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.

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.

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