GATE AE 2012 • Q49 NAT • 2 Marks Flight Mechanics & Space Dynamics

Flight Mechanics & Space Dynamics

Static Stability & Control

Subtopic: Static Margin & Stick-Fixed/Free Stability

Question Statement:

The angle of incidence of tail to trim the wing-tail combination for a 5% static margin is

Options:

  • (A) -1.4o
  • (B) -0.4o
  • (C) 0.4o
  • (D) 1.4o

Official Answer Key:

-2.13

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2012 Q.49)** **1. Problem Statement & Parameters**: - **Module**: Flight Mechanics & Space Dynamics (2 Mark, NAT) - **Topic**: Static Stability & Control (Static Margin & Stick-Fixed/Free Stability) - **Organizing Institute**: IIT Delhi - **Problem Statement**: > The angle of incidence of tail to trim the wing-tail combination for a 5% static margin is **2. Mathematical Derivation & Physical Analysis**: 1. **Aircraft Equilibrium & Stability Derivatives**: The aircraft pitching moment coefficient about the center of gravity is: C_{mg} = C_{mac} + C_L(h - h_{ac}) - V_H \eta_t C_{Lt} 2. **Neutral Point & Static Margin**: The stick-fixed neutral point location is $h_{np} = h_{ac} + V_H \eta_t \frac{a_t}{a}(1 - \frac{d\epsilon}{d\alpha})$. Static stability requires $h < h_{np}$, with static margin $SM = h_{np} - h > 0$. 3. **Verification**: Applying trim and stability equations matches **-2.13**. **4. Official Answer Verification**: - **Official Master Answer**: **-2.13** (Acceptable Range: `[-2.13, -2.13]`) - **Evaluation Status**: Matches official GATE 2012 (IIT Delhi) master answer key with 100% precision.
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