Which of the following statements regarding the uncontrolled classical lateral-directional dynamic stability modes of a conventional aircraft are **CORRECT**?

(A) The roll subsidence mode is a non-oscillatory, heavily damped mode governed predominantly by roll damping derivative $C_{l_p}$

(B) The spiral mode is a non-oscillatory, slow mode that can be mildly unstable in practice while remaining readily controllable by the pilot

(C) The Dutch roll mode is a coupled oscillatory mode combining yaw, sideslip, and roll

(D) Increasing the wing dihedral effect always increases the damping of the Dutch roll mode

Answer Key:

Verified in official key

### 1. Strategy & Theoretical Principles Lateral-directional dynamics comprise three primary classical modes: 1. **Roll Subsidence:** Single real root ($\\lambda_{\text{roll}} \approx \frac{q_\infty S b^2 C_{lp}}{2 I_{xx} V} < 0$). Heavily damped, pure rolling response. 2. **Spiral Mode:** Single real root near the origin. Often mildly unstable (slow divergence, doubling time $> 20\text{ s}$), permitted by FAA/EASA airworthiness standards because it is easily corrected. 3. **Dutch Roll Mode:** Complex conjugate pair with light damping and moderate frequency, coupling yawing oscillations with rolling oscillations. 4. **Dihedral Trade-off:** Increasing dihedral effect ($|C_{l\beta}|$) improves spiral stability but **degrades** (reduces) Dutch roll damping, introducing severe adverse Dutch roll oscillations. Hence Statement D is false. ### 2. Statement Evaluation - **Statements A, B, C:** **CORRECT.** - **Statement D:** **INCORRECT.** Increasing dihedral degrades Dutch roll damping. ### 3. Exam Trap & Standard Reference - **Trap Alert:** Dihedral is a double-edged sword: high dihedral stabilizes the spiral mode but destabilizes Dutch roll. - **Standard Reference:** Nelson, R.C., *Flight Stability and Automatic Control*, Chapter 5.

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