(Solved): 10. Consider a camber line given by the equation cz=cx(cxa)(cx1) where 0a1 ...

10. Consider a camber line given by the equation $\frac{z}{c}=\frac{x}{c}\left(\frac{x}{c}?a\right)\left(\frac{x}{c}?1\right)$ where $0?a?1$ is a non-dimensional parameter that will help you change the shape of the airfoil. a) Find the location where the camber has a maximum magnitude (in terms of a). b) Now, consider the case of $a=0$ for the following questions. Use thin airfoil theory to determine the lift coefficient $c_l$ of the camber line as a function of angle of attack $?$. c) What is the lift slope $d{c}_l/d?$ ? d) What is the zero-lift angle of attack? (Solution: a) $\frac{x}{c}=\frac{a+1?\sqrt{(a+1{)}^2?3a}}{3}$, b) $C_l=?\left(2??\frac{3}{4}\right)$, c) $2?$, d) $\frac{3}{8}$.)