GATE 2026 AE – Question 57

Flight Mechanics & Space Dynamics · Airplane performance: drag polar, take-off and landing, climb and descent, ceilings, range and endurance, load factor, turning flight, V-n diagram, winds · 2 marks · Numerical answer

$W_A$ and $W_B$ are the respective maximum take-off weights of an aircraft for two ambient air conditions given below.

Condition A: $p = 1$ bar, $T = 50\,^oC$; Condition B: $p = 0.66$ bar, $T = -30\,^oC$

If all other parameters relevant for take-off are kept the same in these two conditions, the ratio $W_B/W_A$ is ________ (rounded off to 3 decimal places).

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Correct answer: 0.860 to 0.890

Explanation

With all other lift-related take-off parameters fixed, allowable weight scales with air density: $W\propto\rho$. The ideal-gas relation gives $W_B/W_A=\rho_B/\rho_A=(0.66/1)(323.15/243.15)=0.877$. Taking the square root instead assumes a separate runway-acceleration constraint not specified in the keyed comparison.

Official GATE 2026 answer key: https://gate2026.iitg.ac.in/doc/download/2026/Keys/AE_Keys.pdf