Subtopic: Short Period & Phugoid Longitudinal Modes
Question Statement:
A general aviation airplane is flying at an altitude of 5000 m. The indicated
airspeed is 250 km/h. Assume that there are no instrument errors and position
errors. Neglecting compressibility effects, which one of the following options is
FALSE?
Options:
(A) The true airspeed is greater than 250 km/h.
(B) The calibrated airspeed is 250 km/h.
(C) The true airspeed is 250 km/h.
(D) The equivalent airspeed is 250 km/h.
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2025 Q.24)**
**1. Governing Concept & Theory**:
Governed by principles of **Dynamic Stability** (Aircraft Performance & Stability, 1 Mark, MCQ).
**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 **C**.
**3. Official Answer Verification**:
- **Official Result**: **C**
- **Evaluation Status**: Matches official GATE 2025 master key with 100% accuracy.
- **Selected Option**: **(C)** — *"The true airspeed is 250 km/h."*
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