Dynamic Lateral Directional Modes Questions and Answers

Answer: A

The quartic splits into three recognisable pieces: the Dutch roll as a complex pair, the roll subsidence as a large negative real root, and the spiral as a small real root that may sit on either side of the origin. That is why the lateral problem has three named modes where the longitudinal has two. Two complex pairs would describe two oscillations, which the lateral problem does not have. Four large negative real roots would leave no oscillation at all. A single pair accounts for only two of the four roots.

Answer: B

Dutch roll is a coupled oscillation in which sideslip generates both a yawing moment through the fin and a rolling moment through dihedral effect, so the aeroplane wags its nose and rocks its wings together, usually about half a cycle out of phase. A pure yaw oscillation with no roll would need zero dihedral effect, which no practical configuration has. A slow bank divergence is the spiral mode. An aperiodic roll decay is the roll subsidence, the third and fastest of the three.

Answer: C

The spiral is the slowest lateral root, a gradual change of bank and heading that on many aeroplanes is mildly divergent: left alone, a small bank tightens into a descending turn. It is tolerated because it is slow enough for a pilot or an autopilot to correct without effort. A rapid sideslip oscillation is the Dutch roll. A fast roll-rate decay is the roll subsidence. Pitching motion belongs to the longitudinal problem entirely, which decouples from this one for small perturbations.

Answer: D

Roll subsidence is aperiodic and fast, its time constant equal to the reciprocal of the roll damping, \( \tau_R = -1/L_p \), typically a few tenths of a second. It is what makes a roll rate settle almost at once when the ailerons are held steady. It does not oscillate, so a one-cycle-per-second figure belongs to the Dutch roll. Being the fastest root, it cannot be the slowest, which is the spiral. And it is stable on any conventional aeroplane, since roll damping from the wing is always present.

Answer: A

Dutch roll is the oscillation, roll subsidence the fast time constant and the spiral the slow divergence, so A-Q, B-P, C-R. The numbers are worth carrying: a Dutch roll period of three to six seconds with a damping ratio around 0.1, a roll time constant of 0.2 to 0.5 seconds, and a spiral that doubles in twenty seconds or more when it is divergent at all. Swapping the first two confuses an oscillation with a decay, and attributing tens of seconds to the Dutch roll would make it as slow as a phugoid.

Answer: B

Short period is a longitudinal mode, a fast pitching oscillation in angle of attack; the other three are the roots of the lateral-directional problem. For small perturbations about symmetric flight the two sets of equations decouple, which is exactly why they are solved separately and why mixing the mode names is a common examination error. The phugoid is the other longitudinal root, and it is worth keeping the two lists distinct in memory: two longitudinal oscillations, one lateral one.

Answer: C

It is the Dutch roll. Sideslip is the state that couples yaw to roll: the fin turns the nose into the relative wind while the dihedral effect lifts the leading wing, and the two moments together sustain the oscillation. The spiral does involve sideslip but is not an oscillation, and it is driven by the imbalance between the same two derivatives rather than by their combination. Roll subsidence is a roll-rate decay that needs no sideslip at all, and the phugoid is longitudinal.

Answer: D

Both statements are correct. The name comes from the alternating lean of a Dutch skater, and it is apt because the motion is a combination of yaw and roll rather than either alone. A pilot sees the nose describing a small figure while the wings rock, and passengers in a rear cabin feel it most because the yaw component gives them the largest lateral displacement. The etymology is not merely decorative: it captures the coupling that makes the mode hard to damp with dihedral alone.

Answer: A

The Dutch roll is the awkward one: its damping comes mainly from the yaw damping derivative, which falls with altitude, and the dihedral effect that helps the spiral works against it. That is why a yaw damper is standard equipment on swept-wing transports rather than an option. The roll subsidence is always well damped by the wing itself. The spiral needs no damping in the same sense, being aperiodic and slow enough to correct. The short period is longitudinal and is dealt with by a pitch damper.

Answer: B

A large ratio of bank amplitude to sideslip amplitude means the roll component dominates and the aeroplane is felt to rock its wings. Configurations with strong dihedral effect, including heavily swept wings at high lift coefficient, behave this way, and it is why a swept-wing aeroplane's Dutch roll is described as a wing rock while a straight-wing aeroplane's is more of a nose wag. The ratio says nothing about whether the mode is oscillatory, and nothing at all about the spiral, which is a separate root.