Problem $6$: A light airplane weighs $10,000.$ Its payload is anticipated to be $\backslash (2,000\backslash$mathrm$\{$~N$\}\backslash ).$ Its wingspan is $12$ m and its chord measures $1\mathrm{.}8$ m $.$ The plan area used in airfoil drag calculations is actually the chord length times the wingspan, as shown in the figure to the right.

The figure below shows lift and drag coefficients for an airfoil with $\backslash (\backslash$operatorname$\{$Re$\}=$v $\backslash$mathrm$\{$c$\}/$ v $\backslash ),$ where c is the chord length. Notice that $\backslash (\backslash$alpha $\backslash )$ is the angle of attack. Assume the air density is $\backslash (1\mathrm{.}2\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ).$

a$)$ Using the plot on the left, predict the required takeoff speed if an angle of attack of $\backslash (8^\{\backslash$circ$\}\backslash )$ is desired. $[\backslash (34\mathrm{.}0\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )]$

b$)$ Predict the stall speed for a conventional airfoil $($this will use the maximum lift coefficient$).[\backslash (23\mathrm{.}2\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )]$

c$)$ Calculate the power required by the airfoil during cruise at $\backslash (50\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Assume that the design lift coefficient is $0\mathrm{.}4.$ Remember that power is force times velocity. $[10,200$ W$]$