
165Wind Energy
© 2008 Taylor & Francis Group, LLC
The maximum power output of C
pmax
= C
pBetz
= 0.59 occurs at a = 1/3, while the maximum
nondimensional thrust of 1.0 occurs at a value of a = 0.5. When power is maximum at a = 1/3,
C
T
= 8/9.
Also note that the axial induction factor theory is not valid for a > 0.5. Equation 3.38
shows that the speed of the wake, U
wake
, behind the turbine decreases as the axial induction
factor increases from 0.0 to 0.5. At a = 0.5, the wake speed equals zero. For values of a > 0.5,
the wake speed would be negative (Figure 3.23), violating the assumptions of this simple
theory. Figure 3.23 illustrates the wake t