Environmental Engineering Reference
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a small effect on its dynamics. The K 3 term in ( 8.7 ) and ( 8.8 ) represents the added
mass of the air moved with the yawing tail fin. For the case where the wind
direction does not change, x n and f for a delta wing tail fin are:
r
K 1
I
r
K 1
I þ K 3
x n ¼
ð 8 : 9a Þ
and
K 2
K 2
f ¼
p
K 1 I þ K 3
p
K 1 I
ð 8 : 9b Þ
2
ð
Þ
2
The approximations in ( 8.9a , b ) are valid when the added mass can be ignored.
Note that the natural frequency is proportional to the wind speed, but the damping
ratio is determined only by the geometry and inertia.
A wind tunnel test of a one-quarter model tail fin of the 500 W turbine in
Fig. 6.1 is shown in Fig. 8.5 . The model was mounted to the wind tunnel working
section floor. There was also a ceiling that is not visible, but no side walls. At the
top left can be seen the inside of the wind tunnel contraction. The wind direction is
parallel to the model's tail arm. In other words, the tail fin was not yawed when the
photograph was taken. U, the wind speed, was kept constant while the fin was
released from a number of different yaw angles. The subsequent yaw angle was
measured as a function of time. Figure 8.6 compares a typical result to the
response predicted by both methods. Note that the release angle of 40 should be
large enough to invalidate the small angle approximation, but repeated experi-
ments over a range of release angles failed to detect any nonlinearities in
behaviour due to large angles. For example, the measured period in Fig. 8.6 does
not alter significantly as the yaw reduces and the small angle approximation should
become valid. The pseudo-static method under-predicts the damping ratio, while
USB slightly over-predicts it. Both over-estimate the natural frequency, by an
Fig. 8.6 Response of the
model tail fin in 15 m/s wind
tunnel testing for a release
angle of 408 [ 21 ]
50
experimental
40
usb theory
pseudo-static
30
20
10
0
0
0.2
0.4
0 .6
0.8
1
1.2
1.4
-10
-20
-30
time (s)
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