sin αst

ROTOR THEORY
blade for optimum performance under certain assumptions, which is elaborated in the
next section.
Notable assumptions when using the described BEM theory is that the prevailing wind is
uniform and aligned with the rotor axis, and that the blades rotate in the rotor plane, per-
pendicular to the rotor axis. Due to factors such as wind shear, yaw error and turbulence,
real performance may differ from the modelled performance. The force and power output
that is calculated using the BEM theory is referred to as nominal output in the present
project thesis.
B.2 Optimum blade shape
Using the BEM theory described in the previous section it is possible to approximate the
blade shape that would provide the maximum power given the following parameters:
� Tip-speed ratio (�)
� Number of blades (B)
� Radius (R)
� Lift (Cl) and drag (Cd) characteristics of the airfoil (at optimum angles of attack)
The approximation of the ideal blade shape can be carried out using different theories such
as Betz or Schmitz [12, p. 121-132]. Betz encloses several assumptions:
� No wake rotation (a’ = 0)
� No drag (Cd = 0)
� No tip loss (F = 1)
� Axial interference factor (a) of 1/3 in each annular element
Schmitz’ theory does not presume a value of zero for the tangential interference factor and
hence takes into account wake rotation, which originates from a rotating flow behind the
rotor. This theory can therefore be seen as an augmented and a more accurate version
than the Betz’ theory, and it is hence used in the determination of the blade shape for an
ideal rotor.
One can determine the angle of relative wind � and the chord of the blade c for each ele-
ment of the ideal rotor [12, p. 132]:
2 � 1 �
� = atan� �
3 � � �
8� r
c =
( 1 � cos( �)
)
B Cl (B.18)
(B.19)
135