Problem 4. (20pts) Consider a wing-body model with $C_{m_{ac,wb}} = -0.022$, $\bar{x}_{cg} = 0.33$, $x_{ac,wb} = 0.22$, $a_{wb} = 0.08$. The area and chord of the wing are 0.1 $m^2$ and 0.1 m, respectively. Now assume that a horizontal tail is added to this model. We have the flowing parameters: $l_t = 0.17m$, $S_t = 0.02m^2$, $i_t = 2.5^\circ$, $a_t = 0.1$ per degree, $\epsilon_0 = 0$ and $\partial \epsilon / \partial \alpha = 0.4$.
X_NP / c = 0.3217, For alpha = 9.38 deg $C_{m_{cg}} = -0.0458$
Obtain the linearized y-force equation using the above trim condition. Show your work and clearly write down the result. Are the longitudinal and lateral linearized dynamics of the airplane in this case decoupled?
