The Unsteady Aerodynamics of Turbine Yaw and Over-Speed Protection - Small Wind Turbines: Analysis, Design, and Application - page 161

Fig. 8.13 Rear view of the
500 W turbine showing tail
fin. Photo from Wright [ 21 ]

Equation 8.15 below expresses the equilibrium between the gravitational and
aerodynamic moments of the tail fin at furl axis tilt angle w, where m tf is the total
mass of the tail fin assembly, r cm is the distance from the furl axis to the centre of
mass of the tail fin assembly, r cp is the distance from the furl axis to the fin centre
of pressure, and F is the aerodynamic normal force acting on the fin. Note that in
its unfurled position at w = 0, the tail fin is constrained by a rubber stopper.

m tf gr cm cos w sin d Fr cp cos d ¼ 0 ð 8 : 15 Þ

where d is the furl axis offset angle defined in Fig. 8.14 .
A much more complete analysis of furling is given by Bikdash et al. [ 23 ] and
other measurements and analysis are given by Jonkman and Hansen [ 24 ]. In
practice, furling has a number of drawbacks. In marginal furling conditions or
gusty winds the tail fin may continually furl and unfurl and so not shut down the
turbine. There is evidence that high yaw rates occur during either furling or
unfurling as shown by the data in Fig. 8.15 for the furling tail fin of Fig. 8.14 . Note
that the bottom graph shows the furl angle between the tail arm and the rotor axis:
the highest yaw rates occur during furling and unfurling and are associated with
higher X than in Fig. 8.11 . It is also very difficult to design a furling system to act
in a particular way from theoretical calculations, so some trial and error is usually
required. This problem arises partly from the need for furling to protect against
two quite different situations. Furling is routinely required when the turbine is
producing full power and the wind speed increases, where from Chaps. 2 and 5 , the
thrust coefficient is close to unity. Much less often, the turbine will lose its load
and the blades accelerate to the runaway state where the thrust coefficient may be
significantly higher, judging from Fig. 2.2 .