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.

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]

Worldtech Asked on 3rd February 2021 in Aeronautics.
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    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

    techAir Answered on 8th February 2021.
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