sin αst

CONCEPTUALISATION
the kinetic wind energy, transform it into mechanical energy in a shaft and finally into
electrical energy in a generator.
The maximum available power in the wind can be obtained if theoretically the wind speed
after the rotor is reduced to zero: Pmax,theo = ½ρAV 3 , where ρ is the air density, V is the wind
speed and A is the area where the wind speed is reduced [11, p. 3]. For a typical horizontal-
axis wind turbine the area is equal to the swept rotor area, without subtraction of the hub
area, as indicated on figure 4.1.
16
Figure 4.1: Swept rotor area of horizontal-axis wind turbine [11, p. 4]
In practice it is not possible to reduce the speed of the wind after the rotor to zero using a
wind turbine, so a power coefficient Cp is added to the before mentioned theoretical equa-
tion: Pmax = Cp½ρAV 3 . The power coefficient thus represents the ratio between the actual
power obtained and the maximum available power. It can also be seen as a parameter
indicating the size of the wind turbine, as a lower Cp will require a larger swept rotor area
to provide a given power output. The theoretical maximum for Cp is denoted the Betz limit
and is equal to 16/27 (or 0.593) [11, p. 4]. To this date there has not been designed any
wind turbine capable of exceeding this limit, which is named after the German aerody-
namicist, Albert Betz [3, p. 45].
� Lift and drag
When a body is exposed to an air flow it experiences an aerodynamic force. The force is
caused by pressure on the surface of the body and by viscous friction between the air and
the boundary layer around the object. The aerodynamic force that is in the direction of the
wind is called drag. When a streamlined body, such as an airfoil, is exposed to an air flow it
experiences a more complex resulting aerodynamic force that may be decomposed into
two components:
� Drag - The component parallel to the direction of the air flow
� Lift - The component perpendicular to the direction of the air flow
This is illustrated on figure 4.2, showing the forces and the moment that act on an airfoil
subjected to a two-dimensional flow [11, p. 6].
�
A�D 4
2