To determine the propulsive efficiency, we first need to find the drag force acting on the aircraft.
The drag force can be calculated using the drag equation:
Drag Force = 0.5 * Air Density * Velocity^2 * Wing Surface Area * Drag Coefficient
First, let's calculate the air density at the given altitude using the International Standard Atmosphere model:
Air Density = 1.225 * e^(-0.000118 * altitude)
Air Density = 1.225 * e^(-0.000118 * 3400) ≈ 0.812 kg/m^3
Now, we can calculate the drag force:
Drag Force = 0.5 * 0.812 * (72)^2 * 28 * 0.01
Drag Force ≈ 6352 N
Next, we need to calculate the lift force acting on the aircraft.
The lift force can be calculated using the lift equation:
Lift Force = 0.5 * Air Density * Velocity^2 * Wing Surface Area * Lift Coefficient
Lift Force = 0.5 * 0.812 * (72)^2 * 28 * 0.555
Lift Force ≈ 17551 N
Now, we can calculate the induced drag force using the lift and drag forces:
Induced Drag Force = Lift Force^2 / (0.5 * Air Density * Velocity^2 * Wing Surface Area * Oswald Factor)
Induced Drag Force = 17551^2 / (0.5 * 0.812 * (72)^2 * 28 * 0.7)
Induced Drag Force ≈ 2882 N
The remaining drag force is the parasite drag:
Parasite Drag Force = Drag Force - Induced Drag Force
Parasite Drag Force ≈ 6352 - 2882
Parasite Drag Force ≈ 3470 N
Now, we can calculate the power required to overcome the parasite drag:
Power Required = Parasite Drag Force * Velocity
Power Required = 3470 * 72
Power Required ≈ 249840 W
The propulsive power is equal to the power required, so it is 249840 W.
To calculate the propulsive efficiency, we need to know the power output of the engines. Since each engine is rated at 98 kW, the total power output is 2 * 98 kW = 196 kW = 196000 W.
Propulsive Efficiency = (Power Output / Power Required) * 100
Propulsive Efficiency = (196000 / 249840) * 100
Propulsive Efficiency ≈ 78.45 %
Therefore, the propulsive efficiency in this flight condition is approximately 78.45%.
A twin-engined propeller aircraft is equipped with two engines, each rated at 98 kW shaft power. During cruise flight at 72 m/s at an altitude of 3400 metres, the aircraft experiences a lift coefficient of 0.555. Its wing surface area is 28 square metres, with an average chord length of 2 metres. Its zero-lift drag coefficient is 0.01 and its span efficiency (or Oswald) factor is 0.7.
Determine the propulsive efficiency (in percent) in this flight condition.
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