Dynamic Lateral Directional Modes Questions and Answers

Answer: A

A steady turn has a steady yaw rate, and an unfiltered damper would read that as a disturbance and hold rudder against the turn. The washout passes the oscillatory Dutch roll frequencies and blocks the steady component, so the damper works in the turn without fighting it. Increasing low-frequency gain is the opposite of what a washout does. Blocking the Dutch roll would defeat the whole purpose. Adverse yaw is handled by aileron design and by rudder coordination, not by this filter.

Answer: B

The yaw damping and side-force derivatives both carry a factor of dynamic pressure, which falls with density at a given Mach number, so the damping ratio degrades as the aeroplane climbs. Combined with sweep, this is why the yaw damper matters most in the cruise. Higher true airspeed does not rescue it. Fixing Mach number fixes neither density nor dynamic pressure. And the mode does not turn aperiodic; it simply oscillates for longer, which is precisely the complaint.

Answer: C

The classical criterion is \( L_\beta N_r - N_\beta L_r > 0 \), which is the sign of the last coefficient of the lateral quartic. Read physically, dihedral effect acting with yaw damping must outweigh fin stiffness acting with the rolling moment due to yaw rate. That is why dihedral improves spiral stability and a large fin degrades it, and why the two cannot both be pushed hard. Adding the terms instead of subtracting them abandons the balance the criterion expresses; the other two combinations are not the criterion at all.

Answer: D

Evaluating the criterion:

\[ \begin{aligned} L_\beta N_r &= (-20)(-0.40) = 8.0 \\ N_\beta L_r &= (3.0)(2.0) = 6.0 \\ L_\beta N_r - N_\beta L_r &= +2.0 \end{aligned} \]

Positive, so the aeroplane is spirally stable, though not by a wide margin. Reducing the dihedral effect to \( -15 \) would take the first product to 6.0 and put the mode exactly on the boundary. Roll damping does not enter the criterion, so the last option is wrong on the face of it, and the sign errors in the other two come from mishandling the product of two negative derivatives.

Answer: A

More dihedral makes \( L_\beta \) more negative, which raises the first product in the spiral criterion and so improves spiral stability, while increasing the roll response to sideslip and therefore degrading Dutch roll damping. This is the central compromise of lateral design, and it is why aeroplanes with plenty of sweep are sometimes given anhedral to claw damping back. Claiming both improve, or both degrade, misses the trade entirely; the last option has it exactly backwards.

Answer: B

A larger fin raises \( N_\beta \), which raises the Dutch roll frequency and increases the second product in the spiral criterion, degrading spiral stability. It is the mirror image of the dihedral trade, and between them the two changes define the designer's room for manoeuvre: fin volume for directional stiffness, dihedral for spiral stability, and a yaw damper to buy back the Dutch roll damping neither of them supplies. Nothing about a bigger fin lowers the frequency, and it certainly does not leave the modes untouched.

Answer: C

The doubling time is \( t_2 = \ln 2/\sigma = 0.693/0.035 = 19.8 \ \mathrm{s} \), so the aeroplane sits right on the 20-second requirement and is compliant to the accuracy of the measurement. A divergent spiral is acceptable precisely because it is slow: twenty seconds is many times a pilot's reaction time, and any autopilot holds wings level without effort. The other options come from using the root directly, or from confusing the doubling time with the time constant \( 1/\sigma = 28.6 \) seconds.

Answer: D

A slowly tightening descending turn over minutes is the spiral mode, mildly divergent, which is the normal condition for many aeroplanes and the reason hands-off flight eventually needs a correction. A divergent Dutch roll would oscillate at a period of seconds and would be obvious immediately. Roll subsidence is a fast decay, not a slow growth. A divergent phugoid changes speed and height without a bank angle developing, so the turn rules it out.

Answer: A

Both statements are correct. Specifications do not require spiral stability outright; they require that if the mode diverges, it does so slowly, typically quoting a minimum time to double amplitude. A pilot glancing at the attitude indicator every few seconds corrects a twenty-second divergence without conscious effort, and a wing leveller removes the workload altogether. What is not acceptable is a rapid spiral, which can lead to a steep descending turn if attention lapses.

Answer: B

Left alone, the bank increases, the nose drops, speed builds and the turn tightens: a graveyard spiral, dangerous not because it develops quickly but because it develops unnoticed, especially without an external horizon. It is a distinct phenomenon from a spin, which requires stall and autorotation rather than a slow bank divergence. Pitch-up is a longitudinal high-incidence problem. Aileron effectiveness is unaffected: the controls work perfectly throughout, which is what makes the recovery straightforward once the condition is recognised.