Finite Wing Theory Questions and Answers

Answer: C

The dependence on lift coefficient is quadratic, not linear, which is precisely why induced drag matters so much in slow flight and so little in cruise. The other three statements are correct: the mechanism is the tilted lift vector, the elliptical case with e equal to one is the minimum, and no viscosity is needed for any of it.

Answer: D

Raising the aspect ratio at fixed area lengthens the span, steepens the lift curve because the induced angle shrinks, and moves the lift outboard so the root bending moment grows. The induced drag coefficient is the one quantity that falls, since it varies inversely with aspect ratio.

Answer: A

An elliptical planform produces the distribution directly, but it is not the only way to get it: taper combined with washout can approach it closely, and that is how production wings are actually built. The remaining three statements are all correct descriptions of the elliptical case and of why it is used as the reference.

Answer: B

This is the case that catches people out. With no lift anywhere on an untwisted wing there is no circulation, so nothing is shed, there is no downwash and the lift vector has nothing to tilt. The induced drag is exactly zero. Profile drag, of course, remains, but that is a different mechanism altogether.

Answer: C

The factor is defined against the elliptical loading, which is the minimum-induced-drag case for a given lift and span, so a planar wing cannot better it and e cannot exceed one. Winglets appear to break the rule only because they are non-planar and effectively raise the span; referred to the geometric span, the apparent efficiency can then be reported above one.

Answer: D

The lift coefficient enters as a square and the aspect ratio as a simple inverse, so the two changes give a factor of four divided by a factor of two. The net result is a doubling. Answering unchanged is the trap, and it comes from treating both dependences as linear.

Answer: A

The counter-rotating tip vortices drive air downward in the region between them and upward outside them. The downwash is what causes induced drag on the wing itself; the upwash outboard is what a following aircraft in echelon, or a bird in a V formation, can use to reduce its own induced drag.

Answer: B

On an untwisted wing the zero-lift angle is unchanged, because at zero lift there is no circulation, no shed vorticity and therefore no induced angle to shift it. Finite span changes the slope of the curve and pushes the stall to a larger geometric angle, but it leaves the intercept on the angle axis exactly where the section put it.

Answer: C

The factor is defined so that the elliptical case, which is optimal, scores one, and every other planar loading scores less. It appears in the denominator of the induced drag coefficient, so a lower value means more drag for the same lift. It is a property of the spanwise loading and planform, not of the section.

Answer: D

A higher wing loading means more lift must be carried on the same span, so the circulation and with it the tip vortex both strengthen. The other three all act to weaken it, either by obstructing the flow round the tip or by reducing the circulation that has to be shed in the first place.