To derive the moment equation around the center of gravity (CG) of the King Air 200 aircraft, we need to consider the forces and moments acting on the airplane.
Let's denote the following variables:
- L: Total lift
- L_H: Tail lift
- l_cg: Distance from the CG to the aerodynamic center (AC)
- l_H: Tail arm
- M_ac: Aerodynamic center moment
The moment equation can be derived as follows:
1. First, consider the wing lift and the tail lift moments:
- The moment generated by the wing lift is L_cg = L * l_cg. This is because the wing lift acts at the CG.
- The moment generated by the tail lift is L_H * l_H. This is because the tail lift acts at a distance l_H from the CG.
2. Next, consider the moment generated by the aerodynamic center:
- The moment generated by the aerodynamic center is M_ac.
3. Finally, sum up all the moments and set them equal to zero (for static, longitudinal stability):
L_cg + L_H * l_H + M_ac = 0
This is the moment equation around the center of gravity of the King Air 200 aircraft, as a function of the total lift L, the tail lift L_H, the center of gravity distance l_cg, the tail arm l_H, and the aerodynamic center moment M_ac.