Question

For a longitudinally statically stable aircraft, which one of the following represents the relationship between the coefficient of pitching moment about the center of gravity \(C_{m_{cg}}\) and absolute angle of attack \(\alpha_a\)? (Note: nose–up moment is positive.)

• A. A
• B. B
• C. C
• D. D

Hint:

Static stability check: slope of moment coefficient curve must be negative (\(\partial C_m/\partial \alpha < 0\)). This ensures an increase in \(\alpha\) generates a nose–down restoring moment.

Answer 1

The Correct Option is D

Step 1: Static stability condition.
For an aircraft to be longitudinally statically stable, a small increase in angle of attack (\(\alpha\)) should produce a restoring (nose–down) moment. - Nose–up moment is defined as positive. - Hence, with increasing \(\alpha\), \(C_m\) must decrease. \[ \frac{\partial C_m}{\partial \alpha} < 0 \]

Step 2: Graphical requirement.
The slope of \(C_m\) vs \(\alpha\) should be negative. That eliminates (A) and (C), because both have positive slope.

Step 3: Distinguish between (B) and (D).
For a real aircraft: - At \(\alpha = 0\), \(C_m\) is typically not zero; it has a negative (nose–down) or slightly negative constant trim moment to balance lift. - To trim at some positive \(\alpha\), the line should cross zero at a finite \(\alpha\). - This corresponds to a line with negative slope and an intercept above the origin. Option (D) matches this condition.

Final Answer:
\[ \boxed{\text{(D) Negative slope with intercept above origin}} \]