Subtopic: Pitch Angle, Flight Path Angle, and Angle of Attack
Question Statement:
For an airplane flying in a vertical plane, the angle of attack is $3^\circ$, the horizontal and vertical components of velocity in wind axes are 300 km/h and 0 km/h, respectively. If the pitch angle is $9^\circ$, the climb angle of the airplane is _________ degrees (round off to the nearest integer).
Official Answer Key:
6.0
Step-by-Step Solution & Explanation
### **Detailed Step-by-Step Solution (GATE AE 2019 Q.28 / AE Q.18)**
**1. Intuitive Physical Setup & Given Parameters**:
- Angle of attack: $\alpha = 3^\circ$
- Pitch attitude angle: $\theta = 9^\circ$
- Longitudinal flight in vertical plane.
**2. Step-by-Step Mathematical Derivation**:
1. **Fundamental Kinematic Angular Relation**:
In longitudinal flight mechanics, the pitch angle $\theta$ (angle between fuselage reference line and horizontal) is the sum of the flight path (climb) angle $\gamma$ (angle between velocity vector and horizontal) and the angle of attack $\alpha$ (angle between fuselage reference line and velocity vector):
$\theta = \gamma + \alpha$
2. **Solving for Climb Angle ($\gamma$)**:
$\gamma = \theta - \alpha$
3. **Numerical Substitution**:
$\gamma = 9^\circ - 3^\circ = 6^\circ$
**3. Comprehensive Options & Distractor Analysis**:
- **Question Type**: Numerical Answer Type (NAT).
- **Exact Evaluation**: **6.0 degrees** (Acceptable Range: [5.98, 6.00]).
**4. Official Master Key & Exam Takeaway**:
- **Official Answer**: **6.0**
- **Golden Rule of Flight Mechanics**: $\theta = \gamma + \alpha$ in zero-wind vertical plane.
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