The Unsteady Aerodynamics of Turbine Yaw and Over-Speed Protection - Small Wind Turbines: Analysis, Design, and Application - page 155

significant if x c, and will tend to be negated by the increase in inertia. In the
next section, the effects of changing planforms will be discussed and shown not to
significantly alter the lift slope. In other words, there is little the turbine designer
can do to increase the damping ratio of conventional tail fins. On the other hand,
the twin-delta tail fin studied by Ebert and Wood [ 3 ] had a damping ratio of around
0.8.

Yaw performance with the rotor stationary is extremely important in practice. It
was pointed out in Chap. 6 that wind direction changes are often greater at low
wind speeds where the turbine spends more time starting, so the ability of the tail
fin to provide yaw on its own is critical. Yaw behaviour when the turbine is
producing power is discussed in Sect. 8.5 , where it is shown that the rotor provides
yaw stability and the tail fin is less critical.

8.4 Planform Effects on Tail Fin Performance

The analysis of tail fin behaviour started with delta wings because their lift and
drag, and centre of pressure are well-known. However, the turbine designer may
wish to use a more pleasing shape for the fin or one with a higher lift slope.
Unfortunately, there is less information available for planforms other than delta
wings. One way to discuss the yaw behaviour of any fin is to assume that it is
characterised by the ''generalised'' natural frequency and damping ratio, found
from USB by neglecting the added mass and assuming that K 1 can be expressed as
K 1 ¼ 1

2 qAKU 2 r 0

ð 8 : 10 Þ

where r 0 = x ? x cp is the distance from the yaw axis to the centre of pressure,
located x cp from the leading edge. Thus

r

qAKr 0
2I

x n ¼ U wake

ð 8 : 11a Þ

and

qAK
8Ir 0

r

Þ 2

f ¼ c þ x ð ð 8 : 11b Þ

and the K 2 0 term in ( 8.7 ) can be similarly modified if predictions of turbine yaw
behaviour are required. Polhamus [ 17 ] computed the behaviour of ''arrowhead''
and ''diamond'' planforms which are modifications of a standard delta as shown in
Fig. 8.8 . The indentation i is taken as positive for diamond and negative for an
arrowhead. The aspect ratio is unaffected by any indentation (Fig. 8.8 ).
Polhamus's results can be fitted by a relationship of the form

K ¼ A ðÞ K P0 þ A ð K P1 ½ ð 8 : 12 Þ