Pressure Distribution Analysis $(45\backslash \%)$

A thin airfoil has the following $$\backslash$Delta c$\_$p $=$ c$\_\{$p$,$lower$\}$ c$\_\{$p$,$upper$\}$$ distribution at $$\backslash$alpha $=0^\backslash$circ$$,$

$$

$\backslash$Delta c$\_$p $=2\backslash$frac$\{$x$\}\{$c$\}(1-\backslash$frac$\{$x$\}\{$c$\})$

$$

$\backslash$begin$\{$enumerate$\}[$label$=(\backslash$alph$*)]$

$\backslash$item Compute the lift coe$$cient $($$c$\_$l$$),$ center of pressure $($$x$\_$cp$$),$ aerodynamic center $($$x$\_\{$ac$\}$$$),$ and stability margin $($SM$)$ of the airfoil at $$\backslash$alpha $=0^\backslash$circ$$.$

$\backslash$item Determine the formula for $$\backslash$Delta c$\_$p$(\backslash$frac$\{$x$\}\{$c$\})$$ at an arbitrary $$\backslash$alpha$ and provide a computer generated plot of $$\backslash$Delta c$\_$p$(\backslash$frac$\{$x$\}\{$c$\})$$ for $$\backslash$alpha $=5^\backslash$circ$$.$

$\backslash$item Determine $($numerically is acceptable$)$ a camber line $z$\_$c$(\backslash$frac$\{$x$\}\{$c$\})$$ that is consistent with the given pressure distribution, and provide a computer$-$generated plot of the camber line. Also present the $B$\_$n$ values up to $n $=10$$$.$

$\backslash$end$\{$enumerate$\}$