Subtopic: Longitudinal Static Stability & Neutral Point
Question Statement:
Which of the following statements is/are TRUE about the stability of an aircraft?
Options:
(A) Static stability of an aircraft is sufficient to guarantee its dynamic stability
(B) Static stability of an aircraft is related only to its initial tendency to return towards
the equilibrium position from which it is disturbed
(C) An aircraft may be dynamically unstable even if it is statically stable
(D) Dynamic stability is related to the time history of aircraft motion after being
disturbed from its equilibrium position
Official Answer Key:
B, C, D
Step-by-Step Solution & Explanation
### **Detailed Step-by-Step Solution (GATE AE 2026 Q.23)**
**1. Intuitive Physical Setup & Given Parameters**:
The question asks to evaluate foundational statements regarding the static and dynamic stability of an aircraft (MSQ).
**2. Step-by-Step Analytical Derivation**:
1. **Definition of Static Stability**:
- Static stability refers solely to the **initial tendency** of the aircraft to return to its equilibrium trimmed state following a disturbance.
- If restoring moments act initially towards equilibrium, the aircraft is statically stable. Statement B is **TRUE**.
2. **Definition of Dynamic Stability**:
- Dynamic stability describes the **time history** of the resulting motion (whether oscillations dampen out, sustain, or diverge over time). Statement D is **TRUE**.
3. **Relationship Between Static and Dynamic Stability**:
- Static stability is a **necessary but not sufficient** condition for dynamic stability.
- An aircraft that is statically stable can undergo divergent (undamped) oscillations, rendering it dynamically unstable (e.g., negative damping in Dutch roll or short-period pitch). Statement C is **TRUE**.
- Statement A claims that static stability is *sufficient* to guarantee dynamic stability, which is completely false. Statement A is **FALSE**.
**3. Comprehensive Options & Distractor Analysis**:
- **(A) Static stability of an aircraft is sufficient to guarantee its dynamic stability**: ❌ **INCORRECT**. A statically stable aircraft may exhibit divergent oscillations (dynamic instability).
- **(B) Static stability of an aircraft is related only to its initial tendency to return towards the equilibrium position from which it is disturbed**: ✅ **CORRECT**. Classic definition of static stability.
- **(C) An aircraft may be dynamically unstable even if it is statically stable**: ✅ **CORRECT**. Lack of aerodynamic damping can cause oscillatory divergence even with positive static stiffness.
- **(D) Dynamic stability is related to the time history of aircraft motion after being disturbed from its equilibrium position**: ✅ **CORRECT**. Precise definition of dynamic stability.
**4. Official Master Key & Exam Takeaway**:
- **Official Answer Key**: **B, C, D**
- **Exam Takeaway**: Static stability = initial tendency (stiffness $\partial C_m/\partial \alpha < 0$); Dynamic stability = time evolution (damping derivatives $C_{mq} + C_{m\dot{\alpha}} < 0$). Static stability never guarantees dynamic stability!
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