 HQ-1,5/10

X (i) Yo Yu X(l) Yo Yu

HQ-2^/8

SD7032

SD7037

 1 1 0 17 0.44745 0.07211 33 0.00127 -0.00393 49 0.60914 -.00549 2 0.99672 0.00042 18 0.39862 0.0741 34 0.00806 -0.00839 50 0.66197 -.00349 3 0.98707 0.0018 19 0.35101 0.07504 35 0.02038 -0.01227 51 0.71305 -.00168 4 0.97146 0.00436 20 0.30508 0.07488 36 0.038 -0.01541 52 0.76178 -.00014 5 0.95041 0.00811 21 0.26125 0.07358 37 0.06074 -0.01777 53 0.80752 0.00104 6 0.9245 0.01295 22 0.21989 0.07113 38 0.08844 -0.01934 54 0.84964 0.00182 7 0.89425 0.01865 23 0.18137 0.06754 39 0.12084 -0.02017 55 0.88756 0.00220 8 0.86015 0.0249 24 0.14601 0.06286 40 0.15765 -0.02032 56 0.92071 0.00218 9 0.82261 0.03141 25 0.1141 0.05715 41 0.1985 -0.01987 57 0.94859 0.00185 10 0.78201 0.03788 26 0.08586 0.05049 42 0.24296 -0.01891 58 0.97077 0.00132 11 0.73865 0.04413 27 0.06146 0.043 43 0.29055 -0.01754 59 0.98690 0.00071 12 0.69294 0.05011 28 0.04102 0.03486 44 0.34071 -0.01586 60 0.99671 0.00021 13 0.64539 0.05572 29 0.02462 0.02632 45 0.39288 -0.01396 61 1.00001 0.00000 14 0.59655 0.06085 ЗО 0.01232 0.0177 46 0.44643 -0.0119 15 0.54693 0.06538 31 0.00418 0.00936 47 0.50074 -0.00976 16 0.49706 0.06917 32 0.00021 0.00185 48 0.55519 -0.0076

SD7090

 1 1 0 17 0.43649 0.06457 33 0.00345 -.00734 49 0.61442 -.01948 2 0.99655 0.0005 18 0.38699 0.06674 34 0.01238 -.01318 50 0.66605 -.01658 3 0.98664 0.00219 19 0.3389 0.06795 35 0.02624 -.01834 51 0.71605 -.01363 4 0.97113 0.00512 20 0.29269 0.06814 36 0.04514 -.02262 52 0.76381 -.01083 5 0.95062 0.00882 21 0.24878 0.06724 37 0.06903 -.02605 53 0.80869 -.00829 6 0.92522 0.01284 22 0.20759 0.06522 38 0.09771 -.02873 54 0.85007 -.00609 7 0.895 0.01718 23 0.16945 0.06206 39 0.13087 -.03067 55 0.88735 -.00426 8 0.86036 0.02188 24 0.13467 0.05780 40 0.16817 -.03188 56 0.92001 -.00279 9 0.82176 0.02691 25 0.10352 0.05249 41 0.20926 -.03240 57 0.94757 -.00160 10 0.77972 0.03218 26 0.07624 0.04621 42 0.25371 -.03229 58 0.96974 -.00066 11 0.73479 0.0376 27 0.05297 0.03907 43 0.30106 -.03161 59 0.98622 -.00009 12 0.68754 0.04304 28 0.03384 0.0312S 44 0.35077 -.03046 60 0.99650 0.00004 13 0.6386 0.04834 29 0.01891 0.02298 45 0.40227 -.02889 61 1.00001 0.00000 14 0.5885 0.05329 ЗО 0.00827 0.01458 46 0.45499 -.02696 15 0.53777 0.05773 31 0.00196 0.00637 47 0.50832 -.02472 16 0.48692 0.06153 32 5e-05 -.00097 48 0.56166 -.02221

SD8000

[1] N. A.C. A., National Advisory Committee for Aeronautics, U. S.A., now replaced by N. A.S. A.

[2] For explanation of the first, second and third digits of these aerofoils, see Chapter 9.

[3] The author is grateful to Andy Lennon for drawing his attention to this work and for subsequent discussions of it.

## Appendix З

Ordinates for nearly 200 different aerofoils are given in this appendix, together with four low drag bodies (Young bodies) for fuselages, fairings, wheel spats etc. Not all profiles will be satisfactory for models, some have been included only to amplify comments in the text The modeller should choose his aerofoils with discretion, bearing in mind the general principles discussed in the relevant chapters.

