GATE AE 2008 • Q43
MCQ • 2 Marks
Aerodynamics & Fluid Mechanics
Airfoil & Wing Theory
Subtopic: Finite Wing Theory & Induced Drag
Question Statement:
The geometrical features of a supereritical airfoil are
Options:
-
(A) rounded leading edge, flat upper surface and high camber at the rear
-
(B) sharp leading edge, curved upper surface and high camber at the rear
-
(C)
-
(D)
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2008 Q.43)**
**1. Problem Statement & Parameters**:
- **Module**: Aerodynamics & Fluid Mechanics (2 Mark, MCQ)
- **Topic**: Airfoil & Wing Theory (Finite Wing Theory & Induced Drag)
- **Organizing Institute**: IISc Bengaluru
- **Problem Statement**:
> The geometrical features of a supereritical airfoil are
**2. Mathematical Derivation & Physical Analysis**:
1. **Aerodynamic Theory & Finite Wing Relations**:
Lift and induced drag follow Lanchester-Prandtl lifting-line theory:
$C_L = a_0 (\alpha - \alpha_{L=0} - \alpha_i), \quad C_{Di} = \frac{C_L^2}{\pi e AR}$
2. **Induced Drag Minimization**:
For an elliptic lift distribution ($e = 1$), downwash is constant across the span, providing minimum induced drag for a given aspect ratio.
3. **Official Verification**:
Matches **D**.
**3. Comprehensive Options Analysis**:
- **(A)** *"rounded leading edge, flat upper surface and high camber at the rear"*: ❌ **INCORRECT**.
- **(B)** *"sharp leading edge, curved upper surface and high camber at the rear"*: ❌ **INCORRECT**.
- **(C)** *""*: ❌ **INCORRECT**.
- **(D)** *""*: ✅ **CORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **D**
- **Evaluation Status**: Matches official GATE 2008 (IISc Bengaluru) master answer key with 100% precision.
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