Problem

We want to analyze the aerodynamic performances of a trapezoidal wing with a plant$-$form

as in Figure $1($all dimensions given in meters$).$ The wing mounts two triple slotted Fowler

flaps. The efficiency factor $($Oswald factor$)$ of the wing is $e=0\mathrm{.}94.$ The wing is build

employing NACA $4415$ airfoils with the following characteristics:

$c_l=0\mathrm{.}2+5\mathrm{.}92(in$ rad $)$

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

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 approxi$-$

mated by the following expression:

$c_{l_{\text{m}\text{a}\text{x}}}=2\frac{c^{\text{'}}}{c}$

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 $(c_{l_{\text{m}\text{a}\text{x}}})$ by means of the

following expression:

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

Based on the data given in Figure $1,$ calculate:

Chord in the root and tip of the wing, wing$-$span and enlargement. Wet wing surface

and surface wet by the flaps. Aircraft swept measured from the leading edge $(15$pts$).$

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 $16$ :