A Wing of Small Aspect Ratio

Подпись: (10.20)

The technique of quadruplication demonstrated above can also be applied to a wing of finite aspect ratio. For example, for a flat wing of small aspect ratio, the integral formulation leads to the equation

where hx = h/X, X is the aspect ratio (/i«A« 1), and r(z) is the circulation of the velocity. The kernel of equation (10.20) has the same structure as that of (10.2). Therefore, the approach considered earlier is applicable here, too. Replacing for hx ->• 0 the integral operator by a corresponding differential one

Подпись: 27ГПодпись: 2 - c (z - 02 + ШІ (10.21)

we obtain the equation

d[60]r _ в dz2 2 h

Подпись: (10.22)Integrating (10.22) and imposing the condition of zero loading at the tips of the wing, finally, we obtain the following expression for the lift coefficient of a small-aspect-ratio wing:

Подпись:_ ex _ ex2

y 6h 6 h ’

which is identical to formula (3.69), obtained from the boundary problem formulation.