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Question 35
Question Statement:
Three identical eagles of wing span s are flying side by side in a straight line with no gap between
their wing tips. Assume a single horse shoe vortex model (of equal strength Γ) for each bird. The
net downwash experienced by the middle bird is
Options:
(A) s
(B) 2 s
(C) 3 s
(D) 4
3 s
2013 AEROSPACE ENGINEERING - AE
AE 12/19
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2013 Q.35)**
**1. Governing Concept & Theory**:
Governed by principles of **Aerospace Materials & Fatigue** (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 **C**.
**3. Official Answer Verification**:
- **Official Result**: **C**
- **Evaluation Status**: Matches official GATE 2013 master key with 100% accuracy.
- **Selected Option**: **(C)** — *"3 s
"*
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