WIND ENERGY SYSTEMS - Cd3wd

Chapter 3—Wind Measurements 3–11
Figure 7: Anemometer response to a step function change in wind speed.
next time constant, τ increases by 0.63 of the amount remaining, and so on until it ultimately
reaches its final value.
During the transient period the anemometer will indicate a wind speed u i different from
the actual ambient wind speed u. This indicated wind speed will be proportional to the
anemometer angular velocity ω.
u i = K i ω (10)
For a cup-type anemometer, the tip speed of the cups will be approximately equal to
the wind speed, which means that K i would be approximately the radius of rotation of the
cup assembly. Propeller type anemometers will have a higher tip speed to wind speed ratio,
perhaps up to a factor of five or six, which means that K i would be proportionately smaller
for this type of anemometer.
At equilibrium, u i = u o and ω = ω o ,so
u o = K i ω o (11)
When Eqs. 10 and 11 are substituted into Eq. 8 we get an expression for the indicated
wind speed u i :
u i = K i ω = K i
[ ωo u i
K i ω o
+(u o − u 1 ) ω o
K i ω o
e −t/τ ]
Wind Energy Systems by Dr. Gary L. Johnson November 12, 2001