## Maximum Theoretical Power

The maximum power/area can be found by plotting the curve P/A versus a (Equation 6.20) or by using calculus. The answer is a = 1/3 or 1. Of course, a = 1 means that there is no reduction of wind speed and the disk does not take out any power. For a = 1/3, the maximum power is

16 27

Therefore, the maximum power coefficient, from Equation 6.6, is CP = 16/27 = 0.59. Real rotors will have smaller power coefficients due to drag, tip and hub losses, losses due to rotation of the wake, and frictional losses; however, measured values can reach 50% (which includes drive train and generator). This is another reason lift devices are used to generate electricity, compared to drag devices, as the maximum theoretical power coefficients are 50% versus 20%. However, the farm windmill, which has some of the same characteristics as a drag device (large solidity, low tip speed ratio) is well designed for the application of pumping low volumes of water.

Region 1

Region 1

Region 2 (wake)

Rotational flow

Rotor

FIGURE 6.5 The rotor imparts a rotation to the wake.

Region 2 (wake)

Rotational flow

Rotor

FIGURE 6.5 The rotor imparts a rotation to the wake.

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Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

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