A Wing of Small Aspect Ratio
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
(10.21)
we obtain the equation
d[60]r _ в dz2 2 h
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:
_ ex _ ex2
y 6h 6 h ’
which is identical to formula (3.69), obtained from the boundary problem formulation.