The Horns Rev windfarm is 15 miles off the west coast of the Danish penninsula,

Question

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?v=BOnfbTyMnzA. 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?

Explanation / Answer

abswer- height of turbine is h= 198m

diameter of turbine is d= 31.5 m

1 million N-m touque is equivalent to 32000N which is euivalent 3200kg

length of the propelloer blade is 63m

distance between blades and rotation axis is = 31.5m

power of turbine is 6MW

power= tourque * angular velocity

6MW= touque*120 radian per minute

tourque= 6/120 = 0.05

the list of all torque acting on turbines wind turbine design are process of defining the form and specifications of wind tubine to extract energy from the wind. Generator touque is used to control the speed to rotor speed in order to capture as much power as possible and the second tourque is applied there is aerodynamic tourque.

the mechanism of wind turbines are following principles

1- Bernolli theory of flight

2- Newton second and third law to motion

the third law of motion states that every action have equal and opposite reaction.

this means the force of aerofoil pushing the air downwards creating the downwash, is accompanied by an equal and opposite force from the air pushing the aerofoils upward and hence providing the aerodynamic lift. It is thus the turning of air flow which creates the lift.

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