Prandtl Lifting Line Theory

14.4.2.1 Vortex Sheet

Describe briefly the vortex sheet behind a finite wing with sharp trailing edge and explain whether the velocity components (u, v, w) have jumps and why.

14.4.2.2 Designing for Tip Vortices

In general, the wing loading is such that Г’ ^ as y ^ ±b/2, an indication of strong tip vortices.

Combine modes 1 and 3 to satisfy Г'(±b/2) = 0, given that the total lift is (CL)t-o at take-off.

Find A1 and A3 in terms of (CL)t-o and wing aspect ratio AR.

Sketch the corresponding distributions of circulation and downwash (Use sin 3t = sin t (4 cos21 – 1)).

Show that there is upwash near the wing tips.

14.4.2.3 Induced Drag

Calculate the induced drag and the gain/loss compared to the elliptic loading.

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