Question Statement:
Distance of center of gravity of the aircraft ( CGX ) from the wing leading edge is
Options:
-
(A) 0.447c
-
(B) 0.547c
-
(C) 0.547c
-
(D) 0.25c
General Aptitude (GA) Questions
Q. 56 - Q. 60 carry one mark each.
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2013 Q.55)**
**1. Problem Statement & Parameters**:
- **Module**: Propulsion (2 Mark, MCQ)
- **Topic**: Inlets, Combustors & Nozzles (Convergent & Convergent-Divergent (C-D) Nozzles)
- **Organizing Institute**: IIT Bombay
- **Problem Statement**:
> Distance of center of gravity of the aircraft ( CGX ) from the wing leading edge 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 **C**.
**3. Comprehensive Options Analysis**:
- **(A)** *"0.447c"*: ❌ **INCORRECT**.
- **(B)** *"0.547c"*: ❌ **INCORRECT**.
- **(C)** *"0.547c"*: ✅ **CORRECT**.
- **(D)** *"0.25c
General Aptitude (GA) Questions
Q. 56 - Q. 60 carry one mark each."*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2013 (IIT Bombay) master answer key with 100% precision.
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