Energy Solutions to Air Pollution and Global Warming - Air Pollution and Global Warming: History, Science, and Solutions - page 328

wind speed. The reason for the regeneration of the
wind past a turbine is as follows. As wind speeds first
decrease within a wake, the vertical and horizontal gra-
dients in wind speed increase. In other words, outside
the wake the wind speed remains fast, whereas within
the wake the wind speed is slower, so the gradient in
wind speed increases. The larger gradient in wind speed
causes faster winds from outside the wake to flow into
the wake, both vertically (from aloft, downward) and
horizontally. In addition, the deficit in wind speed in
the wake increases the horizontal pressure gradient and
thus increases the pressure gradient force. The wind
speed in the wake must then partly regenerate to ensure
geostrophic balance (Section 6.2.1).
Transmission and distribution losses are losses that
occur between the power source and end user of electric-
ity. Transmission losses are losses of energy that occur
along a transmission line due to resistance. Distribution
losses occur due to step-up transformers, which increase
voltage from an energy source to a high-voltage trans-
mission line and decrease voltage from the high-voltage
transmission line to the local distribution line. The aver-
age transmission plus distribution losses in the United
States in 2007 were 6.5 percent (Energy Information
Administration, 2011b). The overall system efficiency
of a wind farm, accounting for array, transmission, and
distribution losses, typically ranges from

total energy) and then dividing by the energy
produced per turbine E t gives 4.6 million turbines
at a wind speed of 7 m s −1 and 3.0 million tur-
bines at a wind speed of 8.5 m s −1 . The average
of these two is 3.8 million wind turbines, the esti-
mate provided in Table 13.4.

The footprint on the ground of an energy device is
the actual land area of the top surface of soil touched by
the device. It differs from the spacing area, which is the
area between devices required to reduce interference of
one device with the other, as just illustrated for wind.
Separation of devices is also needed for wave and tidal
farms.
In the case of wind turbines, the footprint consists pri-
marily of the area of the turbine's tubular tower plus that
of the base on which it sits (generally 4-5 m in diameter
total). Whereas wind turbines have foundations under
the ground larger than their bases on the ground, such
underground foundation areas are not footprint because
the foundations are covered with dirt, allowing vegeta-
tion to grow and wildlife to flourish on top of them. The
footprint area for wind also does not include temporary
or unpaved dirt access roads because most large-scale
wind farms will go over areas such as the Great Plains
and some desert regions, where photographs of several
farms indicate that unpaved access roads blend into the
natural environment and are often overgrown by vege-
tation. Offshore wind farms do not require any roads.
In farmland locations, most access roads have dual pur-
poses, serving both agricultural fields and turbines. In
cases where paved access roads are needed, 1 km 2 of
land provides about 200 km (124 miles) of linear road-
way5mwide; thus, access roads would not increase
the footprint requirements of wind farms more than a
small amount.
The footprint area also does not include transmis-
sion because the actual footprint area of a transmission
tower is smaller than is the footprint area of a wind
turbine. This is due to the fact that a transmission tower
consists of four narrow metal support rods separated
by distance that penetrate the soil to an underground
foundation. Many photographs of transmission tow-
ers indicate more vegetation growing under the towers
than around the towers because areas around the tow-
ers are often agricultural or used for other purposes,
whereas the area under the tower is vegetated soil.
Because the land under transmission towers supports
vegetation and wildlife, it is not considered footprint

0.85-
0.9. Thus, such losses reduce estimated wind energy
resources in likely developable locations (e.g., in Table
13.3) by 10 to 15 percent.

t =

Example 13.2
Given a world end-use power demand of 11.5 TW
in 2030 for all purposes, calculate the number
of wind turbines from Example 13.1 needed to
power 50 percent of the world's energy. Assume
the system efficiency due to array, transmission,
and distribution losses in the low wind speed
case is 0.85 and in the high wind speed case
is 0.9.

Solution
From Equation 13.1, the annual energy output
of the individual turbine in Example 13.1 ranges
from E t 11.0-16.7 million kWh yr −1 for the

low and high wind speed cases, respectively.
Multiplying world end-use power demand of
11.5 TW in 2030 by H

=

8,760 h yr −1 gives the
world end-use energy demand for all purposes
of 1.01

=

10 14 kWh yr −1 .Multiplying this number
by one-half (because wind will supply half the

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