Fundamentals of wind energy - Wind Power Generation and Wind Turbine Design - page 11

where g 0 is the acceleration of gravity at the ground and D is the diameter of the
earth. However, for the acceleration of gravity g , the variation in height can be
ignored because D is much larger than 4 z .
In addition, temperature is inversely proportional to the height. Assume that d T /
d z = c , it can be derived that

−
⎛⎞

gcR /

T
pp T =

(10)

⎜ ⎝⎠

0

0

where p 0 and T 0 are the air pressure and temperature at the ground, respectively.
Combining eqns (6) and (10), it gives

− (/ gcR + 1) − (/ gcR + 1)

⎛⎞ T ⎛ cz ⎞

rr = = r 1 +

(11)

⎜⎟ ⎜ ⎟

0 0

⎝⎠ T ⎝ T ⎠

0 0

This equation indicates that the density of air decreases nonlinearly with the height
above the sea level.

4.1.3 Wind power density
Wind power density is a comprehensive index in evaluating the wind resource
at a particular site. It is the available wind power in airflow through a per-
pendicular cross-sectional unit area in a unit time period. The classes of
wind power density at two standard wind measurement heights are listed in
Table 1 .
Some of wind resource assessments utilize 50 m towers with sensors installed at
intermediate levels (10 m, 20 m, etc.). For large-scale wind plants, class rating of
4 or higher is preferred.

Table 1: Classes of wind power density [ 17 ].

10 m height 50 m height

Wind power
class

Wind power
density (W/m 2 )

Mean wind
speed (m/s)

Wind power
density (W/m 2 )

Mean wind
speed (m/s)

1 <100 <4.4 <200 <5.6

2 100-150 4.4-5.1 200-300 5.6-6.4

3 150-200 5.1-5.6 300-400 6.4-7.0

4 200-250 5.6-6.0 400-500 7.0-7.5

5 250-300 6.0-6.4 500-600 7.5-8.0

6 300-350 6.4-7.0 600-800 8.0-8.8

7 >400 >7.0 >800 >8.8