Problem $1$

Given an airplane with the following characteristics $($see also the figure below$)$

mass $=7000kg,Sw=30m^2,b=9m$

The airplane is flying at sea level at an equivalent air speed of $140\frac{m}{s}.$

The airplane's lateral stability coefficients are:

$C_n=-1\mathrm{.}0,C_q=-0\mathrm{.}12,$ roll coefficient, $C_f==+0\mathrm{.}1,$ roll coefficient

${}_v=0\mathrm{.}9,{}_N(1+\frac{d}{d})=1\mathrm{.}0,C_{Mv}=3\mathrm{.}0,$

${}_{\text{r}\text{i}\text{m}\text{i}}=0\mathrm{.}4,C_{\frac{N}{}}=-0\mathrm{.}3.,{}_{**}=0,A_{}=45.$

The airplane fuselage length is $14$ m and $CG$ position is $7$ m from the nose.

a$)$ Design the size and position of the vertical tall fie, find the area $S_v,$ and distance lv$,$

of the vertical tail $AC$ to $CG,$ and height, $,$ of vertical tail $AC$ above $FRL.)$ such that

$C_N$ is maximized under the given conditions.

b$)$ Calculate $C_N$ of the airplane for the above design. Find the maximum deflection of

the rudder, $r_m.($in degrees$),$ needed to trim the airplane to zero yaw moment,

$C_N=0,$ for a maximal side wind of $30$ ms at the above flight conditions.

c$)$ Determine the wing position $($is it a high, centered or low wing?$)$