Finite Wing Theory Questions and Answers

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.

Answer: A

A winglet moves the tip vortex outboard and upward and spreads its vorticity, so the wing behaves as though it had a larger span without the bending moment a true span extension would impose. Induced drag falls accordingly. The added wetted area does raise friction drag slightly, so a winglet only pays at high lift coefficients.

Answer: B

The theorem states that lift per unit span equals the product of the density, the free-stream velocity and the circulation about the section. In lifting-line theory this relation converts the spanwise circulation distribution into the spanwise lift distribution, which is why the circulation distribution is the quantity actually solved for.

Answer: C

The span is mapped onto an angular coordinate and the circulation written as a sine series, whose terms automatically vanish at both tips as they must. Substituting the series into the fundamental equation and satisfying it at a set of stations gives a linear system for the coefficients, from which lift and induced drag follow.

Answer: D

When the sine series is integrated across the span, orthogonality kills every term but the first, so the lift coefficient depends on the first coefficient alone. Induced drag is different: it involves the sum of every coefficient weighted by its index, which is why the higher harmonics add drag while contributing nothing to lift.

Answer: A

Lift picks out only the first coefficient, whereas induced drag is a weighted sum over all of them, each term entering as a square and therefore positive. Any harmonic beyond the first therefore costs drag and returns no lift. The elliptical loading is exactly the case in which all the higher coefficients vanish.

Answer: B

Reducing the tip incidence keeps the tip sections further from their stalling angle than the root, so the root stalls first. The stall then spreads outboard, the ailerons remain in attached flow, and roll control survives into the stall. It also shifts the loading inboard, which relieves the wing bending moment.

Answer: C

The rectangular planform carries a higher local lift coefficient inboard than outboard, so the root reaches its stalling value first. That is a benign characteristic, since the ailerons stay effective. A highly tapered wing has the opposite tendency and usually needs washout to correct it.