GATE 2024 AE – Question 64

Aerodynamics · Airfoils and wings: coefficients, Kutta-Joukowski theorem, thin airfoil theory, finite wing theory, critical and drag divergence Mach numbers · 2 marks · Numerical answer

An airplane of mass 1000 kg is in a steady level flight with a speed of 50 m/s. The wing has an elliptic planform with a span of 20 m and planform area 31.4 m$^2$. Assuming the density of air at that altitude to be 1 kg/m$^3$ and acceleration due to gravity to be 10 m/s$^2$, the induced drag on the wing is _________ N (rounded off to 1 decimal place).

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Correct answer: 63.38 to 64.02

Explanation

In level flight the lift equals the weight, $L = 1000 \times 10 = 10000$ N. For an elliptic wing $D_i = \frac{L^2}{\pi q\,b^2}$ with $q = \frac{1}{2}\rho V^2 = 1250$ Pa, so $D_i = \frac{10^8}{\pi \times 1250 \times 400} = 63.7$ N.