GATE AE 2019 • Q28 NAT • 1 Mark Flight Mechanics & Space Dynamics

Flight Mechanics & Space Dynamics

Atmospheric Flight Mechanics

Subtopic: Range and Endurance of Jet & Propeller Aircraft

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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