An aircraft with mass of 400,000 kg cruises at 240 m/s at an altitude of 10 km. Its lift to drag ratio at cruise is 15. Assuming g as 9.81 m/s2, the power (in MW) needed for it to cruise is _______ (accurate to two decimal places).Correct answer is '62.00 to 63.50'. Can you explain this answer?

Question

Answer

Given data:
- Mass of aircraft (m) = 400,000 kg
- Cruise velocity (V) = 240 m/s
- Altitude (h) = 10 km = 10,000 m
- Lift to drag ratio (L/D) = 15
- Acceleration due to gravity (g) = 9.81 m/s^2

Step 1: Calculate Lift and Drag forces
- Lift force (L) = Weight of the aircraft = m * g = 400,000 kg * 9.81 m/s^2 = 3,924,000 N
- Drag force (D) = L / (L/D) = 3,924,000 N / 15 = 261,600 N

Step 2: Calculate Power required for cruising
- Power (P) = Thrust * Velocity = Drag force * Velocity
- P = D * V = 261,600 N * 240 m/s = 62,784,000 W = 62.78 MW

Therefore, the power needed for the aircraft to cruise is approximately 62.78 MW. The answer falls within the range of 62.00 to 63.50 MW as provided.

Similar GATE Doubts

Gross weight of an airplane is 7000 N, wing area is 16 m2, and the maximum lift coefficient is 2.0. Assuming density at the altitude as 1.23 kg/m3, the stall speed (in m/s) of the aircraft is _________ (accurate to two decimal places). Correct answer is '18.80 to 18.90'. Can you explain this answer?

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