## 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. 