Question

For an airplane having directional (weathercock) static stability, which of the following options is/are correct?

• A. The airplane when disturbed in yaw, from an equilibrium state, will experience a restoring moment
• B. The variation of yawing-moment coefficient \(C_n\) with sideslip angle \(\beta\) will look like the shown straight line with positive slope (through the origin)
• C. The airplane will always tend to point into the relative wind
• D. The airplane when disturbed in yaw will return to equilibrium state in a finite amount of time after removing the disturbance

Hint:

Static directional stability \(\Rightarrow\) \(\partial C_n/\partial\beta > 0\) (restoring weathercock moment). Dynamic return-to-equilibrium depends on damping and cannot be inferred from static stability alone.

Answer 1

The Correct Option is A, B, C

Step 1: Static directional (weathercock) stability criterion.
Static stability in yaw requires a restoring yawing moment for a given sideslip, i.e. \(\displaystyle \frac{\partial C_n}{\partial \beta} > 0\). This gives a line through the origin with positive slope in the \(C_n\)-\(\beta\) plot. Hence (A) and (B) are True.
Step 2: "Points into the relative wind."
A weathercock-statically-stable airplane tends to align its nose with the oncoming flow when perturbed (the classic "weathervane" effect). This statement encapsulates the same tendency (static, not time response). \(\Rightarrow\) (C) is True.
Step 3: Dynamic vs static.
Statement (D) asserts time-dependent return to equilibrium in finite time — this requires dynamic stability (adequate damping), not guaranteed by static stability alone. \(\Rightarrow\) (D) is False.
\[ \boxed{\text{Correct: (A), (B), (C).}} \]