Design of Wind Turbines - Wind Energy: Renewable Energy and the Environment - page 101

where C D is the drag coefficient. Drag coefficients, C D , for different shapes are given in Marks'
Handbook [13], but the simplest procedure is to use C D 1 for round pipes and wires and for flat
plates perpendicular to the wind. Flat plates at an angle to the wind will experience some lift and
drag like an airfoil, and these data are available.
The force/area is also the pressure, so the wind blowing against an object creates a pressure. If
the winds are high enough, as in hurricanes and tornadoes, the pressure will destroy buildings and
topple trees and power poles.
From Equations 6.9 and 6.10, the power loss due to drag from struts can be calculated. Notice
that it is proportional to velocity cubed:

P 0.5 R vCAv

2

0.5 R vCA

3

(6.11)

D D

The power loss from struts for a 4 kW giromill was so large that the struts were redesigned to an
airfoil shape to reduce drag. Notice that fuel efficiency for vehicles can be improved by reducing the
drag coefficient for vehicles and by slowing down.
The power coefficient for a drag device can be calculated from the relative wind speed, as seen
by the drag device and the speed of the device. The relative velocity of the wind as measured by a
sensor mounted on the drag device is

vvu

r 0

again, where v 0 is the wind speed and u is the speed of the device. Then the power per unit area
from Equation 6.9 is

P
A

2 2

0.5 R vCu = 0.5 R( v uCu ) (6.12)

r D 0 D

Notice that at u 0 and u v 0 , the power is zero. In other words, there is no power output
if the drag device is not moving, and the drag device cannot move faster than the wind. From
Equations 6.7 and 6.12, the maximum power coefficient for a drag device can be calculated. The
maximum power coefficient, C P (max) 4/27 0.15, which occurs when the drag device is moving
at u 1/3 the wind speed. This maximum power coefficient is for a drag coefficient around 1.
Some drag devices can have a drag coefficient greater than 1, so the maximum power coefficient
could be as high as 20%. The maximum power coefficient can be found using calculus or can be
estimated from a spreadsheet or graph of P/A versus wind speed (Equation 6.12) for various val-
ues of u , from 0 to v 0 . Low efficiency is another reason there are not commercial drag devices for
generating electricity.

6.5 LIFT DEVICE
A lift device can produce on the order of 100 times the power per unit surface area of blade versus
a drag device. See Rohatgi and Nelson [14, chap. 6] for more details.

EXAMPLE 6.1

Suppose we have a two-blade wind turbine, each blade is 5 m long, 0.1 m wide. As a drag device, the
capture cross section is 1 m 2 . As a lift device in a HAWT, its capture cross-sectional area is 78.5 m 2 .
If the difference in efficiencies is included, the ratio of the power out per blade area for the lift device
over the drag device is over 300.