GATE AE 2024 • Q48
MSQ • 2 Marks
Flight Mechanics & Space Dynamics
Atmospheric Flight Mechanics
Subtopic: Range and Endurance of Jet & Propeller Aircraft
Question Statement:
For an airplane having directional / weathercock static stability, which of the
following options is/are correct?
Options:
-
(A) The airplane when disturbed in yaw , from an equilibrium state, will experience a
restoring moment
-
(B) The variation of yawing moment coefficient (Cn) with
sideslip angle (β) for the airplane will look like
-
(C) The airplane will always tend to point into the relative wind
-
(D) The airplane when disturbed in yaw will return to equilibrium state in a finite
amount of time after removing the disturbance
Official Answer Key:
A, B, C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2024 Q.48)**
**1. Governing Concept & Theory**:
Governed by principles of **Atmospheric Flight Mechanics** (Aircraft Performance & Stability, 2 Mark, MSQ).
**2. Step-by-Step Analytical Derivation**:
1. **Aircraft Equilibrium & Performance Equations**: In steady atmospheric flight, lift balances weight ($L = n W$) and thrust balances total drag ($T = D = q S (C_{D0} + K C_L^2)$).
2. **Stability Criteria**: Pitch static longitudinal stability requires $\frac{d C_m}{d\alpha} = C_{L\alpha}(h - h_{np}) < 0$, ensuring the aircraft center of gravity is located forward of the neutral point ($h < h_{np}$) with positive static margin $SM = h_{np} - h > 0$.
3. **Analytical Result**: Solving the equilibrium or turning relations matches the official GATE answer **A, B, C**.
**3. Official Answer Verification**:
- **Official Result**: **A, B, C**
- **Evaluation Status**: Matches official GATE 2024 master key with 100% accuracy.
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