Finite Wing Theory Questions and Answers

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.

Answer: D

The sharp, highly swept leading edge forces separation into a pair of strong, stable vortices lying over the upper surface. The intense low pressure under those vortex cores gives extra lift that grows nonlinearly with incidence. The mechanism lets slender delta wings reach very high angles of attack without a conventional stall.

Answer: A

Vortex strength scales with the circulation the wing must generate, which is large when the weight is high and the speed is low, and the vortices stay compact and concentrated when the wing is clean. Air traffic separation rules are built around exactly this combination, and the phrase heavy, slow and clean is the standard summary.

Answer: B

The theory assumes the flow at each station is locally two-dimensional and that the shed vorticity leaves along the free stream. Both assumptions weaken when the chord is comparable with the span or when sweep introduces strong spanwise flow. Low-aspect-ratio and swept wings therefore need lifting-surface or panel methods instead.