GATE AE 2008 • Q40
MCQ • 2 Marks
Aerodynamics & Fluid Mechanics
Airfoil & Wing Theory
Subtopic: Thin Airfoil Theory & Camber Effects
Question Statement:
The variation of downwash along the span of an untwisted wing of elliptic planform is
Options:
-
(A) sinusoidal
-
(B) parabolic
-
(C) elliptic
-
(D) constant
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2008 Q.40)**
**1. Problem Statement & Parameters**:
- **Module**: Aerodynamics & Fluid Mechanics (2 Mark, MCQ)
- **Topic**: Airfoil & Wing Theory (Thin Airfoil Theory & Camber Effects)
- **Organizing Institute**: IISc Bengaluru
- **Problem Statement**:
> The variation of downwash along the span of an untwisted wing of elliptic planform is
**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 **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"sinusoidal"*: ❌ **INCORRECT**.
- **(B)** *"parabolic"*: ✅ **CORRECT**.
- **(C)** *"elliptic"*: ❌ **INCORRECT**.
- **(D)** *"constant"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2008 (IISc Bengaluru) master answer key with 100% precision.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.
Launch CBT Mock Test