Introduction to Modern Wind Turbines - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 74

where
C T = rotor thrust coeficient

A combination of the momentum theory and test data is required in order to derive an
equation relating a to C T , which is valid for values of a larger than about 0.4. Figure 2-14 [data
from Wilson and Lissaman 1974, Stoddard 1977] shows the momentum theory relationship
at lower induction factors combined with rotor test data at higher induction factors. A simple
empirical equation has been itted here to cover both ranges of a [Spera 2008], as follows:

a = 0.27 C T + 0.10 C T

(2-17)

Figure 2-14. Empirical equation derived for calculating an axial induction factor from
the rotor thrust coeficient. Equation is based on the wind turbine and helicopter test data
shown in the igure. [Data: Lock et al. 1926, Wilson et al. 1976, and Eggleston and Stoddard
1987].

Applying Equation (2-16) to condition (2-14b), a thrust coeficient of 0.933 produces an
induction factor of 1/3 and the theoretical maximum rotor power coeficient. This “theoreti-
cal optimum” point is indicated in Figure 2-14.
One of two approaches can now be taken to produce a rotor power curve for the turbine,
which deines estimated rotor power output, P R , versus free-stream wind speed, U . The irst
approach requires iteration and the second does not, but iteration can be done rapidly in
spreadsheet software.