$c_d=6\mathrm{.}4*{10}^{-3}-1\mathrm{.}2*{10}^{-3}{c}_l+3\mathrm{.}5*{10}^{-3}{c}_l^2.$

Figure $3\mathrm{.}34$: Plant$-$form of the wing $($dimensions in meters$).$

On regard of the effects of the Fowler flaps in the maximum coefficient of lift, it is known that:

The increase of the maximum coefficient of lift of the airfoil $(c_{l_{\text{m}\text{a}\text{x}}})$ can be approximated by the following expression:

$c_{l_{\text{m}\text{a}\text{x}}}=1\mathrm{.}9\frac{c^{\text{'}}}{c}$

being $c$ the chord in the root and $c^{\text{'}}$ the extended chord $($consider $c^{\text{'}}=3[m]).$

The increase of the maximum coefficient of lift of the wing $(C_{L_{\text{m}\text{a}\text{x}}})$ can be related to the increase of the maximum coefficient of lift of the airfoil $(c_{I_{\text{m}\text{a}\text{x}}})$ by means of the following expression:

$C_{L_{\text{m}\text{a}\text{x}}}=0\mathrm{.}92c_{l_{\text{m}\text{a}\text{x}}}\frac{S_{fw}}{S_w}cos$

$96$

$3\mathrm{.}5$ Problems

Based on the data given in Figure $3\mathrm{.}34,$ calculate:

$($a$)$ Chord in the root and tip of the wing. wing$-$span and enlargement. Wet wing surface $(S_w)$ and surface wet by the flaps $(S_{fw}).$ Aircraft swept $()$ measured from the leading edge.

Assuming a clean configuration $($no flap deflection$),$ typical of cruise conditions, and knowing also that the stall of the airfoil takes place at an angle of attack of $15$ :

b$)$ calculate the maximum coefficient of lift of the airfoil.

c$)$ calculate the expression of the lift curve of the wing in its linear range.

d$)$ calculate the maximum coefficient of lift of the wing $($assume that the aircraft $($wing$)$ stalls also at an angle of attack of $150)$

Assuming a configuration with flaps fully deflected, typical of a final approach, calculate:

e$)$ the maximum coefficient of lift of the wing.

It is known that the mass of the aircraft is $4500$ kg $.$ For sea level ISA conditions and force due to gravity equal to $9\mathrm{.}81\frac{m}{s^2}$ :

f$)$ calculate the stall speeds of the aircraft for both configurations