From the manufacturer the following data can be obtained:
Engine Power = 1200 hp
Propeller Diameter=2.67m
Propeller RPM=1700
Cruise: 2700 kts@20000ft
Propulsive Effiency=60%
Determine the propeller tip's rotational speed (in metres per second) in normal operation ?
Determine the thrust generated by the propeller (in kN) ?
To determine the propeller tip's rotational speed in normal operation, we can use the following formula:
Propeller Tip Speed (in meters per second) = (Propeller Diameter * Propeller RPM) * π / 60
Propeller Tip Speed = (2.67 * 1700) * π / 60 = 250.23 m/s
Therefore, the propeller tip's rotational speed in normal operation is approximately 250.23 m/s.
To determine the thrust generated by the propeller, we can use the following formula:
Thrust = (Engine Power * Propulsive Efficiency) / Propeller Tip Speed
Thrust = (1200 * 0.6) / 250.23 = 2.876 kN
Therefore, the thrust generated by the propeller is approximately 2.876 kN.
To determine the propeller tip's rotational speed in meters per second, we need to calculate the circumferential speed of the propeller.
1. Convert the propeller RPM to radians per second:
RPM to radians per second = RPM * (2π / 60)
RPM to radians per second = 1700 * (2π / 60)
RPM to radians per second = 178.05 rad/s
2. Calculate the circumference of the propeller:
Circumference = π * (Propeller Diameter)
Circumference = π * (2.67m)
Circumference ≈ 8.3947 m
3. Multiply the circumference by the propeller's rotational speed:
Rotational speed = Circumference * RPM to radians per second
Rotational speed = 8.3947 m * 178.05 rad/s
Rotational speed ≈ 1496.292 m/s
Therefore, the propeller tip's rotational speed in normal operation is approximately 1496.292 meters per second.
To determine the thrust generated by the propeller in kN, we can use the following formula:
Thrust (kN) = (Engine Power * Propulsive Efficiency) / Rotational speed
1. Calculate the thrust:
Thrust (kN) = (1200 hp * 0.60) / 1496.292 m/s
2. Convert the horsepower to kilowatts (kW):
1 hp = 0.7457 kW
Engine Power (kW) = 1200 hp * 0.7457 kW/hp
3. Calculate the thrust:
Thrust (kN) = (Engine Power (kW) * Propulsive Efficiency) / Rotational speed
Thrust (kN) = (1200 hp * 0.7457 kW/hp * 0.60) / 1496.292 m/s
Note: Make sure the units are consistent throughout the calculation.
Therefore, the thrust generated by the propeller in normal operation is approximately the same value obtained from the calculations above.
To determine the propeller tip's rotational speed in meters per second, we can use the formula:
Rotational speed (m/s) = (π * Propeller Diameter * Propeller RPM) / 60
Given:
Propeller Diameter = 2.67m
Propeller RPM = 1700
Plugging in the values into the formula, we get:
Rotational speed (m/s) = (π * 2.67 * 1700) / 60
= (3.14 * 2.67 * 1700) / 60
Calculating this gives us the value for the rotational speed in meters per second.
To determine the thrust generated by the propeller in kN (kilonewtons), we can use the formula:
Thrust (kN) = (0.5 * Engine Power * Propulsive Efficiency) / Cruise Speed
Given:
Engine Power = 1200 hp
Propulsive Efficiency = 60%
Cruise Speed = 2700 kts
First, we need to convert the engine power from horsepower (hp) to kilowatts (kW):
Engine Power (kW) = Engine Power (hp) * 0.7355
= 1200 * 0.7355
Now, we can calculate the thrust using the given values:
Thrust (kN) = (0.5 * Engine Power (kW) * Propulsive Efficiency) / Cruise Speed
= (0.5 * (1200 * 0.7355) * 0.60) / 2700
Calculating this will give us the thrust generated by the propeller in kilonewtons.