Finite Wing Theory Questions and Answers

Answer: C

An untwisted wing of elliptical planform made from one section gives an elliptical circulation distribution directly, which is why the Spitfire wing is the standard example. The same loading can be approached by combining taper with washout, and modern wings do exactly that, because an elliptical planform is expensive to build.

Answer: D

The span efficiency factor is defined so that the elliptical case gives e equal to one, the minimum-drag reference. Any other loading produces more induced drag for the same lift, and since e appears in the denominator of the induced drag coefficient, that extra drag corresponds to a value of e below one. Typical wings fall around 0.85 to 0.95.

Answer: A

Aspect ratio is the span squared divided by the planform area. For a rectangular wing this reduces to span divided by chord, but the general definition covers tapered and swept planforms as well. The ratio of root chord to tip chord is the taper ratio, a different quantity altogether.

Answer: B

The induced drag coefficient varies inversely with aspect ratio, so a longer, narrower wing of the same area carries the same lift for less induced drag. The tip vortices are further apart and their influence over most of the span is weaker. This is why sailplanes and long-range airliners use slender wings.

Answer: C

Downwash robs each section of part of its geometric angle, so more geometric angle is needed for a given lift coefficient and the curve is flattened. The effect grows as the aspect ratio falls, because the induced angle is inversely proportional to it. A very low aspect ratio wing therefore has a markedly shallow lift curve.

Answer: D

At zero lift the circulation vanishes everywhere on an untwisted wing, so no vorticity is trailed and there is no downwash to change the effective angle. The finite wing therefore reaches zero lift at the same geometric angle as its section. Only the slope of the lift curve is altered, not its intercept.

Answer: A

Flow spills from the high-pressure lower surface round each tip to the low-pressure upper surface. Seen from behind, that gives a pair of counter-rotating vortices whose upper portions move inboard towards the centreline. The consequence is downwash between the vortices and upwash outboard of them.

Answer: B

The vortex pair induces downward flow between the tips and upward flow outside them. This upwash is what a trailing aircraft in echelon formation can exploit, and it is the reason migrating birds fly in a V: each bird sits in the upwash field of the one ahead and reduces its own induced drag.

Answer: C

Kelvin's circulation theorem requires the total circulation round a large circuit enclosing the wing and its wake to stay zero. As bound circulation builds up, an equal and opposite starting vortex is shed and left behind. Together with the bound vortex and the two trailing vortices it completes the closed vortex loop.

Answer: D

Close to the ground the trailing vortices cannot develop normally, an effect modelled by an image vortex system below the surface. The downwash at the wing is reduced, the lift vector is tilted less, and the induced drag falls. Pilots notice the aircraft floating during the landing flare for exactly this reason.