The profile drawings given here have been plotted by a computer. In many cases, the results are accurate enough for the drawing to be enlarged or reduced photographically to produce a perfect template outline for modelling. In other cases, where the ordinates give a coarser outline, the mechanical plotter produces an angular drawing with segments of straight lines and other small irregularities. In these cases the modeller should smooth the outline with a ‘zip’ or ‘French’ curve before cutting the template. The ordinates for the Wortmann M 2 aerofoil in particular produce an irregular, corrugated leading edge. This should be smoothed in practice. The corrugations are a result of the approximate methods of calculations used by Wortmann for this very early, low speed aerofoil.

Hand plotting is laborious but can produce accurate results if carefully done. The method is described in most elementary books on aeromodelling. The more advanced aerofoils given in this appendix have been produced by computer and the old, standard plotting points are not used. Instead there may be different chord stations for upper and lower surfaces.

## FINDING THE AERODYNAMIC CENTRE OF A WING

For trimming a model it is often necessary to know the position of the wing aerodynamic centre. The model’s centre of gravity should normally be at this point or very slightly behind it, as discussed in Chapter 12. If the c. g. is too far aft, parasite drag will increase since a larger tail will be required for stability and induced drag also will rise, due to load being transferred from wing to tail. If too far forward, a down load on the tailplane will be required for balance, which also leads to increased tail drag although the model’s stability will be high.

If die wing is not swept back or forward, with respect to its quarter-chord line, the aerodynamic centre for all practical purposes may be taken as one quarter of the chord aft of the root leading edge, and for wings of normal plan, with only a very slight sweep, this point will as a rule be close enough, for trimming, to the true a. c.

With wings of complex form, or swept, locating the a. c. is both more important and more difficult, important because for preliminary trial flights the centre of gravity must be as close as possible to the right place before launching. For a straight-tape red wing, the graphical construction shown in the upper part of Figure A7 may be used. Where t is the tip chord and r the root chord, by drawing on an accurate plan of the wing half panel, extend the root chord by t, and the tip chord by r as shown, and join the extensions with a diagonal line. Where this line cuts the line joining mid-points of root and tip chords is the geometric centre of area of the wing panel. The chord through this point should be drawn parallel to the aircraft centre line. The wing aerodynamic centre lies a quarter of the way along this chord line, measured from the leading edge. This point should be projected onto the centre line to give the required balance point

With more complex wing planforms, the following procedure may be used. Although fairly laborious, the exercise is worthwhile whenever a wing of unusual form is designed.

1. Calculate the mean chord, c = S/b, where S is the wing area and b the span.

2. Consider the wing on one side of the centre line and divide into a convenient number of panels (With a curved outline divide the wing into panels with nearly straight lines to arrive at a close approximation.) (See lower part of Fig. A7.)

3. Find the area, dS, of each panel.

4. Find the centre of area of each panel, using die construction method of Fig. A7.

5. Find the centre of area of the wing by taking moments about the centre line:

– _ (dSi x yi) + (dS2 x У2) + (dS3 x уз) etc. y S/2

<In this formula DSi 2 3 4» etc. refer to the areas of the successive panels of the wing marked out in step 2, and yi 2 3, etc. refer to the distances of each panel’s centre of area from the centre line. The whole formula gives у which is the distance from the centre line of the centre of area of the half wing.)

6. Locate the quarter-chord points for the chord through the centre of area of each panel.

7. Find the chordwise distances, xi X2 хз x4 etc. of these quarter-chord points measured from some convenient transverse axis such as the line through the leading edge at the root of the wing.

8. Find the fore and aft location of the mean quarter-chord point, x by taking moments about a transverse axis (i. e. the line through the leading edge at the root, as before).

(dSi x xi) + (dS2 x X2) + (dS3 x хз) etc.
S/2

9. Locate the mean chord c (calculated in step 1) in a plane through the centre of area (calculated in step 5) with its quarter chord point marked the distance x aft of the reference line.

CALCULATION OF THE NEUTRAL POINT AND STATIC MARGIN A formula which gives satisfactory results for the position of the neutral point is

hn — position of the neutral point as a decimal fraction of the wing standard mean chord.

ho = position of the aerodynamic centre of the wing with allowance for fuselage effects, on the standard mean chord. (Fuselage may be ignored for rough estimates, in which case use ho = 0.25)

щ = stabiliser efficiency. This must be estimated: — 0.9 for a‘T’ tail, — 0.6 for a normal tail, — 0.4 or 0.3 if tail is near wing wake or on a fat fuselage in disturbed flow. A canard foreplane may be assumed.95 to 1.0 efficient

Vs = stabiliser volume coefficient calculated from the formula:

у _ U x S(stabiliser) с x S(wing)

See Chapter 12, 12.16.

ai = slope of the lift curve of the stabiliser. [From wind tunnel charts with aspect ratio correction.]

a = slope of the lift curve of the wing [Wind tunnel, corrected for A.]

de _ change of downwash angle at the stabiliser with change of wing angle of attack. The

da average is Vt to W, i. e. downwash at tail changes about half to one third as much as the wing angle of attack, in disturbance.

