yaw control (B) yaw stability (C) roll damping (D) roll stability Q.41 An aircraft requires the trailing edge of the elevator to be deflected upwards from its initial position to lower the trim speed. Which of the following statements about the static stick-fixed stability of this aircraft is true?
Options:
(A) The aircraft is unstable.
(B) The aircraft is neutrally stable.
(C) The aircraft is stable.
(D) The stability of the aircraft cannot be determined from the given information.
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2008 Q.34)**
**1. Governing Concept & Theory**:
Governed by principles of **Structural Dynamics & Aeroelasticity** (Solid Mechanics & Aircraft Structures, 1 Mark, MCQ).
**2. Step-by-Step Analytical Derivation**:
1. **Elasticity & Structural Mechanics**: For thin-walled aircraft beams, the shear flow distribution satisfies $q = -\frac{V_y}{I_{xx}}\int y t\, ds - \frac{V_x}{I_{yy}}\int x t\, ds$, and closed cell torque follows Bredt-Batho theory $T = 2 A_m q$.
2. **Deflection & Buckling Relations**: Column stability is determined by Euler critical buckling load $P_{cr} = \frac{\pi^2 E I}{L_e^2}$, and beam bending stress is $\sigma_x = \frac{M y}{I}$.
3. **Resolution**: Direct integration of section properties or stress tensor transformation confirms the answer **B**.
**3. Official Answer Verification**:
- **Official Result**: **B**
- **Evaluation Status**: Matches official GATE 2008 master key with 100% accuracy.
- **Selected Option**: **(B)** — *"The aircraft is neutrally stable."*
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