Finite Wing Theory Questions and Answers

Answer: C

Lifting-line theory concentrates all the bound vorticity onto a single line, which is only reasonable for a slender, unswept wing. A vortex lattice covers the planform with a grid of horseshoe vortices, so chordwise loading and sweep are represented directly. That makes it usable where lifting-line theory fails.

Answer: D

Induced drag varies with the square of the lift coefficient, and the lift coefficient is largest when the aircraft is heavy and slow. During the take-off climb it can exceed all other drag sources combined. In high-speed cruise the lift coefficient is small and profile and wave drag dominate instead.

Answer: A

Zero-lift drag rises with the square of speed while induced drag falls with it, so the total is minimised where the two curves cross and the two contributions are equal. That condition also identifies the speed for best lift-to-drag ratio, and for a jet it is the speed for maximum range in still air.

Answer: B

Holding area fixed and stretching the span raises the aspect ratio, so induced drag falls. The lift is now carried further outboard, however, so its moment about the root grows and the structure must be heavier. Wing design is largely a negotiation between these two effects, and it is why airliners fold their wingtips rather than simply making them longer.

Answer: C

Elliptical loading produces uniform downwash, and the induced angle is the downwash divided by the free-stream speed. It is therefore constant across the span, so every section works at the same effective angle of attack. This is the property that makes the elliptical case both the simplest to analyse and the most efficient.

Answer: D

Induced drag originates in the flow that escapes round the tip from the lower to the upper surface. A plate standing in the way obstructs that path, weakening the tip vortex and raising the effective span. A winglet is a refined end plate that generates a useful forward force of its own instead of merely blocking the flow.

Answer: A

The bound vortex is the vortex line that travels with the wing and models the circulation responsible for lift. It is distinguished from the trailing vortices, which are left in the fluid and remain roughly fixed in space. Its strength varies across the span, and it is that variation which forces vorticity to be shed.

Answer: B

By Helmholtz's theorems the strength of a filament is constant along it, so any change in bound strength between adjacent stations must be balanced by vorticity leaving downstream. The shed strength is therefore governed by the rate of change of circulation with span, not by circulation itself. A tip, where circulation falls quickly to zero, sheds strongly.

Answer: C

Induced drag varies inversely with the span efficiency factor, so a value of 0.8 rather than 1.0 raises the induced drag by a quarter for the same lift, span and speed. The elliptical case is the best achievable, which is why e can never exceed unity for a planar wing.

Answer: D

Each spanwise element contributes a lift per unit span equal to density times velocity times the local circulation. Integrating that from tip to tip gives the total lift. Induced drag follows a similar integral but with the local induced angle included as a weighting, which is what makes it sensitive to the shape of the distribution.