Static Directional Stability Questions and Answers

Answer: C

Correct answer: Yawing moment per degree of rudder

Rudder power is the yawing moment the rudder generates per degree of deflection, usually expressed as the derivative \( C_{n\delta r} \). It measures control authority, not stability.

The distinction matters because the two are sized by different cases. Stability is set by the fin, and asks whether the aeroplane returns to zero sideslip on its own. Rudder power is set by the largest moment that must be balanced - asymmetric thrust after an engine failure, or de-crabbing in a crosswind. Maximum travel and stick force are consequences of the design rather than definitions of the term.

Answer: D

Correct answer: The lowest speed for control after a failure

Minimum control speed in the air, \( V_{MCA} \), is the lowest airspeed at which directional control can be maintained with the critical engine inoperative and the remaining engines at take-off power.

It is fixed by the balance between the asymmetric thrust moment and the rudder's maximum yawing moment. Because rudder moment falls with dynamic pressure while thrust asymmetry does not, there is a speed below which the rudder simply runs out - and that speed is \( V_{MCA} \). It is a control limit, quite separate from the stalling speed, which is a lift limit; certification requires the take-off safety speed to clear both.

Answer: A

Correct answer: Ground minimum control speed

Minimum control speed on the ground, \( V_{MCG} \), is the lowest speed at which, following a sudden engine failure, the take-off can be continued using aerodynamic controls alone - rudder, without nosewheel steering.

Steering is excluded deliberately, because the runway may be wet or contaminated and the nosewheel's grip cannot be relied on. Rotation speed and take-off safety speed are performance speeds set by lift and climb requirements, and decision speed \( V_1 \) is the go or stop point, which must itself be no lower than \( V_{MCG} \).

Answer: B

Correct answer: The aeroplane must be de-crabbed at low speed

On approach the aeroplane is crabbed into wind to track the centreline. Before touchdown the pilot must yaw it straight so that the wheels are aligned with the runway, and that de-crab happens at the lowest speed of the whole approach.

Rudder moment falls with the square of speed, so the demand is at its greatest precisely where the authority is at its least - which is what makes the case critical for rudder sizing. The fin does not stall in a normal crosswind, and the rudder remains effective; the difficulty is the amount of yaw required at low dynamic pressure.

Answer: C

Once the fin stalls, the hinge moment can reverse and drive the surface fully over. A dorsal fin prevents the underlying fin stall and is therefore the standard cure for the phenomenon as well as for the loss of stability.

Answer: D

Correct answer: Sideslip produces both yawing and rolling moments

Sideslip is the common variable. The same disturbance that produces a yawing moment through the fin also produces a rolling moment through dihedral, wing sweep and the fin's own side force acting above the rolling axis.

Because one variable drives both, the two motions cannot be treated separately, and the lateral-directional modes - Dutch roll, spiral and roll subsidence - arise from their coupling. Dutch roll is an oscillation in which yaw and roll alternate; the spiral mode is a slow divergence in which their relative strengths decide whether the aeroplane rolls further in or levels itself.

Answer: A

Correct answer: Spiral instability

The spiral mode is settled by the balance between the two. Strong directional stability makes the aeroplane weathercock quickly into any sideslip that develops in a turn, tightening it; weak lateral stability means dihedral cannot generate the rolling moment needed to bring the wings level.

The result is a slowly tightening spiral, with bank and rate of descent both increasing. The opposite imbalance - strong dihedral effect with a weak fin - gives a poorly damped Dutch roll instead. Longitudinal instability and phugoid divergence belong to the pitching plane and are unaffected by either.

Answer: B

Correct answer: The fin is blanketed by the wing and fuselage wake

At high angle of attack the wing and fuselage shed a broad, low-energy wake, and on a conventional layout the fin sits in it. Reduced local dynamic pressure means less side force for the same sideslip, so the fin's contribution to the yawing moment derivative falls.

The loss is worst where directional control is most needed, near the stall and in spin entry, which is why remedies exist for it: ventral fins that sit below the wake, twin fins placed outboard of it, and strakes that re-energise the flow. Sideslip can certainly occur at high incidence, and fin area is a fixed geometric quantity.

Answer: C

In sideslip the forward wing meets the flow at a lower effective sweep and generates more drag, yawing the nose back. The effect is modest compared with the fin but adds usefully to the total on a swept wing aeroplane.

Answer: D

Correct answer: Place fins in cleaner air, reduce height

Two fins set outboard on the tailplane can be positioned clear of the wake shed by the wing and fuselage at high angle of attack, keeping their effectiveness where a single centreline fin would be blanketed. Splitting the area also halves the height needed for a given fin area, which matters for hangar clearance and for carrier operation.

They also sit in the propeller or jet efflux on some layouts, which raises local dynamic pressure further. The arrangement neither removes the need for rudders - both fins carry them - nor eliminates sideslip, which is a flight condition rather than a design feature.