Which of the following geometric and aerodynamic features contribute positively to directional static stability ($C_{n_\beta} > 0$) of an airplane?

(A) A vertical tail located aft of the aircraft center of gravity

(B) Wing sweepback in high-speed flight

(C) A long, slender tractor fuselage nose located far forward of the center of gravity

(D) Twin vertical stabilizers placed at the wing tips or outside propeller slipstream

Answer Key:

Verified in official key

### 1. Strategy & Theoretical Principles Directional static stability (weathercock stability) requires that a positive sideslip angle $\beta$ produces a restoring positive yawing moment: $$C_{n_\beta} = \frac{\partial C_n}{\partial \beta} > 0$$ ### 2. Statement Evaluation - **Statement A:** **CORRECT.** A vertical fin located aft of the CG experiences a sideforce in positive sideslip whose moment arm produces a positive (stabilizing) yawing moment: $C_{n\beta,tail} = V_v \eta_v a_v (1 + d\sigma/d\beta) > 0$. - **Statement B:** **CORRECT.** Wing sweepback provides a positive stabilizing yawing moment ($C_{n\beta,wing} > 0$) because the advance wing has greater effective sweep and less chordwise drag, while the trailing wing has greater effective chordwise velocity, producing a net stabilizing yawing moment toward the relative wind. - **Statement C:** **INCORRECT.** A fuselage body alone (especially an extended nose forward of CG) is strongly destabilizing ($C_{n\beta,fuselage} < 0$) due to Munk moment / cross-flow side force acting forward of the CG. - **Statement D:** **CORRECT.** Twin vertical fins mounted at the wing tips or vertical endplates increase effective vertical tail area and directional stiffness ($C_{n\beta} > 0$). ### 3. Exam Trap & Standard Reference - **Trap Alert:** A fuselage in sideslip is naturally destabilizing in yaw; vertical tails must be sized to overcome the negative $C_{n_\beta}$ of the fuselage. - **Standard Reference:** Nelson, R.C., *Flight Stability and Automatic Control*, Chapter 3 (Lateral-Directional Static Stability).

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