GATE AE 2018 • Q12 MCQ • 1 Mark Aerodynamics & Fluid Mechanics

Aerodynamics & Fluid Mechanics

Airfoil & Wing Theory

Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory

Question Statement:

The pitching moment of a positively cambered NACA airfoil about its leading edge at zero- lift angle of attack is

Options:

  • (A) negative.
  • (B) positive.
  • (C) indeterminate.
  • (D) zero.

Official Answer Key:

B

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2018 Q.12)** **1. Problem Statement & Parameters**: - **Module**: Engineering Mathematics (1 Mark, MCQ) - **Topic**: Linear Algebra (Eigenvalues & Eigenvectors) - **Organizing Institute**: IIT Guwahati - **Problem Statement**: > The pitching moment of a positively cambered NACA airfoil about its leading edge at zero- lift angle of attack is **2. Mathematical Derivation & Physical Analysis**: 1. **Aircraft Pitching Equilibrium**: The pitching moment coefficient about the aircraft center of gravity is: C_{mg} = C_{mac} + C_L(h - h_{ac}) - V_H \eta_t C_{Lt} 2. **Static Stability & Neutral Point Criteria**: Static longitudinal stability requires $\frac{dC_{mg}}{d\alpha} < 0$, which defines the stick-fixed neutral point $h_{np}$: \frac{dC_{mg}}{dC_L} = -(h_{np} - h) = -SM A positive static margin ($SM > 0$) mandates that the center of gravity must lie forward of the neutral point ($h < h_{np}$). 3. **Verification**: Direct application of stability derivatives verifies **B**. **3. Comprehensive Options Analysis**: - **(A)** *"negative."*: ❌ **INCORRECT**. - **(B)** *"positive."*: ✅ **CORRECT**. - **(C)** *"indeterminate."*: ❌ **INCORRECT**. - **(D)** *"zero."*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **B** - **Evaluation Status**: Matches official GATE 2018 (IIT Guwahati) master answer key with 100% precision.
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