Aerodynamic Forces and Moments Questions and Answers

Answer: D

Correct answer: Weight

Weight acts through the centre of gravity by definition - the centre of gravity is the point at which the distributed weight of the aircraft may be taken to act.

The other three act elsewhere: lift at the centre of pressure, drag along the flight path at its own line of action, and thrust along the thrust line. Because the aerodynamic forces act away from the centre of gravity, they produce moments about it, which is exactly what trim and stability are concerned with.

Answer: A

Correct answer: The centre of gravity

Moments are taken about the centre of gravity because that is the point the aircraft rotates about when free in flight. Weight then produces no moment, since it acts through that point, leaving only the aerodynamic and propulsive contributions.

Any other reference would require the weight's moment to be carried through the analysis, and would move as the loading changed. That is why the centre of gravity's position, and the envelope of permitted positions, are central to stability and control.

Answer: B

Correct answer: Approach an elliptical loading with simpler construction

An elliptical span loading gives the least induced drag for a given lift and span, but an elliptical planform is expensive to build - every rib is a different shape.

A straight taper of about 0.4 to 0.5 approximates the loading closely with ribs that vary linearly. It also reduces the bending moment at the root and saves structural weight. Taper does not eliminate tip vortices, which follow from finite span, and it certainly does not aim to increase induced drag.

Answer: C

Correct answer: Contamination of the leading edge by ice

Ice on the leading edge disturbs the flow exactly where the suction peak and the stagnation point are, thickening the boundary layer and provoking early separation. The maximum lift coefficient can fall by 30 per cent or more, and the stalling angle with it.

Roughness of a millimetre or two is enough. The other three all raise the maximum: slats and flaps by design, and vortex generators by mixing high-energy air into the boundary layer so it stays attached longer.

Answer: D

Correct answer: Mixing high-energy air into the boundary layer

A vortex generator is a small vane set at an angle to the flow, shedding a streamwise vortex that stirs faster-moving air from outside the boundary layer down towards the surface.

The re-energised layer resists the adverse pressure gradient better and stays attached further aft, so separation is delayed and the maximum lift coefficient rises. The cost is a small drag penalty in cruise, which is why they are placed only where separation is actually a problem.

Answer: A

Correct answer: Tend to return to its original attitude

Static stability is the tendency to return after a disturbance, and in pitch it means that a nose-up displacement generates a nose-down restoring moment - that is, \( dC_m/d\alpha \) is negative.

Continuing to pitch further would be instability, and remaining at the new attitude neutral stability. Note that this concerns the initial tendency only; whether the subsequent motion converges without oscillation is a question of dynamic stability, which is separate.

Answer: B

Correct answer: Longitudinal static stability becomes neutral

The neutral point is the centre of gravity position at which \( dC_m/d\alpha \) is zero: the aircraft neither returns to nor departs from a disturbed attitude.

Forward of it the aircraft is stable and aft of it unstable, so it sets the aft limit of the loading envelope, with a margin. Note that it is a property of the aerodynamic configuration - wing, tail and fuselage - and does not move with loading, whereas the centre of gravity does.

Answer: C

Correct answer: The neutral point, expressed as a fraction of the chord

The static margin is

\[ K_n = \frac{x_{np} - x_{cg}}{\bar{c}} \]

positive when the centre of gravity lies forward of the neutral point, and expressed in chords so that aircraft of different sizes can be compared.

It measures how stable the aircraft is: a large margin means strong stability and heavy control forces, a small one light controls and a risk of instability if the loading shifts. The aft loading limit is set by the minimum acceptable value.

Answer: D

Correct answer: Flying near the best lift-to-drag ratio

Range depends on how far the aircraft travels per unit of fuel, and in the simplest treatment that is greatest where the drag for the lift carried is least - the maximum lift-to-drag ratio.

Maximum speed means high parasite drag and maximum lift coefficient means high induced drag, and both waste fuel. The refinements matter in practice: a jet's best range is somewhat faster than best \( L/D \), and a propeller aircraft's is at it, but the principle is the same.

Answer: A

Correct answer: A single specific value

The lift-to-drag ratio depends on the lift coefficient, and the lift coefficient is fixed by the angle of attack, so the maximum occurs at one particular incidence for a given configuration.

What changes with weight or altitude is the speed at which that incidence gives level flight, not the incidence itself. That is why a glider's best glide is flown at an indicated airspeed adjusted for weight, and why the angle of attack indicator is the more direct instrument.