Lateral Stability Questions and Answers

Answer: C

Correct answer: 0.018

The coefficient is a per-degree derivative, so it multiplies the deflection directly:

\[ C_l = 0.0009 \times 20 = 0.018 \]

No radian conversion is needed here, since the derivative is already expressed per degree - the opposite of the sideslip question, where the derivative was per radian. Checking which unit a derivative is quoted in before multiplying is the single most useful habit with these quantities, the two conventions differing by a factor of 57.3.

Answer: D

Correct answer: 60 per cent

The reduction is measured against the original rate:

\[ \frac{30-12}{30} \times 100 = 60\% \]

The distractor 40 per cent is the fraction remaining rather than the fraction lost. The trend itself is the signature of approaching aileron reversal: aerodynamic effectiveness would ordinarily rise with speed, so a roll rate that falls as speed increases means wing twist is progressively cancelling the aileron, and the rate reaches zero at the reversal speed.

Answer: A

Correct answer: 27 degrees per second

Two roll control devices acting together give roughly the sum of their individual rates, since the rolling moments add:

\[ 15 + 12 = 27\ \mathrm{deg/s} \]

The addition is approximate rather than exact, because roll damping rises with roll rate and the devices interact aerodynamically. But it is the right first estimate, and it explains why large transports use spoilers and inboard ailerons together at high speed: neither alone gives adequate roll authority once the outboard ailerons are locked out.

Answer: B

Correct answer: Three times as many cycles

The comparison is a ratio of cycles to half amplitude:

\[ \frac{3}{1} = 3 \]

Cycles to half amplitude is the standard measure of oscillatory damping, and fewer is better. A Dutch roll taking three cycles to halve is poorly damped and tiring to fly, since the oscillation persists visibly after every disturbance. The usual causes are excessive dihedral effect relative to directional stability, and the usual remedy is a yaw damper rather than a change to the airframe.

Answer: C

Correct answer: Both Statement I and Statement II are correct

Both are true, and together they explain why lateral stability works indirectly. A bank angle alone produces no restoring moment: the aeroplane is happy at any bank until something else changes.

What changes is that the tilted lift vector no longer balances weight vertically, so the aeroplane begins to slip towards the lower wing. The sideslip is what the dihedral effect acts on, producing the rolling moment that raises the wing. The chain runs bank, then slip, then roll - which is why \( C_{l\beta} \) is a derivative with respect to sideslip and not to bank.

Answer: D

Correct answer: Both Statement I and Statement II are correct

Both are true and the second is the reason for the first. Sweep contributes a dihedral effect of its own, because in a sideslip the forward wing meets the flow at a lower effective sweep and generates more lift.

On a strongly swept wing that contribution can exceed what is wanted, giving a poorly damped Dutch roll. Anhedral - drooping the wings - subtracts from the total and brings the effective dihedral back into balance. High-wing swept transports such as the C-17 and the An-124 show it plainly, the wing position adding a further contribution to be trimmed away.

Answer: A

Correct answer: Both Statement I and Statement II are correct

Both are true and the second explains the first. Sweep's dihedral effect works through the lift difference between the forward and rear wings in a sideslip, and that difference is proportional to the lift coefficient at which the wing is operating.

Low speed means high lift coefficient, so the effect is strongest there - on approach and in the climb, precisely where good handling matters most. It is why a swept wing's Dutch roll characteristics are worst at low speed and why yaw dampers are most needed in that regime.

Answer: B

Correct answer: Both Statement I and Statement II are correct

Both are true and the second explains the first. In a sideslip the fuselage deflects the flow: on a high wing it pushes flow up under the lower wing and down over the upper one, adding to the dihedral effect; on a low wing the same mechanism subtracts from it.

A low wing design must therefore supply more of the effect geometrically, which is why low wing light aircraft show a marked dihedral angle while high wing types often appear almost flat, both reaching similar effective dihedral.

Answer: C

Correct answer: Both Statement I and Statement II are correct

Both are true and the second is the mechanism of the first. The down-going aileron raises the lift on its wing, and induced drag rises with lift, so that wing carries more drag; the up-going aileron reduces both on the other side.

The resulting drag differential yaws the nose away from the direction of roll. It is largest at low speed and high lift coefficient, where induced drag dominates total drag, and it is countered either by rudder or by the aileron designs - differential and Frise - that add offsetting drag on the rising wing.

Answer: D

Correct answer: Statement I is incorrect but Statement II is correct

The second statement is right, and it refutes the first. A raised spoiler adds drag on the wing it is fitted to, and that is the wing going down - the inside of the turn.

Drag on the inside yaws the nose into the turn, which is favourable yaw, the opposite of what ailerons produce. That is one of the reasons spoilers are attractive for roll control on large aeroplanes: they need no rudder coordination, and they add roll authority without adding wing twist.