GATE AE 2012 • Q17 MCQ • 1 Mark Flight Mechanics & Space Dynamics

Flight Mechanics & Space Dynamics

Static Stability & Control

Subtopic: Control Surfaces (Elevator, Aileron, Rudder)

Question Statement:

In an aircraft, elevator control effectiveness determines

Options:

  • (A) turn radius.
  • (B) rate of climb.
  • (C) forward-most location of the centre of gravity.
  • (D) aft-most location of the centre of gravity.

Official Answer Key:

C

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2012 Q.17)** **1. Problem Statement & Parameters**: - **Module**: Aerodynamics & Fluid Mechanics (1 Mark, MCQ) - **Topic**: Airfoil & Wing Theory (Kutta-Joukowski Theorem & Thin Airfoil Theory) - **Organizing Institute**: IIT Delhi - **Problem Statement**: > In an aircraft, elevator control effectiveness determines **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)** *"turn radius."*: ❌ **INCORRECT**. - **(B)** *"rate of climb."*: ❌ **INCORRECT**. - **(C)** *"forward-most location of the centre of gravity."*: ✅ **CORRECT**. - **(D)** *"aft-most location of the centre of gravity."*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **C** - **Evaluation Status**: Matches official GATE 2012 (IIT Delhi) master answer key with 100% precision.
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