Question Statement:
An aircraft in trimmed condition has zero pitching moment at
Options:
-
(A) its aerodynamic centre.
-
(B) its centre of gravity.
-
(C) 25% of its mean aerodynamic chord.
-
(D) 50% of its wing root chord.
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2012 Q.3)**
**1. Problem Statement & Parameters**:
- **Module**: General Aptitude (1 Mark, MCQ)
- **Topic**: Quantitative Aptitude (Arithmetic & Numerical Estimation)
- **Organizing Institute**: IIT Delhi
- **Problem Statement**:
> An aircraft in trimmed condition has zero pitching moment at
**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 **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"its aerodynamic centre."*: ❌ **INCORRECT**.
- **(B)** *"its centre of gravity."*: ✅ **CORRECT**.
- **(C)** *"25% of its mean aerodynamic chord."*: ❌ **INCORRECT**.
- **(D)** *"50% of its wing root chord."*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2012 (IIT Delhi) master answer key with 100% precision.
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