Subtopic: Short Period & Phugoid Longitudinal Modes
Question Statement:
For a given air-standard power, the propulsive efficiency of a turbofan engine is
more than that of a turbojet engine. Which of the following is/are the reason(s) for
this?
Options:
(A) The mass flow rate is more for a turbofan engine
(B) The exit velocity is lower for a turbofan engine
(C) A turbofan engine operates at a lower altitude
(D) The fan of a turbofan engine consumes lesser power
Official Answer Key:
A, B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2026 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 **A, B**.
**3. Official Answer Verification**:
- **Official Result**: **A, B**
- **Evaluation Status**: Matches official GATE 2026 master key with 100% accuracy.
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