Question

Which of the following statements is/are TRUE about the stability of an aircraft?

• 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

Hint:

Static stability checks only the initial restoring tendency; dynamic stability checks whether the resulting motion grows or decays over time. One does not guarantee the other.

Answer 1

The Correct Option is B, C, D

This question tests the difference between static stability and dynamic stability, two separate ideas that GATE often tests together. Static stability is about the very first moment after a disturbance: does the aircraft's own aerodynamics push it back toward its trim, or push it further away. Dynamic stability is about what happens over time after that first moment: does the resulting motion, an oscillation in most modes, die out, stay the same, or grow.

1. (A) Static stability guarantees dynamic stability: This is false. Static stability only tells us that the initial moment or force after a disturbance opposes the disturbance. It says nothing about the damping of the motion that follows. A classic example is the phugoid mode: an aircraft can be statically stable, it initially tends back to trim, and still show a phugoid oscillation whose amplitude grows with time, which is dynamic instability. So static stability is needed but not enough for dynamic stability.
2. (B) Static stability is only about the initial tendency to return to equilibrium: This is true, by definition. Static stability is checked using the sign of the restoring moment, for longitudinal static stability the sign of \(\partial C_m/\partial \alpha\) with \(C_{m,0}>0\), right at the instant of disturbance. It makes no statement about the time history that follows.
3. (C) An aircraft may be dynamically unstable even if it is statically stable: This is true, and it follows directly from (A) being false. Since static stability does not control the damping of the oscillatory modes, a statically stable aircraft can still have negative damping in a mode such as the phugoid or spiral mode, making it dynamically unstable.
4. (D) Dynamic stability is related to the time history of motion after disturbance: This is true, by definition. Dynamic stability studies how the perturbation quantities, angle of attack, pitch rate, sideslip and so on, evolve with time, whether the oscillation amplitude decays (stable), stays constant (neutral), or grows (unstable).

So the correct statements are (B), (C) and (D); (A) is the false one, because it wrongly claims static stability by itself is enough for dynamic stability.

Let's summarize:

• Static stability is the sign of the initial restoring tendency only.
• Dynamic stability is the behaviour, growth or decay, of the resulting motion over time.
• Static stability is needed but not enough for dynamic stability, so a statically stable aircraft can still be dynamically unstable.

The TRUE statements are (B), (C) and (D).