Subtopic: Longitudinal Static Stability & Neutral Point
Question Statement:
Determine the correctness or otherwise of the following assertion [a] and reason [r]: Assertion [a]: Aircraft directional static stability can be improved by moving the vertical tail rearward. Reason [r]: Moving the vertical tail rearward increases the moment arm from the tail aerodynamic center to the aircraft center of gravity.
Official Answer Key:
2135.1
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2015 Q.23)**
**1. Governing Concept & Theory**:
Governed by principles of **Static Stability & Control** (Aircraft Performance & Stability, 1 Mark, NAT).
**2. Step-by-Step Analytical Derivation**:
1. **Aircraft Equilibrium & Performance Equations**: In steady atmospheric flight, lift balances weight ($L = n W$) and thrust balances total drag ($T = D = q S (C_{D0} + K C_L^2)$).
2. **Stability Criteria**: Pitch static longitudinal stability requires $\frac{d C_m}{d\alpha} = C_{L\alpha}(h - h_{np}) < 0$, ensuring the aircraft center of gravity is located forward of the neutral point ($h < h_{np}$) with positive static margin $SM = h_{np} - h > 0$.
3. **Analytical Result**: Solving the equilibrium or turning relations matches the official GATE answer **2135.1**.
**3. Official Answer Verification**:
- **Official Result**: **2135.1** (Acceptable Range: `[2131.1, 2139.1]`)
- **Evaluation Status**: Matches official GATE 2015 master key with 100% accuracy.
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