Question

$C_m - \alpha$ variation for a certain aircraft is shown in the figure. Which one of the following statements is true for this aircraft? 

• A. The aircraft can trim at a positive $\alpha$ and it is stable.
• B. The aircraft can trim at a positive $\alpha$, but it is unstable.
• C. The aircraft can trim at a negative $\alpha$ and it is stable.
• D. The aircraft can trim at a negative $\alpha$, but it is unstable.

Hint:

A positive slope of the $C_m-\alpha$ curve indicates unstable aircraft behaviour; a negative slope indicates stable behaviour.

Answer 1

The Correct Option is B

Step 1: Determine the trim condition.
Trim occurs where the pitching moment coefficient $C_m = 0$. From the graph, the line crosses the $C_m = 0$ axis at a positive value of angle of attack $\alpha$. Thus, trim occurs at a positive $\alpha$.

Step 2: Determine aircraft stability.
Aircraft longitudinal static stability depends on the slope $\frac{dC_m}{d\alpha}$. \[ \text{Stable if } \frac{dC_m}{d\alpha} < 0, \text{Unstable if } \frac{dC_m}{d\alpha} > 0. \] From the figure, the $C_m - \alpha$ curve has a positive slope. Therefore, \[ \frac{dC_m}{d\alpha} > 0 $\Rightarrow$ \text{aircraft is unstable.} \]

Step 3: Conclusion.
The aircraft trims at a positive angle of attack and it is unstable. Thus, the correct answer is Option (B).