Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
Question Statement:
For a NACA 4415 airfoil, the location of maximum camber, as a fraction of the
chord length from the leading edge, is ______.
Options:
(A) 0.44
(B) 0.40
(C) 0.15
(D) 0.04
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Detailed Step-by-Step Solution (GATE AE 2025 Q.18)**
**1. Intuitive Physical Setup & Given Parameters**:
We are asked to find the location of maximum camber as a fraction of chord from the leading edge for a **NACA 4415** airfoil.
**2. Step-by-Step Mathematical Derivation**:
1. **NACA 4-Digit Series Nomenclature Convention**:
A standard NACA 4-digit airfoil 'NACA $M P X X$' is parameterized as follows:
- **First digit ($M = 4$)**: Maximum camber in percent of chord $\implies 4\% c = 0.04c$.
- **Second digit ($P = 4$)**: Position of maximum camber in **tenths** of chord from the leading edge $\implies 4 \times 0.1c = 0.40c$.
- **Last two digits ($XX = 15$)**: Maximum thickness in percent of chord $\implies 15\% c = 0.15c$.
2. **Evaluation**:
The location of maximum camber is given by the second digit ($P = 4$), which translates to $0.40$ (or $40\%$ of chord length).
**3. Comprehensive Options & Distractor Analysis**:
- **(A) 0.44**: ❌ **INCORRECT**. Erroneously combines the first two digits.
- **(B) 0.40**: ✅ **CORRECT**. The second digit '4' denotes maximum camber position at $40\%$ chord ($0.40c$).
- **(C) 0.15**: ❌ **INCORRECT**. This is the maximum thickness fraction ($15\% c$) given by the last two digits.
- **(D) 0.04**: ❌ **INCORRECT**. This is the maximum camber magnitude ($4\% c$) given by the first digit.
**4. Official Master Key & Exam Takeaway**:
- **Official Answer Key**: **B**
- **Exam Takeaway**: Never confuse the first digit (camber magnitude, $0.04c$) with the second digit (camber location, $0.40c$). The last two digits always represent maximum profile thickness ($0.15c$).