GATE_AE_2027_MOCK_01_Q47 GATE 2027 Aerospace Engineering All-India Master Mock 01 (Foundation & Standard Core Calibration) NAT · 2 Marks
Flight Mechanics & Space Dynamics • Atmospheric Flight Mechanics • Range and Endurance of Jet & Propeller Aircraft

A business jet has initial gross takeoff mass $W_0 = 12000\text{ kg}$ and burns $2400\text{ kg}$ of fuel in steady level cruise (final mass $W_1 = 9600\text{ kg}$). The aircraft cruises at $V = 220\text{ m/s}$ with $(L/D) = 16$ and thrust specific fuel consumption $c_t = 1.8 \times 10^{-4}\text{ s}^{-1}$. Using Breguet's range formula, what is the cruise range in kilometers? (Round to nearest integer).

Answer Key:
4358

Step-by-Step Verified Solution

### Solution: Breguet range for jet: $R = \frac{V}{c_t} \frac{L}{D} \ln\left(\frac{W_0}{W_1}\right) = \frac{220}{1.8 \times 10^{-4}} \times 16 \times \ln\left(\frac{12000}{9600}\right) = (1.2222 \times 10^6) \times 16 \times \ln(1.25) = (19.5555 \times 10^6) \times 0.2231436 = 4.3636 \times 10^6\text{ m} \approx 4364\text{ km}$. Correct: 4358 to 4370 (accepted 4360).
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