An airplane having a weight of \(10,000 N\) is flying at a velocity of \(260\,km/h\) at standard sea level conditions. Find the induced drag, if the wing of the airplane has an area of \(16\,m^2\) and has an aspect ratio of \(7.4\).
An airplane having a weight of \(10,000 N\) is flying at a velocity of \(260\,km/h\) at standard sea level conditions. Find the induced drag, if the wing of the airplane has an area of \(16\,m^2\) and has an aspect ratio of \(7.4\).
[Span efficiency factor , \(e = 0.6\) ]
Induced drag of the airplane, \({D_i} = {q_\infty }S{C_{{D_i}}}\)
Here, \[{S} = 16\,{m^2}\]
\[{\rho _\infty } = 1.225\,kg/{m^3}\]
\[{V_\infty } = \left( {\frac{{260 \times 1000}}{{60 \times 60}}} \right) = 72.2\,m/s\]
\[{q_\infty } = \frac{1}{2}{\rho _\infty }V_\infty ^2\,\]
\[ \Rightarrow {q_\infty } = \frac{1}{2} \times \left( {1.225} \right) \times {\left( {72.2} \right)^2} = 3192.86\,N/{m^2}\]
\[L = W = 10000 = {q_\infty }S{C_L}\]
\[ \Rightarrow {C_L} = \frac{{10000}}{{{q_\infty }S}} = \frac{{10000}}{{\left( {3192.86} \right) \times 16}} = 0.1957\]
\[{C_{{D_i}}} = \frac{{C_L^2}}{{\pi eAR}} = \frac{{{{\left( {0.1957} \right)}^2}}}{{\pi \times 0.6 \times 7.4}} = 0.002746\]
Therefore,
\[{D_i} = {q_\infty }S{C_{{D_i}}} = 3192.86 \times 16 \times 0.002746 = 140.281\,N\]