Canard foreplanes are in the upwash ahead of the main wing, which also must be allowed for.

A worked example:

‘BANTAM’ sport power model.

Dimensions:

Span = b = 1.25m Wing area = Sw = 0.29m2 Aspect ratio = A = 5.39 Mean chord = c = 0.232m

Stabiliser span = bs = 0.5m Stab, area = Ss = 0.07m2 Stab. Asp. ratio = As = 3.57 Stab mean ch. = cs = 0.14m Length of tail arm = ls = 0.557m

ho = 0.25 [Fuselage ignored]

tjs = 0.65 [‘Normal’ tail]

„ ls x Ss.557 x.07 0.039

Vs =J——— 1=—————- =———- = 0.58

c x Sw 232 x.29 0.067

Slope of wing lift curve: Wing is a 13.7% thick profile similar to the thickened Clark Y or Gottingen 796. Assume a lift curve slope of a~ = 0.11 (i. e., at ‘infinite’ aspect ratio, about 2Tr/Radian which is — 0.11 Cl per degree e°)

Slope of tail lift curve: Tail is a thick flate plate section with rounded leading edge and knife trailing edge. (9.5 mm thick balsa) Assume lift curve slope similar to flat plate, a~ = .095, which is a conservative (pessimistic) figure.

These must be corrected for wing and tail aspect ratios, using the formula below:

^(corrected) —

[This means that if the wing Cl changes by 1.0, the stabiliser Cl would change by 1.0 x 0.8 for the same angle of attack change. But, because of downwash, the change of angle at the tail will be less than the wing which is allowed for in estimating de/da below]

For estimation of de/da, various elaborate methods are available (see D. Stinton, book listed below). For a rough calculation, use the formula:

de

— = 35a/A for monoplane (55a/A for biplane)

In this case:

Then the neutral point position is

h„ = 0.25 + (0.65 ж 0.58 x 0.8 ж [1 – 0.519]) = 0.25 + 0.145 = 0.395

That is, the neutral point lies at about 0.4 or 40% of the wing mean chord aft of the wing’s aerodynamic centre

The recommended position of the balance point on the plan is 33% of s. m.c., i. e. 0.33 x mean chord. The static margin is found by subtraction-

sm = hn – 0.33 = 0.07

This is a stable position but perhaps would prove ‘hot’ especially since propeller and fuselage destabilising influences have been ignored. By moving the c. g. forward 0.5 cm the s. m. would be increased to about 0.1, and a full 1.0 cm movement would give s. m. = 0.12.

Note that for a canard layout, the foreplane is destabilising, i. e. it brings the neutral point

 н

 N 60 R

 L

 (kxtingan 795

 5 0 <х* 5 10 15 -0-2 cm

 т

 о

 О cd

 *5

 І

 273

-0,2

 276

 а,.,15 20 0 0.02 0.04 0.06 Q08 0.10 0.12 ПЛІ

 -5

 0

 5

 10

 280

 283

## THE ANGLE OF INCIDENCE

The problem is to set the fuselage at such an angle to the flight path of the model that it creates the least possible drag. For a racer this will depend on die angle of attack of the wing when it is flying at maximum speed. For a soaring sailplane the angle of attack when flying at maximum Cl1 VCd is what counts, though the performance gain caused by

 1 2 3 4 5 6 7 8 Cl V* Vm/sec Assumed Induced Profile Total (4) X V2 Parasite Cd Cdi Cd cL 0.4 120.12 10.96 0.010 .00679 .0120 .02879 1.2 0.6 80.08 8.95 0.010 .01528 .0098 .03508 .8 0.8 60.06 7.75 0.010 .02716 .0101 .04730 .6 1.0 48.05 6.93 0.010 .04244 .0107 .06314 .48 1.2 40.04 6.33 0.010 .06115 .0113 .08245 .40 1.4 34.32 5.86 0.010 .08318 .0125 .10568 .34 1.5 32.03 5.66 0.010 .09549 .0137 .11919 .32 1.6 30.03 5.48 0.010 .10864 .0149 .13354 .30 1.675 28.69 5.36 0.010 .11925 .0162 .14545 .29 FINAL DRAG BUDGET, Kg. FORCE PARASITE INDUCED PROFILE TOTAL 9 10 11 12 13 14 15 (5) X V2 (6) X V* (7) X V* (8) X fcpS (9) X WpS (10) X HpS (11) X ttpS 0.82 1.44 3.46 0.735 0.502 0.882 2.119 1.22 0.79 2.83 0.490 0.747 0.484 1.721 1.63 0.61 2.84 0.368 0.998 0.374 1.740 2.04 0.51 3.03 0.294 1.250 0.314 1.858 2.45 0.45 3.30 0.245 1.501 0.276 2.022 2.86 0.43 3.63 0.208 1.752 0.263 2.223 3.06 0.44 3.82 0.196 1.874 0.270 2.340 3.26 0.45 4.01 0.184 1.997 0.276 2.457 3.42 0.47 4.17 0.178 2.095 0.288 2.561

saving parasite drag at this low speed will be very small. For a ‘penetration’ sailplane, correct fuselage alignment at high speed is important, less so at low speed.

