# 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 $$0.9$$]

Asked on 3rd February 2021 in

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,

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

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