Design of Wind Turbines - Wind Energy: Renewable Energy and the Environment - page 100

FIGURE 6.1 Mass rotating about a point.

The power coefficient is the power delivered by the device divided by the power available in the
wind. Since the area cancels out, the power coefficient, C P , is

power out
power in

power out
0.5

(6.7)

C

P 3

R v

The work or energy to move an object is the force times the distance through which it moves. Remember,
work is a scalar (it has only a value, no direction). Also note, if the force is perpendicular to the motion,
there is no work done (no gain or loss of energy). An example is the motion of the moon around the earth.

W u u Fr Fr $ ( r ) (6.8)

f i

The dot between the vectors means only the parallel component of the F is used ( W F cos k Δ r ),
where Δ r final position - initial position, and k is the angle between F and r .
Divide both sides of Equation 6.8 by time:

W
t

u Fr $

t

Thus, the power is

P Fv (6.9)

6.4 DRAG DEVICE
The power from a drag device (see Figure 5.1) can be calculated from the force on the device and
the velocity of the device, u . From Equation 6.9, P F * u , since force and speed are in the same
direction. The force/area of the air on a stationary object in a wind speed, v , is

F
A

2

0.5 R vC D

(6.10)