WIND ENERGY SYSTEMS - Cd3wd

Chapter 3—Wind Measurements 3–26
It is sometimes necessary to determine the damping ratio and the natural period from wind
tunnel tests on a particular vane. From a strip chart recording we can easily determine the
overshoot h and the damped period τ d , as shown in Fig. 16. The time at which the maximum
occurs can be estimated from the strip chart and can also be computed from Eq. 32 by taking
the time derivative, setting it equal to zero, and solving for t max .Itcanbeshownthat
t max = τ d
2
When this value of t is substituted into Eq. 32 we have
(37)
θ
−ωnξtmax
sin(π + σ)
= 1− e
γ 1 sin σ
= 1+exp
( )
−πξ
√
1 − ξ 2
(38)
Figure 16: Overshoot h and damped period τ d of direction vane tested in a wind tunnel.
By comparing Fig. 16 and Eq. 38, we recognize that
h =exp
( )
−πξ
√
1 − ξ 2
(39)
which yields the following expression for ξ.
ξ =
− ln h
√
π 2 +(lnh) 2 (40)
Wind Energy Systems by Dr. Gary L. Johnson November 12, 2001