Final answer:
The largest wind turbines have rotor diameters up to 220 meters with power outputs of 13 MW. With a rotor diameter of 150 meters and an efficiency of 50%, a turbine can deliver significant power at a wind speed of 13 m/s, often measured in megawatts.
Step-by-step explanation:
The largest wind turbines, such as those recently announced, measure up to 220 meters in rotor diameter and can deliver a maximum power output of 13 megawatts (MW). When considering the power output of turbines, we can apply the concept of power in the wind, which depends on the area swept by the rotor blades, the air density, the wind velocity cubed, and the efficiency of the turbine. Using a sensible efficiency of 50%, we can calculate the expected power output at a given wind speed.
For a turbine with a rotor diameter of 150 meters and an efficiency of 50%, the power at the maximum design wind speed of 13 meters per second (m/s) can be estimated. From the Betz limit, which states the maximum efficiency a turbine can extract from the wind is 59.3%, and considering that modern turbines achieve about 50% efficiency, we apply the necessary formulas to calculate the power output.
One formula that can be utilized for this calculation is P = 0.5 x efficiency x π x (diameter/2)² x air density x wind speed³. Plugging in the appropriate values, we find that a jumbo turbine with a 150m diameter rotor can deliver substantial power, typically in the range of megawatts, under optimal wind conditions.