Question

A general aviation airplane is initially in steady and level flight. The stability coefficient \( \frac{\partial C_m}{\partial q} \) (where \( C_m \) is the airplane pitching moment coefficient and \( q \) is the pitch rate) is negative. The airplane is perturbed with a small nose-up constant pitch rate. Assume that the horizontal tail does not stall during the perturbation, and unsteady effects are neglected. When compared to steady and level flight conditions, which of the following statements is/are true during the perturbed motion?

• A. The angle of attack of the horizontal tail increases.
• B. The contribution of the horizontal tail to the airplane’s pitching moment about the center of gravity is more stabilizing.
• C. The lift generated by the horizontal tail increases.
• D. The contribution of the horizontal tail to the airplane’s pitching moment about the center of gravity is less stabilizing.

Hint:

In negative stability cases, the horizontal tail helps stabilize the aircraft by increasing its lift and pitching moment as the angle of attack increases due to a nose-up perturbation.

Answer 1

The Correct Option is A, B, C

Since the stability coefficient \( \frac{\partial C_m}{\partial q} \) is negative, the airplane is said to be unstable in pitch. When the airplane is perturbed with a small nose-up pitch rate: 
Step 1: Angle of attack of the horizontal tail increases. 
When the airplane experiences a nose-up perturbation, the angle of attack of the horizontal tail increases due to the change in relative airflow. This results in an increased lift force generated by the tail, which helps to counteract the nose-up moment. Therefore, (A) is true. 
Step 2: Contribution of the horizontal tail to the pitching moment is more stabilizing. 
With the increased lift generated by the horizontal tail, it contributes to a more stabilizing pitching moment. This is because the horizontal tail works to counterbalance the nose-up disturbance. Thus, (B) is also true.
 Step 3: Lift generated by the horizontal tail increases. 
The increased angle of attack leads to an increase in the lift produced by the horizontal tail, which aids in stabilizing the aircraft. Therefore, (C) is correct. Thus, the correct answers are (A), (B), and (C).