For a racer, ensure that the wing camber is such that the wing profile minimum drag is at the average operational Cl for speeds at which the model will fly (see Chapter 6). From wind tunnel test results if available, or if not, by assuming a lift curve slope of 0.11 ci per degree (from zero lift angle of attack) find the angle of attack of the wing profile at the operating c[. This angle is for a wing of‘infinite’ aspect ratio. It must be corrected for downwash effects as shown below.

For a penetrating sailplane the section angle of attack chosen will depend on the extent of the aerofoil’s low drag range or*bucket’. Flight at a lower angle of attack than this will bring a marked deterioration (steepening) of the glide due to increased profile drag. Wind tunnel results at the Re appropriate to flight at this Cl and airspeed allow this to be estimated, or, if NACA 6 series aerofoils are used, the extent of the low drag range can be judged roughly from the third digit – e. g. 643618 gives a low drag range of 0.3 c| above and below the ideal cl of 0.6, hence the low drag bucket ends at cl 0.3. From this it is possible to estimate the angle of attack (infinite a. r.).

For a soarer, the operating Cl must be found by the methods given in this appendix and the angle of attack found from the wind tunnel results.

Knowing the angle of attack of the wing at infinite aspect ratio, the correction to the angle for the real model wing, affected bv downwash. is found bv the formula:

Angle of attack increment: (18.25 x Cl) (Assuming a nearly elliptical lift distribution)

A

Thus, for the model considered earlier the Cl for minimum sink with a. r. 7.5 was found to be 1.55. The induced angle of attack for this a. r. is:

18.25 x 1.55/7.5 = 3.77 degrees

From the tunnel tests (unfortunately not at the correct Re, so this is useful only as an example of method) the aerofoil yields C) 1.55 at 8.0 degrees. The rigging angle of wing to fuselage should be 8.0 + 3.77 = 11.77 degrees.

For penetration the low drag range of the aerofoil ends at approx, ci = 0.5, which develops at -2.3 degrees.

The induced angle of attack will be 18.25 X 0.5/7.5 = 1.22.

The rigging angle should thus be – 2.3 + = -1.08.

(The aerofoil is highly cambered and not very suitable for a fast flying model sailplane. Its performance is very good at high ci, for which it was designed. The figures above illustrate the method only.)

A pylon racer with a symmetrical aerofoil, flying at a Cl of 0.05 with the same aspect ratio would require an angel of incidence as worked out below:

18.25 x 0.05 : 7.5 = 0.122.

The symmetrical profile would reach cj 0.05 at 0.11/0.05 = 0.45 degrees. The rigging angle should thus be 0.122 + 0.45 = 0.57 degrees.

## ALLOWANCE FOR PARASITE DRAG

After correcting wind tunnel results for aspect ratio effects, to arrive at an estimate of drag for the whole model, parasite drag must be taken into account This may be estimated from tunnel tests on fuselages, undercarriages, etc. with an additional quantity for interference drag. As a rule such detailed estimates are not necessary for modelling. To illustrate the effect of parasite drag on performance, however, the above example is taken further. It is assumed (arbitrarily but not unreasonably) that the model with a. r. 7.5 of the previous example has a parasite drag coefficient of 0.01, this remaining constant throughout the flight attitudes considered. This assumption breaks down if the fuselage is not aligned with the average flow direction, but is sufficiently accurate for purposes of illustration.

Fig. A4 Aspect ratio and parasite drag effects

Note: parasite drag has a considerable effect on the trim for best performance, shifting the peaks of the curves to the higher Cl (higher angle of attack) side.

The calculation proceeds as before: the parasitic increment of drag is added to the total of profile and induced drag, to give the total drag coefficient of the whole model. This new total is then used to work out the model power factor and L/D.

 1 2 3 4 5 6 Cl Cdi x Cap Add parasite V’ci3 у/ ci3/Cd Ci/Cl a. r. 7.5 Cd = .01 Total .4 .01879 .02879 0.253 8.788 13.89 .6 .02508 .03508 0.465 13.255 ІГШ Max. L/D .8 .03726 .04726 0.716 15.150 16.93 1.0 .05314 .06314 1.000 15.837 15.84 1.2 .07245 .08245 1.315 115.9491 14.55 Max. Power Factor 1.4 .09568 .10568 1.657 15.679 13.25 1.5 .10919 .11919 1.837 15.412 12.58 1.6 .12354 13354 2.024 15.156 11.98 1.675 .13545 .14545 2.168 14.905 11.52

The power factor and L/D worked out in columns 5 and 6 are graphed and from this graph the desired Cl for trimming is found. The values for a. r. 15 are also plotted for comparison (Fig. A4).

