Finite Wing Theory Questions and Answers

Answer: A

The first two are the theory's central assumptions and are correctly stated. The third is false: sweep introduces strong spanwise flow and moves the loading chordwise, neither of which a single lifting line can represent, so swept wings require lifting-surface methods such as the vortex lattice.

Answer: B

The first two are correct: by displacing and diffusing the tip vortex a winglet makes the wing behave as a longer one, and the saving is largest where induced drag is largest. The third is false, since the added surface increases wetted area and therefore raises skin-friction drag slightly.

Answer: C

The first and third are correct. Circulation must rise with weight, and the vortices ultimately break down, the sinusoidal Crow instability being the classic mechanism. The second is the wrong way round: at a given weight a faster aircraft needs less circulation, which is why the hazard is worst behind a heavy aircraft flying slowly.

Answer: D

Induced drag is produced entirely by the trailing vortex system, which is why it is also called vortex drag. Skin friction comes from viscous shear in the boundary layer, wave drag from entropy rise across shocks in compressible flow, and form drag from the pressure deficit left behind by a separated boundary layer.

Answer: A

The bound vortex moves with the wing and carries its circulation; the trailing vortices are left in the fluid behind the tips; the starting vortex is shed at the beginning of the motion with the opposite sense, as Kelvin's theorem requires; and the horseshoe vortex is the bound filament together with its two trailing legs.

Answer: B

These four results are the whole toolkit of lifting-line theory. Kutta-Joukowski converts circulation into lift, Biot-Savart converts the trailing vorticity into downwash, Helmholtz's theorem forces vorticity to be shed where the bound strength changes, and Kelvin's theorem accounts for the starting vortex.

Answer: C

A rectangular wing loads up inboard and so stalls at the root, which is benign because the ailerons keep working. Taper does the opposite and normally needs washout to cure it. The elliptical wing works every section at the same lift coefficient, so it stalls all at once, and a slender delta sustains lift on leading-edge vortices well past the usual stall.

Answer: D

Aspect ratio and taper ratio are both pure planform geometry, the first measuring slenderness and the second the rate at which the chord reduces outboard. Wing loading is a weight per unit area and fixes the lift coefficient needed at a given speed, while the induced drag coefficient ties all of this back to the trailing vortex system.

Answer: A

Every option but the first raises the effective span or improves the loading, and each therefore cuts induced drag. Reducing the aspect ratio does the opposite: the induced drag coefficient varies inversely with aspect ratio, so a shorter, broader wing of the same area carries the same lift for more induced drag.

Answer: B

Lifting-line theory is built for steady, incompressible, inviscid flow over an unswept wing of high aspect ratio; shock waves are entirely outside its scope. The other three are exactly the assumptions it makes, and each of them is what fails when the theory is applied to a swept or low-aspect-ratio wing.