Question Statement:
A trailing edge plain flap deflected downward increases the lift coefficient of an airfoil by
Options:
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(A) Increasing the effective camber of the airfoil.
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(B) Delaying the separation of the flow from the airfoil surface.
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(C) Increasing the local airspeed near the trailing edge.
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(D) Controlling the growth of the boundary layer thickness along the airfoil surface.
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2009 Q.2)**
**1. Problem Statement & Parameters**:
- **Module**: General Aptitude (1 Mark, MCQ)
- **Topic**: Verbal Aptitude (Grammar & Vocabulary)
- **Organizing Institute**: IIT Roorkee
- **Problem Statement**:
> A trailing edge plain flap deflected downward increases the lift coefficient of an airfoil by
**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 **A**.
**3. Comprehensive Options Analysis**:
- **(A)** *"Increasing the effective camber of the airfoil."*: ✅ **CORRECT**.
- **(B)** *"Delaying the separation of the flow from the airfoil surface."*: ❌ **INCORRECT**.
- **(C)** *"Increasing the local airspeed near the trailing edge."*: ❌ **INCORRECT**.
- **(D)** *"Controlling the growth of the boundary layer thickness along the airfoil surface."*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **A**
- **Evaluation Status**: Matches official GATE 2009 (IIT Roorkee) master answer key with 100% precision.
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