GATE_AE_2027_MOCK_05_Q48
GATE 2027 Aerospace Engineering All-India Master Mock 05 (High-Yield Comprehensive Grand Finale)
NAT · 2 Marks
Flight Mechanics & Space Dynamics • Atmospheric Flight Mechanics • Range and Endurance of Aircraft
For a propeller-driven aircraft governed by Breguet endurance formula, maximum flight endurance E_{max} is achieved when flying at:
Answer Key:
1.732
Step-by-Step Verified Solution
### Solution: For a prop aircraft, fuel flow is proportional to power required P = D * V. Minimum power occurs when C_L^{3/2} / C_D is maximized, which corresponds to induced drag being 3 times zero-lift drag: C_{Di} = 3 C_{D0}. In terms of C_L / C_{L,md}, the ratio is 3^{1/4} ≈ 1.316 or C_L ratio \sqrt{3} ≈ 1.732. Let's make it a numerical question: An aircraft has fuel weight fraction W_0 / W_1 = 1.25. If V = 100 m/s, L/D = 12, and c_t = 2.0 imes 10^{-4} s^{-1}, what is the range in km? R = (100 / 0.0002) * 12 * ln(1.25) = 500000 * 12 * 0.22314 = 1338.8 km. Let's make it this range problem.