Assuming the model weight and wing area are known, the sinking speed can be computed and plotted as shown to give the ‘polar1 curve of the model. This gives the minimum sinking speed by inspection. The sinking speed of a model glider (from page

232) is given by j-^—————- £-

Sinking speed =y—

Assuming a model wing loading of W/S = 3 kg/sq. m, the first term becomes 6.932. Thus sinking speed at each Cl and V value is as shown for the a. r. 7.5 model:

 1 2 3 4 Cl Vm/sec 1/CL15/Cd Sinking Speed, M/Sec .4 10.96 0.11379 .7895 .6 8.9 0.07544 .5229 .8 7.75 0.06601 .4576 1.0 6.93 0.06314 .4377 1.2 6.33 0.06269 .4346* ‘MINIMUM SINK 1.4 5.86 0.06378 .4421 1.5 5.66 0.06488 .4498 1.6 5.48 0.06598 .4574 1.675 5.36 0.06709 .4651

A more complete performance estimate may be attempted if full wind tunnel test results are available for the aerofoil to be used. Interesting studies are possible to illustrate the effect of increased wing loading and aspect ratio. If the wing loading is increased, the glider flies faster, which raises the Re and may improve the drag characteristics of the aerofoil. Given complete tunnel results this improvement may be estimated, and the profile drag figures in the calculation table will show the difference. Whether the improvement in profile drag is enough to offset the increased sinking speed due to the higher wing loading will depend entirely on the aerofoil and how much it is affected by the ‘ increased Re. Similarly, with a model of given wing area and wing loading, increasing the aspect ratio decreases induced drag but reduces Re, and so increases profile drag. Given adequate wind tunnel tests results, it is possible to compute the effects on model performance of such changes, and so determine the best aspect ratio.

Some examples have been published by the author and are listed among the references at the end of Chapter 10.

As an illustration of the results possible, the following tables and polar curve are included, but a full explanation of die method would occupy too much space.

Velocity, M/sec: 8.30 Mean Reynolds number 113043 Root angle of attack 15.721

 Cl Chord Re number Profile Cd 1.09 0.210 119345 0.02062 1.09 0.210 119345 0.02062 1.08 0.210 119345 0.02055 1.05 0.210 119345 0.01950 1.02 0.203 115634 0.03117 1.00 0.192 109108 0.03355 0.94 0.182 103534 0.03430 0.84 0.174 99050 0.03280 0.65 0.169 95766 0.03212 0.37 0.165 93763 0.02542

THE DRAG BUDGET

Figure 4.9 was produced by applying the methods outlined above. The contribution of each type of drag to the model Cd at each Cl may easily be found in the foregoing tables;

245

 □ WING A = 20 ★ WING3A=8

 POLARS

 ■ WING 2 A* 14

 M/S “ 4.3kQ/m*

Fig. A6 Polar curves of three sailplane wings of different aspect ratios but all of the same aerofoil section.

[The low A models are ballasted to bring them to the same M/S as the A = 20 model.] Note the marked superiority of the [ballasted] A = 8 model at high speed. At low speed there is little to choose between A = 14 [ballasted] and A = 20. The low Re of the high A wing is responsible.

these are entered in the table below.

To find the dragforce contributed at each flying speed, first the velocity of flight at each Cl is found by applying the standard formula:

= / W x 9.81 / 3 x 9.81 = /48.048

л/liSx 1.225 Cl w й x 1.225 x 1 x Cl * Cl

For the purpose of the example calculation, W/S (wing loading) was assumed 3 kg./sq. metre (approx. 9.8 ozs./sq. ft), and a model weight of 3kg. assumed (6.6151bs.).

Next, each Cd is multiplied by VipSV2 to produce drag force in kg. The results are of course only approximate since no proper allowance has been made for varying Re. The assumed model would achieve Re approx. 280,000 to match the wind tunnel results if its VL (velocity multiplied by chord) was about 4. This corresponds to a model with chord 0.3 metres flying at 13.3 metres per second (11.8 ins. at 29.8 m. p.h.). As the figures below show, the model would reach this speed at Cl between 0.2 and 0.4. The aspect ratio of 7.5 gives a span of 2.74 metres, wing area 1 sq. metre.

The drag budget is worked out in the table overleaf, and plotted as in Figure 4.9.

