Calculate the location of center of pressure of an airfoil section at an angle of attack of 5 degree, whose coefficient of lift, cl is 0.80 and cm,c/4 is -0.08. Consider incompressible flow over the airfoil.

Location of center of pressure is given as  $${x_{cp}} = \left( {\frac{c}{4}} \right) – \frac{{M_{c/4}^\prime }}{{{L^{^\prime }}}}$$

Where${x_{cp}}$  is the distance of center of pressure from the leading edge of airfoil, and ‘c’ is the chord length .$M_{c/4}^\prime$ is moment per unit span about quarter-chord point and ${L^\prime }$ is the lift per unit span; $$\begin{array}{l}{x_{cp}} = \frac{c}{4} – \frac{{M_{c/4}^\prime }}{{{L^\prime }}}\\\frac{{{x_{cp}}}}{c} = \frac{1}{4} – \frac{{\left( {M_{c/4}^\prime /{q_\infty }{c^2}} \right)}}{{\left( {{L^\prime }/{q_\infty }c} \right)}}\end{array}$$ $$\begin{array}{l} = \frac{1}{4} – \left( {\frac{{{c_{m,c/4}}}}{{{c_l}}}} \right)\\ = \frac{1}{4} – \left( {\frac{{ – 0.08}}{{0.80}}} \right)\\ = \frac{1}{4} + 0.1\\ = 0.25 + 0.1\\ = 0.35\end{array}$$ Therefore, location of center of pressure is at 0.35 with respect to chord length.