Finite Wing Theory Questions and Answers

Answer: A

A section is a two-dimensional idealisation with no spanwise flow. On a real wing the pressure difference between the surfaces cannot survive at the tip, so flow spills round it and the wing trails a sheet of vorticity. That sheet induces a downward velocity at the wing itself, and every finite-wing correction follows from it.

Answer: B

Downwash tilts the local relative wind downward through the induced angle. The section therefore meets the flow at the effective angle, which is the geometric angle less the induced angle. Because the section responds only to what it actually sees, a finite wing produces less lift than the same section would in two-dimensional flow.

Answer: C

The local lift acts perpendicular to the local relative wind, and the downwash rotates that wind downward. The lift vector rotates with it, so it acquires a component along the free-stream direction. That streamwise component is induced drag. It is a pressure drag, not a viscous one, and it exists even in an inviscid calculation.

Answer: D

Because the drag is created entirely by the trailing vortex system, it is commonly called vortex drag, and the two names mean the same thing. Form drag comes from pressure losses due to separation, wave drag from shock losses in compressible flow, and interference drag from the meeting of two bodies, so none of those is a synonym.

Answer: A

Prandtl represented the wing by a bound vortex line whose strength varies across the span. By Helmholtz's theorem a vortex filament cannot end in the fluid, so wherever the bound strength changes, vorticity is shed downstream. The result is a superposition of many horseshoe vortices, which together form a continuous trailing sheet.

Answer: B

With constant bound strength the whole circulation is shed as two concentrated line vortices at the tips. The velocity induced by a line vortex varies inversely with distance, so the downwash grows without limit as the tip is approached. Distributing the shed vorticity along the span removes the singularity and gives a physically sensible result.

Answer: C

The Biot-Savart law relates the velocity induced at a point to the strength of a vortex filament element and its position relative to that point, in exact analogy with the magnetic field of a current element. Lifting-line theory uses it to compute the downwash produced at the lifting line by the trailing sheet.

Answer: D

Helmholtz showed that the strength of a vortex filament is constant along its length and that the filament cannot simply stop in the fluid. This is precisely why the bound vortex on a wing must continue as trailing vortices and close through the starting vortex, giving the closed vortex system that lifting-line theory assumes.

Answer: A

The elliptical distribution is the special case in which the induced velocity works out the same at every station. A uniform downwash means a uniform induced angle, so every section operates at the same effective angle of attack. This uniformity is what makes the elliptical case the minimum-induced-drag case.

Answer: B

Induced drag depends on how the lift is spread, not merely on its total. Minimising the induced drag for a fixed lift and span leads to the elliptical loading, for which the downwash is uniform. Any departure from it raises the induced drag, which is expressed through a span efficiency factor less than one.