GATE 2021 AE – Question 64
An aircraft in level flight at 100 m/s has weight 100000 N, wing area 30 m², span 10 m, zero-lift drag coefficient 0.025, elliptic loading and density 1.225 kg/m³. Required thrust is ___ N.
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Correct answer: 9741.70 to 9839.60
Explanation
In steady level flight the thrust equals the drag, and the drag is the sum of the zero-lift drag and the induced drag.
**Dynamic pressure:** $q=\tfrac12\rho V^2=0.5\times1.225\times100^2=6125$ Pa.
**Zero-lift drag:**
$$D_0=q\,S\,C_{D0}=6125\times30\times0.025=4593.75\text{ N}.$$
**Induced drag** with elliptic loading, where $L=W$:
$$D_i=\frac{L^2}{q\,\pi\,b^2}=\frac{(100\,000)^2}{6125\times\pi\times10^2}=\frac{10^{10}}{1\,924\,226}=5196.9\text{ N}.$$
**Thrust required:**
$$T=D_0+D_i=4593.75+5196.9=\mathbf{9790.6\ N}.$$