Wings of large aspect ratio

Induced drag.

It is a result of occurrences of a vortex sheet behind a wing, which keeping demands energy equivalent to work of induced drag force. The computational formulae for definition of are described below.

The induced drag coefficient of a large aspect ratio wing is determined

, (4.9)

Where - induced drag of a flat wing; - additive to induced drag caused by geometrical twist.

We have

, (4.10)

Dependence of induced drag at small angles of attack is approximated by parabola (Fig. 4.13). The induced drag decreases at increasing of wing aspect ratio .

The coefficient is determined by the wing plan form and shows to what extent the distribution of aerodynamic loading differs from the elliptical law, for which . Generally . The expression for is represented as lately, where - Osvald number, .

Value of in contrast to can not be equal to zero in general at (because for non-flat wing various wing cross-sections may have lift coefficients not equal to zero at total ).

General expression for looks like: , where, , , - twist angle of tip cross-section; the values of coefficients and are also undertaken from the diagrams depending on wing plan geometry (, , ), and twist law.

Fig. 4.14. shows the comparison between induced drag of a flat wing and wing having twist.

Fig. 4.13. Induced drag of a flat wing

Fig. 4.14. Induced drag of a flat wing and wing with twist

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