Condition for Vortex Drag Minimum

For the vortex drag Dv to be minimum, the S in Equation (8.13) must be zero. That is, X (or a) must be zero so that the distribution for Dv minimum becomes:

к = k)

=^.

This is an ellipse, thus the vortex distribution for drag minimum is semi-ellipse. The minimum drag distribution produces a constant downwash along the span while all other distributions produce a spanwise variation in induced velocity, as illustrated in Figure 8.9.

It is seen that the elliptic distribution gives constant downwash and minimum drag, non-elliptic distri­bution gives varying downwash.

If the lift for the aerofoils with elliptical and non-elliptical distribution is the same under given con­ditions, the r

(c) equivalent variation of downwash.