# Find the total drag of an airplane.

Find the total drag of an airplane flying at a velocity of \(90\,m/s\) with \(L/D\) ratio maximum. Airplane is weighing \(23000\,N\) and has a wing area of \(20\,m^2\) and an aspect ratio of \(9\).

[Consider Oswald efficiency factor of \(0.9\)]

When airplane is flying at \(Lift/Drag\) ratio of maximum , coefficient of drag at zero lift is equal to coefficient of induced drag.

\(Total\, drag = drag\, at\, zero\, lift + induced\, drag \)

\[{C_D} = {C_{D,0}} + {C_{D,i}}\]

Since \((L/D)\) is here maximum, therefore, \( coefficient\, of\, drag\, at\, zero\, lift =coefficient\, of\, induced\, drag\),

\[{C_{D,0}} = {C_{D,i}}\]

Therefore,

\[{C_D} = 2{C_{D,i}}\]

\[{C_{D,i}} = \frac{{C_L^2}}{{\pi eAR}}\]

\[L = \frac{1}{2}{\rho _\infty }V_\infty ^2S{C_L}\]

At, a steady level flight, \(L=W\)

\[ \Rightarrow {C_L} = \frac{{2W}}{{{\rho _\infty }V_\infty ^2S}} = \frac{{2 \times 23000}}{{1.225 \times {{\left( {90} \right)}^2} \times 20}} = 0.232\]

\[{C_{D,i}} = \frac{{C_L^2}}{{\pi eAR}} = \frac{{{{\left( {0.232} \right)}^2}}}{{\pi \times 0.9 \times 9}} = 0.0021\]

Therefore,

\[{C_D} = 2 \times \left( {0.0021} \right) = 0.0041\]

Total drag,

\[D = \frac{1}{2} \times {\rho _\infty } \times V_\infty ^2 \times S \times {C_{D}}\]

\[ \Rightarrow D = \frac{1}{2} \times 1.225 \times {\left( {90} \right)^2} \times 20 \times 0.0041 = 406.823\,N\]