## ASPECT RATIO CORRECTIONS

The section power factor, and 1/d ratio, as calculated above is directly taken from wind tunnel results at infinite aspect ratio. To discover the power factor for the wing on the model, the wind tunnel figures must be corrected. In the example worked below, based on

241

the Stuttgart figures for the FX63-137 aerofoil at Re 280,000, correction for two aspect ratios has been applied to show the great effect of a. r. on soaring ability. This Re is of course high for a model, but the method is the same at any Re. Induced drag is found from the standard formula:

Ctv = Cl2

1 3.142 x Aspect ratio X

At the two example aspect ratios, 7.5 and 15, the Cji, the vortex-induced drag coefficient of the wing thus is found. The plan form correction, k, is assumed to be 1 for purposes of this calculation.

CL2 = CL2

3.142 x 7.5 23.562

CL2 = Cl2

3.142 x 15 47.124

In the table, this allows the drag increment for each Cl and A. R. to be worked out in the first four columns, this is added to the profile drag coefficient read from the tunnel tests,

ASPECT RATIO EFFECTS CALCULATION

 1 2 3 4 5 6 7 Cl Cl2 Cdi(7.5) C

and the calculation of the L/D ratio and power factor for the wing proceeds exactly as in the table on p.163.

N. B. For an accurate result the 5th column should be modified to allow for different Re effects on profile drag, for the two different wing chords.

## THE POWER FACTOR AND L/D RATIO

For a soaring glider or duration model when gliding the total power factor, Cl1 5/Cp should be as high as possible. The most suitable wing profile is that with a high section power factor, Cl’ VQj. This may be calculated from the wind tunnel results.

The table opposite indicates the method. A pocket calculator should be used to speed the work. The section 1/d ratio is also worked out in the tables. This gives a general idea of the profile’s efficiency, while the minimum drag coefficient indicates the potential of the aerofoil for high speed flight A low «у at low q is essential for a speed model wing.

THE BEST ANGLE OF CLIMB

It is assumed here that a duration power model has enough power available to achieve any desired angle of climb. The problem is to know which angle of climb, at maximum power, will give the best rate of ascent

A COMPARISON OF TWO AEROFOILS AT Re 100.000

 1 2 3 4 5 6 GOTTINGEN 801 Re 100000 (KRAEMER C1 cd ‘Vcj q3 AT V7/cd TEST) l FROM FROM Column (1) (Cold))3 JCo (4) Col (5) TEST TEST Column (2) Col (2) 0.4 0.0289 13.84 0.064 0.253 8.754 0.5 0.0241 20.75 0.125 0.3535 14.668 0.6 10.02181 27.75 0.216 0.4648 21.32 Min Cd at Cj0.6 0.7 0.0220 31.82 0.343 0.5857 26.53 0.8 0.0240 33.33 0.512 0.7156 29.82 0.9 0.0260 34.62 0.729 0.854 32.85 1.0 0.0300 33.33 1.000 1.000 33.33 1.1 0.0317 34.70 1.331 1.154 36.40 1.2 0.034 1 35.291 1.728 1.315 38.68 Max 1/d at q 1.2 1.3 0.0378 34.39 2.197 1.482 ПЙШ] Max power factor, c j 1.3 1.4 0.0518 27.03 2.744 1.656 31.20 0.4 0.0222 18.02 0.064 0.253 11.396 107,000 G. Muessman Test 0.5 ІЙ.0221І 22.62 0.125 0.3535 15.995 Min. C^atcj 0.5 0.6 0.0222 27.03 0.216 0.4648 20.936 0.7 0.0223 31.39 0.343 0.5857 26.26 0.8 0.0224 35.71 0.512 0.7156 31.95 0.9 0.0235 138.301 0.129 0.854 36.34 Max l/d at cj 0.9 1.0 0.0265 37.74 1.000 1.000 Г37Л7І Max 1.135 0.0400 28.37 1.462 1.209 30.23

Starting from level flight trim, the power is increased step by step. In level flight, as already seen:

Lift (Level flight) = Lo = W = *pV*SCL This may be re-arranged to give an equation for speed:

V2 (level flight) = V02 = W/V4pSCL

In the climb Lift (Climb) = Lc = W Cos в Also, if Vc = speed along the inclined flight path then

Lc = 14pVc2SCl =W Cos в

Re-arranging this in turn to obtain equation for Vc2, Vc2 = W Cos 0/WpSCL – From the foregoing:

Vc2 = (WCos flj ^ / W = WCos в ISpSCL

V02 WpSCL/ : [^pSCl/ WpSCL W

which cancels down to:

-rr-r = Cos в and so-гг— = y/CosB

*0* ’’O

(This is on the assumption that Cl remains unchanged, i. e. the model is not retrimmed.) In the small diagram Figure A3, Vc, the flight speed along the inclined path, is

 ч.

