Category Model Aircraft Aerodynamics

DESIGNING NEW AEROFOILS

Posted by admin in Model Aircraft Aerodynamics on May 8, 2016

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

МАСА 0010 L. E. radius
1.10 Percent

МАСА 0009 L E. radius
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 894OSB LE. radio*
l. OParcant

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

Banadak 883088 LE. radiu* 0.7 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	1.00000	0.00000	17	0.44745	0.07211	33	0.00127	-.00393	49	0.60914	-.00549
2	0.99672	0.00042	18	0.39862	0.07410	34	0.00806	-.00839	50	0.66197	-.00349
3	0.98707	0.00180	19	0.35101	0.07504	35	0.02038	-.01227	51	0.71305	-.00168
4	0.97146	0.00436	20	0.30508	0.07488	36	0.03800	-.01541	52	0.76178	-.00014
5	0.95041	0.00811	21	0.26125	0.07358	37	0.06074	-.01777	53	0.80752	0.00104
6	0.92450	0.01295	22	0.21989	0.07113	38	0.08844	-.01934	54	0.84964	0.00182
7	0.89425	0.01865	23	0.18137	0.06754	39	0.12084	-.02017	55	0.88756	0.00220
8	0.86015	0.02490	24	0.14601	0.06286	40	0.15765	-.02032	56	0.92071	0.00218
9	0.82261	0.03141	25	0.11410	0.05715	41	0.19850	-.01987	57	0.94859	0.00185
10	0.78201	0.03788	26	0.08586	0.05049	42	0.24296	-.01891	58	0.97077	0.00132
11	0.73865	0.04413	27	0.06146	0.04300	43	0.29055	-.01754	59	0.98690	0.00071
12	0.69294	0.05011	28	0.04102	0.03486	44	0.34071	-.01586	60	0.99671	0.00021
13	0.64539	0.05572	29	0.02462	0.02632	45	0.39288	-.01396	61	1.00001	0.00000
14	0.59655	0.06085	ЗО	0.01232	0.01770	46	0.44643	-.01190
15	0.54693	0.06538	31	0.00418	0.00936	47	0.50074	-.00976
16	0.49706	0.06917	32	0.00021	0.00185	48	0.55519	-.00760

SD7090

1	1.00000	0.00000	17	0.43649	0.06457	33	0.00345 -.00734	49	0.61442	-.01948
2	0.99655	0.00050	18	0.38699	0.06674	34	0.01238 -.01318	50	0.66605	-.01658
3	0.98664	0.00219	19	0.33890	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	0.89500	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	0.03760	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	0.63860	0.04834	29	0.01891	0.02298	45	0.40227 -.02889	61	1.00001	0.00000
14	0.58850	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	0.00005	-.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

Posted by admin in Model Aircraft Aerodynamics on May 6, 2016

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

Posted by admin in Model Aircraft Aerodynamics on May 6, 2016

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:

— = 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

N 60 R

(kxtingan 795

5 0 <х* 5 10 15 -0-2 cm

О cd

273

-0,2

276

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

ПЛІ

-5

280

283

THE ANGLE OF INCIDENCE

Posted by admin in Model Aircraft Aerodynamics on May 6, 2016

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)

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

Posted by admin in Model Aircraft Aerodynamics on May 5, 2016

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

Posted by admin in Model Aircraft Aerodynamics on May 5, 2016

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.

Подпись: Coi (a.r. 7.5) = Подпись: CDi (a.r. 15) = 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<u(15)	PROFILE Cd	Cdi + Cdp	Cdi + Cdp
from tests	Cl x Cl	Ci2/23.562	Ci2/47.124	From tests	a. r. = 7.7	a. r. = 15
0.4	0.16	0.00679	0.00395	0.012	0.01879	0.01595
0.6	0.36	0.01528	0.00764	0.0098	0.02508	0.01744
0.8	0.64	0.02716	0.01358	0.0101	0.03726	0.02368
1.0	1.00	0.04244	0.02122	0.0107	0.05314	0.03192
1.2	1.44	0.06115	0.03056	0.0113	0.07245	0.04186
1.4	1.96	0.08318	0.04159	0.0125	0.09568	0.05409
1.5	2.25	0.09549	0.04775	0.0137	0.10919	0.06145
1.6	2.56	0.10864	0.05432	0.0149	0.12354	0.06922
1.675	2.81	0.11925	0.05963	0.0162	0.13545	0.0783
8	9	10	11	12
Cl/Cd	Cl/Cd	VCl3	/CL3/Cdi + Cdp JCtVCdi + Cdp
a. r. 7.5	a. r. 15		a. r. 7.5	a. r. 15
21.3	25.078	0.253	13.46	15.86
123.92	34.401	0.465	18.54	26.66	Compare Max. L/D
21.47	33.78	0.716	І19.22І	30.24
18.82	31.33	1.000	18.82	31.33	Compare Max.
16.56	28.66	1.315	18.15	[зЩ	Power factors
14.63	25.88	1.657	17.32	30.63
13.31	24.41	1.837	16.82	29.21
12.95	23.11	2.024	16.38	29.89
12.36	22.09	2.168	16.01	28.59

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

Posted by admin in Model Aircraft Aerodynamics on May 4, 2016

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?

Posted by admin in Model Aircraft Aerodynamics on May 4, 2016

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%.

Подпись: .032 = CL 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:

Подпись: V = 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:

Подпись: V Sin о 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

Posted by admin in Model Aircraft Aerodynamics on May 4, 2016

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

Подпись: CL (min sink) = 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

Posted by admin in Model Aircraft Aerodynamics on May 3, 2016

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).

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The old plane — nonsense, pilots think - there was an attack

The Israeli Apache will subject to peeling

The aviation industry began to move

Category Model Aircraft Aerodynamics

DESIGNING NEW AEROFOILS

Appendix З

FINDING THE AERODYNAMIC CENTRE OF A WING

THE ANGLE OF INCIDENCE

ALLOWANCE FOR PARASITE DRAG

ASPECT RATIO CORRECTIONS

THE POWER FACTOR AND L/D RATIO

WHAT SHOULD THE CAMBER BE?

WORKING OUT THE LIFT COEFFICIENT

SYSTEMS OF UNITS