Discussion
Consider the following statements about longitudinal dynamic stability.
1. An aeroplane can be statically stable and dynamically unstable
2. An aeroplane can be statically unstable and dynamically stable
3. Static stability is a necessary condition for a convergent oscillation
Which of the statements given above is or are correct?
Answer: D
Statements 1 and 3 hold. Static stability only guarantees an initial tendency to return, so an aeroplane can meet it and still oscillate divergently, which is the case of a positive \( E \) with a negative Routh discriminant. Statement 3 is the same coin's other face: without static stability the last coefficient goes negative and a real divergent root appears, so no convergent oscillation is possible. Statement 2 is therefore false for the bare airframe, and this is where care is needed: an augmented aeroplane appears to contradict it, but there the control system has supplied the missing stiffness and the effective airframe is no longer statically unstable.
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