Chapter 4, Problem 4.6P

The NACA 4412 airfoil has a mean camber line given by $\frac{z}{c}=\{\begin{array}{cc}0.25\left[0.8\frac{x}{c}-{\left(\frac{x}{c}\right)}^2\right]& \text{for}0\ge \frac{x}{c}\ge 0.4\\ 0.111\left[0.2+0.8\frac{x}{c}-{\left(\frac{x}{c}\right)}^2\right]& \text{for}0.4\le \frac{x}{c}\le 1\end{array}$

Using thin airfoil theory, calculate

(a) ${\alpha }_{L=0}$

(b) $c_l$ when $\alpha =3°$