Step-by-step Instant Solution
The Horns Rev windfarm is 15 miles off the west coast of the Danish penninsula, near Ejsberg. You can see a movie of the windfarm here: http://www.youtube.com/watch?. There are 171 wind turbines like this spread out over the shallow North Sea floor, some of which (the Horns Rev 2 field) can generate 6 MW of power. As we discussed in class (and also in the 4th edition) the work done by a torque is (torque x rotation angle in radians). To get the power from the wind then it is (torque x angular velocity in radians per second). Assuming no losses, the 6 MW electrical power generated must correspond to an equivalent 6 MW of power done by work from the wind on the turbines. Since there are three blades, then each blade must have 2 MW of power done on it from the wind. A typical rotation speed is 20 rotations per minute, which corresponds to 40pi or 120 radians per minute, or 2 radians per second. That means the TORQUE provided by the wind must be 2 MW/2 radians per second = 1 million Newton-meters of torque.
These turbines are absolutuely gigantic. Look here: http://en.wikipedia.org/wiki/Wind_turbines (see "Record-Holding turbines" at the bottom). The Enercon 6 MW E-126 is 198 meters (650 ft!) tall, and the turbine is 126 meters (413 ft!) in diameter. That means each propeller blade is 63 m (206 ft!) long. If we assume that the wind force on the turbine blade acts at its center, 31.5 meters from the rotation axis, then the 1 million Newton-meters of torque from the wind, corresponds to a force from the wind on the turbine of 32,000 Newtons which is equivalent to the weight of a mass of 3200 kg, which is 6400 pounds or a little over 3 tons on each of the three propellar (turbine) blades!
In this short essay, consider that there is an extremely large force from the wind on the turbine which provides a torque which does work (and generates a lot of power). Answer the following questions in your essay:
1. What is the net torque on the turbine? How do you know? List all the torques on the turbine which make this happen.
2. Considering that there is a giant force from the wind ON the turbine blade, how is Newton's 3rd law satisfied? How could you tell that Newton's 3rd law is satisfied?
Paper#9255902 | Written in 27-Jul-2016Price : $17.85