GATE AE 2022 • Q24
MSQ • 1 Mark
Flight Mechanics & Space Dynamics
Dynamic Stability
Subtopic: Short Period & Phugoid Longitudinal Modes
Question Statement:
If aො, b, ĉ are three mutually perpendicular unit vectors, then aො ⋅ ൫ b × ĉ൯ can take
the value(s)
Official Answer Key:
B, C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2022 Q.24)**
**1. Governing Concept & Theory**:
Governed by principles of **Dynamic Stability** (Aircraft Performance & Stability, 1 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 **B, C**.
**3. Official Answer Verification**:
- **Official Result**: **B, C**
- **Evaluation Status**: Matches official GATE 2022 master key with 100% accuracy.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.
Launch CBT Mock Test