Blade Design, Manufacture, and Testing - Small Wind Turbines: Analysis, Design, and Application - page 128

Fig. 7.2 Variation in power
coefficient and blade radius
with tip speed ratio for rated
power

1.4

1.2

1

R
C P,r
Betz-Joukowsky limit

0.8

0.6

0.4

0.2

4 5 6 7 8

Tip speed ratio for rated power, λ P

550 r.p.m. is a good choice on these grounds. Further comments on electrical
system safety can be found in Chap. 11 . The curve shown in Fig. 7.1 as a solid
line from this point is the operating trajectory of the turbine assuming constant-
k and constant (and hopefully maximum) efficiency operation. Thus the gen-
erator will always operate below the maximum torque curve which is normally
set by limits to heat generation and temperature. Note, however, that most
generators can safely produce excess power for limited time. With rated X and
power fixed at those values, the main blade parameters can be expressed as
functions of R:

2 1 : 2 10 3 pR 2 ¼ 0 : 541 R 2

754 = 0 : 74

C P ; r ¼

1

ð 7 : 3 Þ

and

k P ¼ 550 2p

10 60 R ¼ 5 : 759R

Note that the subscript ''r'' has been added to indicate that the power
coefficient refers to the power extracted by the blades not the output electrical
power. The calculation of C P,r includes the efficiency of 74% from Fig. 7.1 to
make it directly applicable to the blade element calculations. The variation of
R and C P,r with k P are shown in Fig. 7.2 . Again, it can be argued that the
choice of minimum R is the best, but it is wise not to expect too high a C P from
a small turbine; recall the data in Table 1.1 . Choosing R = 1.06 m gives
k P = 6.10 and C P,r = 0.481 from Eq. 7.3 . The value of k P is unremarkable but
that for C P,r is an ambitious design target. It gives an output power coefficient
C P of 0.361.
Of the values in Table 7.1 that have not yet been discussed, the choice of
starting k and blade density will be familiar from Chap. 6 . Neither is critical to the