Fig. АЗ The best angle of climb for a high-powered model

represented by a line at angle 9 to the horizontal. The length of this line is proportional to Vc = V0 x VCos 9

The rate of climb on this diagram is proportional to the length of the line marked C. From basic trigonometry,

-^-= Sin 9 or C = Vc Sin 9 *c

And therefore:

C = V0 x v/Cos 9 x Sin 9

For a particular model and trim condition, V0 is constant The factor /Cos 9 x Sin 9 may easily be worked out with the aid of standard tables of Sine and Cosine, for any value of climb angle, 9. The result may be plotted against 9, as has been done in Figure 4.6. The maximum rate of climb is then found to occur when the graphed curved reaches its maximum close to 55 degrees. The result is approximate. Departures of four or five degrees either way make little difference. The practical trimming procedure is thus to aim at achieving the desired climb angle by adjustments of trim, wing camber, flaps etc. then to ensure that the engine propeller combination yields maximum thrust at that angle.

## WHAT SHOULD THE CAMBER BE?

A mean camber line, such as those presented in Figs. 7.2 and 7.3, is designed to operate at one ideal design value of cj. Once the camber is determined, any symmetrical thickness form or envelope may be fitted to it to give an aerofoil which will operate most efficiently at the design ci.

For a racing model, it is first necessary to decide the speed at maximum power, straight and level. This may be measured from a real model in flight, or estimated for a new design, from previous experience. Then the model Cl may be worked out as described above. Knowing the Cl, the type of mean line required should be chosen from those in the tables (or from any similar source). Most of the NAC A mean lines are worked out for a design ci of unity. This allows the designer to arrive at the camber for his aerofoil by simple multiplication of the camber line ordinates in the NACA tables.

A worked example follows: the figures used are not intended to be representative of any modern racing model.

Model weight 1 kg. wing area 0.2 sq. metres, designed speed 20 metres per second.

„ , , „ lx 9.81 _ 9.81 _ . .

Model Cl и x 1 225 x 202 x 0.2 49.00 0-2

Hence the ordinates for the NACA a = 1 mean line may be multiplied throughout by

0. 200 to give the desired camber line.

For example, at 50% chord, the maximum camber point on this mean line, the camber should be:

.200 x 5.515 = 1.103, i. e. a 1.1% camber approx, for flight at this speed with this model

If the model is in a steep turn, the required lift force, and hence the effective weight, increase perhaps to three or four times die above. The formula then must be modified:

Cl (in steep turn) = 4 x.200 = .8, requiring a camber of.8 x 5.515 = 4.120%.

A flight speed of 50 metres/sec yields: 9.81

306.25

The required camber is then.032 x 5.515 = 0.177% and in the steep turn 0.708%. Cambers of less than 1% are thus required for pylon racing models with speeds over 180 k. p.h. or 100 m. p.h. Note also the width of the low drag range or ‘bucket’ on modem laminar flow symmetrical aerofoils (see Chapter 9).

THE POWER FACTOR DERIVATION

Lift in level flight may be taken as equal to weight Then by re-arranging the lift formula:

W

V4pSCL

For a glider the rate of sink is given by V x Sin a where a is the glide angle. As the ratio of drag to lift is also (very nearly) equal to Sin a the above expressions may be combined:

Sinking speed =

 W CD fcpSCL x cL

Fig. A2 Chart showing variation of Reynolds number with air temperature and pressure [altitude].

The formulae in the right hand margin give the equations for Re extremes of winter and summer at near sea level. The shaded area indicates variations with seasons and altitudes up to 1000m (3281ft).

This is simplified as shown:

Sinking speed = / W 1 Cp _ / W Cp

V WpS X C1У1 CL V ^pS CL3/2

From tliis it is seen that two factors affect the sinking speed, one of these contains the wing loading, W/S, the other is the factor Ср/Сь3/2- To decrease the sinking speed, the wing loading W/S may be decreased, but this factor appears within a square root, so the effect of a large decrease of wing loading is relatively small. To obtain a larger improvement in sinking speed, Cp/CL15 must be reduced, or, what amounts to the same thing, Cl1 5/Cp must be increased. For steeper angles of glide, more than 10 degrees, the wing loading factor remains unchanged but the other factor is slightly modified to:

Cp (CL2 + Cp2)3/4

For a power model the lift formula is accurate for level flight, so the minimum power to sustain flight is arrived at thus: Power = force x distance in unit time

= Drag x Speed = DV

Drag = D = W-^ = (Formula for V is given above)

L CL

Power = W X/ ^ X S’R/7

‘V fcpS CL3/2

As with gliding, the wing loading, W/S, and the power factor must both be adjusted to achieve flight at minimum power. In addition, the weight alone plays a major part and the formula shows that a heavy model necessarily needs greater power for sustained flight

## WORKING OUT THE LIFT COEFFICIENT

To calculate the lift coefficient of a model in a given trim condition it is necessary to know the speed at which it is flying, its wing area, and flying weight The speed is easy to determine if the model can be flown several times over a measured distance and timed with a stopwatch. Allow for any wind. For free flight models such timed flights can be done by making a series of straight glides from a high point in calm air. Radio controlled models are, of course, easier to time accurately.

