To derive the moment equation around the center of gravity of the King Air 200, we need to consider the forces and moments acting on the aircraft. Here's how we can proceed:
1. Draw a free-body diagram of the aircraft, showing the forces and moments acting on it.
2. Identify the forces and moments relevant to this analysis:
- Total lift (L): This is the lift force acting on the wings, which is assumed to act through the center of lift.
- Tail lift (Lt): This is the lift force acting on the tail, which is assumed to act through the tail's center of lift.
- Center of gravity distance (d): This is the distance between the center of gravity and the wing's center of lift.
- Tail arm (Lc): This is the distance between the center of gravity and the tail's center of lift.
- Aerodynamic center moment (Mc): This is the moment acting on the aircraft about the center of gravity due to the aerodynamic forces acting through the aircraft's aerodynamic center.
3. Write down the moment equation:
Sum of moments about the center of gravity = -L * d + Lt * Lc + Mc
4. Simplify the equation:
-L * d + Lt * Lc + Mc = 0
This is the moment equation around the center of gravity of the King Air 200 as a function of the total lift (L), tail lift (Lt), center of gravity distance (d), tail arm (Lc), and aerodynamic center moment (Mc).