Dynamic Lateral Directional Modes Questions and Answers

Answer: A

A few tenths of a second: roll damping from the wing is strong, so the rate settles almost as fast as the ailerons can be moved. Three to five seconds describes a sluggish transport at low speed and would fail most Level 1 requirements. Thirty seconds is the spiral's timescale entirely. A millisecond is faster than any rigid-body mode of a whole aeroplane, and belongs to the actuator rather than the airframe.

Answer: B

That is directional, or weathercock, stability, supplied chiefly by the fin. Lateral stability concerns the rolling response to sideslip, the dihedral effect, which is a different derivative and a different requirement. Longitudinal stability is the pitching case. Spiral stability is a property of one dynamic mode and depends on the balance between the directional and lateral derivatives rather than on either alone, which is exactly why it is not a synonym for either of them.

Answer: C

They are coupled with a phase difference that depends on the configuration, commonly a quarter to a half cycle. The phase decides whether a pilot perceives a wag with a little rock or a rock with a little wag, and flight test measures it alongside the roll-to-sideslip ratio. Exact phase or antiphase are special cases real aeroplanes do not sit at. Independence would mean no coupling, and then there would be no Dutch roll to discuss at all.

Answer: D

At large sideslip the fin can stall, its restoring moment collapses, and the rudder's own hinge moment drives it to the stops and holds it there, so the sideslip is sustained rather than corrected. A dorsal fin is the classic cure, keeping the flow attached to much larger angles. It is not a mechanical jam, and not damper saturation, which is an augmentation limit rather than an aerodynamic one. Loss of rudder effectiveness at speed is a separate compressibility or aeroelastic question.

Answer: A

Low speed at high altitude is the worst corner: low dynamic pressure weakens the damping derivatives while the high lift coefficient strengthens the sweep contribution to dihedral effect, so the mode is both slow and roll-dominated. High speed at low altitude is the best case for the same two reasons reversed. The other two combinations get one factor favourable and one adverse, which is why certification explores the corners of the envelope rather than its middle.

Answer: B

Plenty of dihedral with a modest fin puts the spiral criterion firmly positive and keeps the Dutch roll's roll content moderate at cruise lift coefficients, so the aeroplane is docile in both slow modes - which is why trainers are built this way. A poorly damped Dutch roll with a fast spiral is the swept-wing jet's problem, not this one's. Roll subsidence is stable on any conventional wing, and the short period is longitudinal and unaffected by either change.

Answer: C

The decay time is \( \ln 2/(\zeta\omega_n) \) in each case:

\[ \begin{aligned} t_{1} &= \frac{0.693}{0.06 \times 1.4} = 8.3 \ \mathrm{s} \\ t_{2} &= \frac{0.693}{0.18 \times 1.4} = 2.8 \ \mathrm{s} \end{aligned} \]

so 8.3 s to 2.8 s, a threefold improvement matching the threefold rise in damping ratio, since the frequency is unchanged. The second option scales only part way. The third and fourth use a different frequency. With frequency fixed, decay time is simply inversely proportional to the damping ratio.

Answer: D

Eight degrees is three doublings from one, and each takes 25 seconds:

\[ t = 3 \times 25 = 75 \ \mathrm{s} \]

so a minute and a quarter. That arithmetic is why a divergent spiral is tolerated: the growth is exponential but so slow that any instrument scan catches it. 25 s allows one doubling, to two degrees. 200 s would be eight doublings and a bank past 250 degrees. 50 s reaches four degrees, which is two doublings rather than three.

Answer: A

Mass far out along the span raises rolling inertia with the square of the distance, so the roll response becomes sluggish: the time constant lengthens and the rate achieved for a given aileron moment falls. That is why roll performance is quoted per store configuration. Dihedral effect is aerodynamic and largely unchanged by the mass. Yawing inertia rises far less than rolling inertia for tip stores. And a faired store still has its mass.

Answer: B

The first two are correct: the last coefficient carries the sign of \( L_\beta N_r - N_\beta L_r \), and the large negative real root is the roll subsidence. The third is wrong, because the lateral quartic holds one complex pair and two real roots, which is what gives three modes rather than two. Expecting two pairs imports the longitudinal structure into the lateral problem, and it is the single most common confusion on this topic.