Calculate the lift, drag and moment coefficient about quarter chord per unit span of an airfoil.

Calculate the lift, drag and moment coefficient about quarter chord per unit span of an airfoil which is at an angle of attack of \({7\, ^ \circ }\) with a flow velocity of \(40\, m/s\) at standard sea level conditions. The airfoil has a chord length of \(1\, m\).

[For this airfoil; \({c_l} = 0.85\,,{c_{{m_{c/4}}}} =\, – 0.028,\,{c_d} = 0.075\)]

 

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    The dynamic pressure for the airfoil is

    \[{q_\infty } = \frac{1}{2}{\rho _\infty }V_\infty ^2 = \frac{1}{2} \times 1.225 \times {\left( {40} \right)^2} = 980N/{m^2}\]

    Area per unit span, \(S = 1 \times (c) = 1 \times 1 = 1\)

    Therefore, lift per unit span,

    \[L = {q_\infty }S{c_l} = 980 \times 1 \times 0.85 = 833\,N\]

    Drag per unit span,

    \[D = {q_\infty }S{c_d} = 982 \times 1 \times 0.075 = 73.5\,N\]

    Moment about the quarter chord per unit span,

    \[{M_{c/4}} = {q_\infty }Sc{c_{{m_{c/4}}}} = 980 \times 1 \times 1 \times \left( { – 0.028} \right) = – 27.44Nm\]

    Answered on 13th January 2021.
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