The Unsteady Aerodynamics of Turbine Yaw and Over-Speed Protection - Small Wind Turbines: Analysis, Design, and Application - page 164

the mass. The main advantages of pitching over furling is that the former should
occur over much narrower range of wind speeds, so there should be much less
power loss associated with a mean yaw angle, as shown in Fig. 8.16 , and no large
yaw rates as the tail furls. In other words, pitching should be more precise and
definite. On the other hand, the balance between the moments can be upset by
strong gyroscopic moments from Eq. 8.1 particularly as that moment can act for or
against pitching depending entirely on the sign of the yaw rate. If nothing else, the
gyroscopic effects limit pitching to micro-turbines and possibly mid-range tur-
bines, using the categorisation of Chap. 1 . The reason is that the thrust will scale as
R 2 and its typical moment will scale as R 3 whereas the rotor inertia scales as R n ,
where 4 \ n \ 5, see Table 1.7 , and typical X as R -1 . The IEC safety standard
described in Chap. 9 specifies that the maximum yaw rate is not a strong function
of R. Thus the gyroscopic moment should scale as R n-1 , so that it will overtake the
thrust moment as rotor size increases.

8.7.3 Exercises

1. The rotor of a wind turbine is located distance d from the yaw axis. Assume that
the blades are not coned in operation. Show that the relationship between J and
the blade's yaw moment of inertia, I b , as a function of azimuthal angle w,is

I b ¼ m b d 2 þ J sin 2 w
Take the origin for w as the blade being vertical upwards andw is positive in the
direction of blade rotation. Also assume that c/r 1so that the blade's mass is
concentrated in the radial direction. Find the average and peak-to-peak varia-
tion in I b with w for rotors with (a) two blades, (b) three blades, and (c) four
blades.
2. Derive Eq. 8.4 .
3. With a set-up similar to Fig. 8.5 , how would you devise an experiment to
determine the significance of the added mass for the tail fin response?
4. A delta tail fin of constant thickness t is made from a material of density q tail .
Show that its mass moment about the yaw axis is

I tail ¼ q tail bct x 2 2 þ 2xc 3 þ c 2 4

600 mm

1250 mm

865 mm

yaw axis