To determine the propeller tip's rotational speed in meters per second, we first need to calculate the circumference of the propeller and then determine how far the tip travels in one rotational cycle. The rotational speed can be calculated as follows:
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Calculate the radius of the propeller: \[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{2.67 \text{ m}}{2} = 1.335 \text{ m} \]
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Calculate the circumference of the propeller: \[ \text{Circumference} = 2 \pi \times \text{Radius} = 2 \pi \times 1.335 \text{ m} \approx 8.38 \text{ m} \]
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Convert the RPM to rotations per second: \[ \text{RPM} = 1700 \text{ rpm} \implies \text{Rotations per second} = \frac{1700}{60} \approx 28.33 \text{ rps} \]
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Calculate the tip speed of the propeller: \[ \text{Tip speed} = \text{Circumference} \times \text{Rotations per second} = 8.38 \text{ m} \times 28.33 \text{ rps} \approx 237.63 \text{ m/s} \]
Now, let's calculate the thrust generated by the propeller.
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Convert engine power from horsepower to watts: \[ 1 \text{ hp} \approx 745.7 \text{ W} \implies 1200 \text{ hp} = 1200 \times 745.7 \text{ W} \approx 894840 \text{ W} \]
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Calculate the effective power output that contributes to thrust using propulsive efficiency: \[ \text{Effective power} = \text{Engine power} \times \text{Propulsive efficiency} = 894840 \text{ W} \times 0.60 \approx 536904 \text{ W} \]
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Convert the speed to meter per second for thrust calculation: \[ \text{Cruise speed} = 270 \text{ kts} = 270 \times 0.51444 \text{ m/s} \approx 138.87 \text{ m/s} \]
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Thrust can be calculated using the power and speed: \[ \text{Thrust} = \frac{\text{Effective power}}{\text{Cruise speed}} = \frac{536904 \text{ W}}{138.87 \text{ m/s}} \approx 3867.95 \text{ N} \]
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Convert thrust from newtons to kilonewtons: \[ \text{Thrust} \approx 3.87 \text{ kN} \]
Summary:
- The propeller tip's rotational speed is approximately 237.63 m/s.
- The thrust generated by the propeller is approximately 3.87 kN.