One of the engines of the F$-4$C fighter fails in the SLUF. In order to keep force and

moment balance, the following three equations should be fulfilled:

$-0\mathrm{.}08+0\mathrm{.}05{}_a+0\mathrm{.}017{}_r+\frac{L_T}{(/bar(q))Sb}=0$

$1\mathrm{.}42+0\mathrm{.}05{}_a-0\mathrm{.}7{}_r+\frac{F_{}{y}_e}{(/bar(q))Sb}=0$

$-23\mathrm{.}18-0\mathrm{.}51{}_a+3\mathrm{.}06{}_r+\frac{Wsincos}{(/bar(q))S}=0$

where $W=173,000N\frac{,}{b}ar(q)=45,375\frac{N}{m2},S=49m2,b=11\mathrm{.}8m,=0\mathrm{.}3$deg,$F_{}=60kN,y_e=1m,L_T=1000N.m.$

In order to balance the aircraft in the lateral direction with $=0$ and $=0\mathrm{.}3$deg :

$($a$)$ Calculate rudder deflection angle and aileron deflection angle.

$($b$)$ Calculate the bank angle of the aircraft after the moments are balanced.