Fundamentals of wind energy - Wind Power Generation and Wind Turbine Design - page 10

A

u

Figure 3: Swept area of wind turbine blades .

where l is the length of wind blades and r is the radius of the hub. Thus, by doubling
the length of wind blades, the swept area can be increased by the factor up to 4.
When l >> 2 r , A p l 2 . ≈

4.1.2 Air density
Another important parameter that directly affects the wind power generation is the
density of air, which can be calculated from the equation of state:

p
RT

r =

(6)

where p is the local air pressure, R is the gas constant (287 J/kg-K for air), and T
is the local air temperature in K.
The hydrostatic equation states that whenever there is no vertical motion, the
difference in pressure between two heights is caused by the mass of the air layer:

d

p =− r g d z (7)

where g is the acceleration of gravity. Combining eqns (6) and (7), yields

d p g

=− d z ( 8 )

p T

The acceleration of gravity g decreases with the height above the earth's
surface z :

⎛ 4 z ⎞

gg = 1 −

⎜ ⎟ (9)

0

⎝ ⎠

D