Dynamic Lateral Directional Modes Questions and Answers

Answer: C

Rate feedback augments damping and displacement feedback augments stiffness, on whichever axis the signal and the surface share, so A-Q, B-R, C-P. The rule generalises: measure a rate and you add damping to that axis, measure a displacement and you add stiffness. It is the fastest way to reason about an unfamiliar control law, and it explains why a yaw damper does nothing for the spiral, which needs a bank-angle loop instead.

Answer: D

The nose moving opposite to the roll at entry is adverse yaw, produced by the extra induced drag on the wing whose aileron went down and by the yawing moment due to roll rate. Differential or Frise ailerons, spoilers, or an aileron-rudder interconnect reduce it, and rudder coordination handles the rest. A divergent Dutch roll would oscillate rather than show one consistent initial direction. Spiral instability develops over tens of seconds. Rudder lock needs large sideslip and a stalled fin.

Answer: A

Both are true and the reason explains the assertion. A large fin makes the yawing moment with sideslip strongly positive, raising the frequency, but damping depends on the yaw rate and side force derivatives, which grow only in proportion to the tail arm and shrink with density. The result is a fast, poorly damped wag at altitude. It is the lateral echo of the longitudinal case, where a large static margin gives a quick short period that may still need a pitch damper.

Answer: B

The roll subsidence is a first-order mode, so its time constant specifies it completely and everything else follows: the time to half amplitude is \( 0.693\tau \) and the 63 per cent time is \( \tau \) itself. Frequency and damping ratio describe a second-order mode and do not apply here. A period does not exist for an aperiodic root. Doubling time applies only to a divergence, and this mode converges on every conventional aeroplane.

Answer: C

The structural difference is exactly this: one oscillation and two real roots, against the longitudinal problem's two oscillations and no real roots. That is why lateral handling is specified with a time constant, a doubling time and a damping ratio - three different kinds of number - while longitudinal handling uses two damping ratios and two frequencies. The lateral problem certainly has an oscillation, is a quartic, and depends on speed and altitude as strongly as its longitudinal counterpart.

Answer: D

The sequence is 1, 2, 3, 4, 5, and each step depends on the one before it: the aeroplane must be trimmed before the input means anything, the input must be released before the free motion exists, and peaks cannot be measured before the trace is recorded. The damper is switched off deliberately, because the requirement is written on the bare airframe as well as on the augmented one.

Answer: A

The two constraints catch different faults: the ratio governs the shape of the decay while the product governs its speed in seconds, so a low-frequency mode can satisfy the ratio and still wallow for twenty seconds. Specifying both closes that gap. Both come from one trace and one set of instruments. The ratio is perfectly measurable by logarithmic decrement. And the product does not determine the frequency; it is a product of it.

Answer: B

Rate feedback to the rudder adds to the yaw damping term alone, so the damping ratio rises and the stiffness that sets the frequency is untouched. More fin area raises stiffness and damping together, so the frequency moves. Less yawing inertia raises both as well, by dividing every derivative by a smaller number. More dihedral increases the roll content and generally makes the damping ratio worse, which is the trade at the heart of this topic.

Answer: C

Aeroplane Q has the largest damping ratio, \( 0.30/1.53 = 0.20 \), and the only strongly positive spiral root, so it diverges in the spiral while being the best damped in the oscillation. That is exactly what the design trade predicts: whatever gave Q its damping - less dihedral effect, more fin, or a damper - cost it spiral stability. P is spirally stable and less well damped, and R is the worst damped of the three while only marginally divergent.

Answer: D

The ratio compares two amplitudes within the mode's eigenvector, so a value of four means four degrees of bank for every degree of sideslip - a roll-dominated Dutch roll, characteristic of a swept wing at high lift coefficient and felt as a wing rock. It says nothing about the decay, which is the damping ratio's business, and nothing about the other two modes, which are separate roots with timescales of their own.