Center of pressure

Example: Calculate the location of center of pressure of a airfoil section at an angle of attack of ${{\rm{5}}^{\rm{o}}}$, whose coefficient of lift, ${{\rm{c}}_{\rm{l}}}$ is 0.80 and ${{\rm{c}}_{{\rm{m,c/4}}}}$ is -0.08.Consider incompressible flow over the airfoil.

Solution:-

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.