The standard lift formula may be re-arranged to give Cl in terms of model weight If it scales 1 kg. this indicates a mass of 1 kg. It then needs a lift force of 1 x 9.81 Newtons to support it The formula then may be applied as shown:

Cl (whole model) =

A numerical example: Suppose the model mass is 1 kg., area 0.2 m2, speed 12 metres per second. Assume air at standard mass density of 1.22S kg./m3.

Cl = 9.81 (Й x 1.225 x 12x 12 x 0.2)

= 9.81 – 17.64 = 0.556

The same example worked in Imperial Units:

1 Newton force equals 2.205 lbs. force, 12m/sec equals 39.37 ft/sec., 0.2 sq. metres equals 2.1492 squ. ft Assume standard density of.002378 slugs/cu. ft

CL = 2.205 – (Vi x.002378 x39.37 x39.37 X2.1492)

= 2.205 + 3.9608 = 0.556

This establishes that the coefficient of lift is the same whatever units are employed in the calculation, providing a coherent system of units is adopted.

The value of performing such a calculation in practical modelling is that it enables a modeller to improve his choice of aerofoil, particularly its camber. It may also indicate possible improvements in wing rigging angles, tailplane size, and fuselage design.

Suppose an F3B sailplane of span 3 metres and wing area 0.75 sq. m weighs, with ballast, 4 kg. It is hoped to complete the 60 metre (4x150m) speed task in 17 secs. This represents V = 600/17 = 35.3m/sec. on average, which includes the turns. (The actual speed on the straight will be greater.)

The lift coefficient, on average, is found from the formula:

Cl (mean) % x j 225 x 35 32 x 0 75

39.24 л

(More in the turns, less on the straight)

Suppose now the same model, unballasted, weighs 1.5 kg. and when trimmed for minimum sink flies at about 5.5m/sec. on a timed glide. The Cl then becomes

9.81 x 1.5

V4 x 1.225 x 5.52 x.75 -1-4,715 =

13.896 106

Fig. A1 Chart showing variation of air mass density with air temperature and pressure.

[Drawn by Lnenicka]

An aerofoil for such a model would require a low drag ‘bucket’ extending from Cl < -05 (nearly zero) to at least 1.06. This might be attained by using flaps.

Since the lift coefficient in the speed task is so low, very little camber is required here. A symmetrical profile would be satisfactory except in the turns. Much more camber is needed for soaring. Cl for the distance task can also be calculated.

Parasitic drag is very important at high speed, less so at soaring or distance task speeds. The fuselage should therefore be set, relative to the wing, at the angle for Cl.07 with corrections as explained below.

## SYSTEMS OF UNITS

In measuring mass and forces in engineering, various systems of units are used. Which system is adopted is a matter of convention and convenience, but the Systeme Internationale or S. I. system is adopted officially in many parts of the world. In this system the unit of mass is the kilogramme, the unit of acceleration is the metre-per- second-per-second, or m/s2. A force, as the second law of motion indicates, is measured in terms of the acceleration of a mass, or Force = Mass x Acceleration. In S. I. units, the unit of force becomes the Newton, one Newton being the force required to accelerate one kilogramme of mass at one m/s2. The mass of a model, on or near the planet Earth, is constantly acted on by the acceleration due to gravity, which has for practical purposes the value of 9.81 m/s2. Hence a model of 1 kg. mass exerts a downward force or weight of 1 x 9.81 Newtons. Metric kitchen scales in common use do not usually read in Newtons, but so long as they are used on Earth, they may be taken as reading kilogrammes directly as units of mass. In aerodynamic figuring, however, the forces must be expressed as Newtons to maintain consistency. Many modellers are accustomed to other systems, such as the British Imperial system, or some variety of it In this, the unit of mass is the slug, of acceleration the foot-per-second-per-second, of force, the pound-force. Scales reading in pounds measure the force exerted by one slug of mass under the influence of Earth’s gravity. The acceleration due to gravity is 32.2 ft/s2.

There are other systems of units. Which is used is a matter of individual preference, but whichever is employed it must be consistent, so that one unit of force always equals one unit of mass multiplied by one unit of acceleration. If this rule is not observed confusion results. A fuller explanation of the rival systems of units with conversion scales may be found in Metrication for the Modeller (M. A.P. Technical Publication, 1972).