GATE AE 2012 • Q49
NAT • 2 Marks
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
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(C) 0.4o
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(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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